M7960 Dynamical Systems

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Written and oral examination. For admission to exam students need to submit three homework assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught every week.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.

M7960 Dynamical Systems

Faculty of Science
Spring 2024
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 2. to Sun 26. 5. Mon 8:00–9:50 M5,01013
  • Timetable of Seminar Groups:
M7960/01: Mon 19. 2. to Sun 26. 5. Tue 12:00–13:50 M6,01011, P. Liška
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Written and oral examination. For admission to exam students need to submit three homework assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2023
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 16:00–17:50 M2,01021
  • Timetable of Seminar Groups:
M7960/01: Tue 12:00–13:50 M4,01024, P. Liška
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Written and oral examination. For admission to exam students need to submit three homework assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2022
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
doc. RNDr. Michal Veselý, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 12:00–13:50 M1,01017
  • Timetable of Seminar Groups:
M7960/01: Thu 8:00–9:50 M6,01011, P. Liška
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Written and oral examination. For admission to exam students need to submit three homework assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2021
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Mgr. Petr Liška, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 1. 3. to Fri 14. 5. Tue 16:00–17:50 online_M4
  • Timetable of Seminar Groups:
M7960/01: Mon 1. 3. to Fri 14. 5. Wed 12:00–13:50 online_M3, P. Liška
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Written and oral examination. For admission to exam students need to submit three homework assignments.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2020
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Michal Veselý, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7960/01: Tue 10:00–11:50 M3,01023, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling.
Learning outcomes
After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • EDELSTEIN-KESHET, Leah. Mathematical models in biology. Philadelphia: Society for Industrial and Applied Mathematics, 2005, xliii, 586. ISBN 0898715547. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Teacher's information
The lessons are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents. The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics. Assessment in all cases may be in Czech and English, at the student's choice.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2019
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 2. to Fri 17. 5. Tue 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7960/01: Mon 18. 2. to Fri 17. 5. Tue 10:00–11:50 M3,01023, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
spring 2018
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M4,01024
  • Timetable of Seminar Groups:
M7960/01: Thu 10:00–11:50 M4,01024, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2017
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 20. 2. to Mon 22. 5. Tue 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M7960/01: Mon 20. 2. to Mon 22. 5. Tue 10:00–11:50 M6,01011, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2016
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7960/01: Thu 10:00–11:50 M3,01023, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
    recommended literature
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
    not specified
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2015
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 8:00–9:50 MS1,01016
  • Timetable of Seminar Groups:
M7960/01: Tue 10:00–11:50 MS1,01016, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2014
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M7960/01: Mon 10:00–11:50 M3,01023, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Examination: written and oral. One written test will be realized during the semester. It is required to obtain at least half of the total amount of points. The exam is composed of a written and an oral part. The written part consists of three exercises. It is necessary to obtain at least 1,5 from possible 3 points.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2013
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 MS1,01016
  • Timetable of Seminar Groups:
M7960/01: Thu 10:00–11:50 MS1,01016, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, class exercises 2 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2012
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M7960/01: Thu 10:00–11:50 M6,01011, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, class exercises 2 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2011
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 8:00–9:50 M6,01011
  • Timetable of Seminar Groups:
M7960/01: Thu 10:00–11:50 M6,01011, J. Kalas
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, class exercises 2 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2006
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Timetable
Thu 10:00–11:50 UP1
Prerequisites (in Czech)
Matematická analýza (diferenciální a integrální počet, věta o implicitní funkci). Lineární algebra (matice). Základy z obyčejných diferenciálních rovnic.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Vzhledem k možnému rozsahu spíše základní kurs dynamických systémů, drobné seznámení s nelineárními jevy a chaosem.
Syllabus (in Czech)
  • 1)Úvod, motivační přiklady, základní pojmy. 2)Jednodimenzionální diskrétní dynamické systémy. 3)Lineární systémy. 4)Analýza pevných bodů a periodických orbit. 5)Hyperbolické systémy.
Assessment methods (in Czech)
Předmět je zakončen ústní zkouškou.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Autumn 2003
Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Prerequisites (in Czech)
Matematická analýza (diferenciální a integrální počet, věta o implicitní funkci). Lineární algebra (matice). Základy z obyčejných diferenciálních rovnic.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Vzhledem k možnému rozsahu spíše základní kurs dynamických systémů.
Syllabus (in Czech)
  • 1)Úvod, motivační přiklady, základní pojmy. 2)Jednodimenzionální diskrétní dynamické systémy. 3)Lineární systémy. 4)Analýza pevných bodů a periodických orbit. 5)Hyperbolické systémy.
Assessment methods (in Czech)
Předmět je zakončen zkouškou.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2010

The course is not taught in Spring 2010

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ondřej Došlý, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction in the modern theory of dynamical systems.
At the end of the course students should be able to understand the concept of dynamic system (discrete and continuous), and the main techniques used for analysis of such systems.
Syllabus
  • Dynamics in Nature and Mathematics,
  • one-dimensional dynamics by iterations (quadratic maps),
  • reccurence and chaos (Sharkovski's Theorem),
  • analysis near fixed points (Hartman-Grobman Theorem, invariant manifolds),
  • analysis near periodic solution,
  • hyperbolic attractors (shifts, horseschoe, solenoid attractor, Lorenz attractor).
Literature
  • KATOK, A. B., Boris HASSELBLATT and Leonardo MENDOZA. Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press, 1995, xviii, 802. ISBN 0521341876. info
Teaching methods
Lectures
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2009

The course is not taught in Spring 2009

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction in the modern theory of dynamical systems.
At the end of the course students should be able to understand the concept of dynamic system (discrete and continuous), and the main techniques used for analysis of such systems.
Syllabus
  • Dynamics in Nature and Mathematics,
  • one-dimensional dynamics by iterations (quadratic maps),
  • reccurence and chaos (Sharkovski's Theorem),
  • analysis near fixed points (Hartman-Grobman Theorem, invariant manifolds),
  • analysis near periodic solution,
  • hyperbolic attractors (shifts, horseschoe, solenoid attractor, Lorenz attractor).
Literature
  • KATOK, A. B., Boris HASSELBLATT and Leonardo MENDOZA. Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press, 1995, xviii, 802. ISBN 0521341876. info
Assessment methods
oral exam
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2008

The course is not taught in Spring 2008

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2007

The course is not taught in Spring 2007

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Autumn 2005

The course is not taught in Autumn 2005

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Prerequisites (in Czech)
Matematická analýza (diferenciální a integrální počet, věta o implicitní funkci). Lineární algebra (matice). Základy z obyčejných diferenciálních rovnic.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Vzhledem k možnému rozsahu spíše základní kurs dynamických systémů.
Syllabus (in Czech)
  • 1)Úvod, motivační přiklady, základní pojmy. 2)Jednodimenzionální diskrétní dynamické systémy. 3)Lineární systémy. 4)Analýza pevných bodů a periodických orbit. 5)Hyperbolické systémy.
Assessment methods (in Czech)
Předmět je zakončen zkouškou.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Autumn 2004

The course is not taught in Autumn 2004

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Prerequisites (in Czech)
Matematická analýza (diferenciální a integrální počet, věta o implicitní funkci). Lineární algebra (matice). Základy z obyčejných diferenciálních rovnic.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Vzhledem k možnému rozsahu spíše základní kurs dynamických systémů.
Syllabus (in Czech)
  • 1)Úvod, motivační přiklady, základní pojmy. 2)Jednodimenzionální diskrétní dynamické systémy. 3)Lineární systémy. 4)Analýza pevných bodů a periodických orbit. 5)Hyperbolické systémy.
Assessment methods (in Czech)
Předmět je zakončen zkouškou.
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
spring 2012 - acreditation

The information about the term spring 2012 - acreditation is not made public

Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Ordinary differential equations: Linear and nonlinear systems of differential equations, existence and uniqueness of solutions, dependence of solutions on initial values and parameters, basics of the stability theory.
Linear algebra: Systems of linear equations, determinants, linear spaces, linear transformation and matrices, canonical form of a matrix.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction to the theory of dynamical systems. Attention is paid to continuous dynamical systems, to the theory of autonomous systems of differential equations, and to mathematical modelling. After passing the course, the student will be able: to define and interpret the basic notions used in the fields mentioned above; to formulate relevant mathematical theorems and statements; to use effective techniques utilized in these subject areas; to apply acquired pieces of knowledge for the solution of specific problems; to analyse selected mathematical dynamic deterministic models.
Syllabus
  • 1. Survey of selected resuts from the theory of ordinary differential equations.
  • 2. Autonomous equations - basic notions and properties, elementary types of singular points of two-dimensional systems, classification of singular points of linear and perturbed linear systems, the structure of a limit set in R2, Poincaré-Bendixson theory, Dulac criterion, characteristic directions.
  • 3. General concept of a dynamical system, continuous and discrete dynamical systems.
  • 4. Notion of a mathematical model, classification of models, basic steps of the process of mathematical modelling, formulating a mathematical model, dimensional and mathematical analysis of mathematical models. Selected mathematical models in natural sciences.
Literature
  • VERHULST, Ferdinand. Nonlinear differential equations and dynamical systems. Berlin: Springer Verlag, 1990, 277 s. ISBN 3-540-50628-4. info
  • PERKO, Lawrence. Differential equations and dynamical systems. 2nd ed. New York: Springer-Verlag, 1996, xiv, 519. ISBN 0387947787. info
  • KALAS, Josef and Zdeněk POSPÍŠIL. Spojité modely v biologii. 1. vyd. Brno: Masarykova univerzita, 2001, vii, 256. ISBN 802102626X. info
  • BRAUN, Martin. Differential equations and their applications : an introduction to applied mathematics. 2nd ed. New York: Springer-Verlag, 1978, xiii, 518. ISBN 0-387-90266-X. info
Teaching methods
lectures and class exercises
Assessment methods
Teaching: lecture 2 hours a week, class exercises 2 hours a week. Examination: written and oral.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2011 - only for the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Josef Kalas, CSc. (lecturer)
Guaranteed by
doc. RNDr. Josef Kalas, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course is an introduction in the modern theory of dynamical systems.
At the end of the course students should be able to understand the concept of dynamic system (discrete and continuous), and the main techniques used for analysis of such systems.
Syllabus
  • Dynamics in Nature and Mathematics,
  • one-dimensional dynamics by iterations (quadratic maps),
  • reccurence and chaos (Sharkovski's Theorem),
  • analysis near fixed points (Hartman-Grobman Theorem, invariant manifolds),
  • analysis near periodic solution,
  • hyperbolic attractors (shifts, horseschoe, solenoid attractor, Lorenz attractor).
Literature
  • KATOK, A. B., Boris HASSELBLATT and Leonardo MENDOZA. Introduction to the modern theory of dynamical systems. Cambridge: Cambridge University Press, 1995, xviii, 802. ISBN 0521341876. info
Teaching methods
Lectures
Assessment methods
Oral exam
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught every week.
The course is also listed under the following terms Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.

M7960 Dynamical Systems

Faculty of Science
Spring 2008 - for the purpose of the accreditation

The course is not taught in Spring 2008 - for the purpose of the accreditation

Extent and Intensity
2/0/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Ladislav Adamec, CSc. (lecturer)
Guaranteed by
doc. RNDr. Ladislav Adamec, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Ladislav Adamec, CSc.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Language of instruction
Czech
Further Comments
The course is taught once in two years.
The course is taught every week.
The course is also listed under the following terms Spring 2011 - only for the accreditation, Autumn 2003, Spring 2006, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (recent)