M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Josef Šilhan, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2024
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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Josef Šilhan, 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. Tue 12:00–13:50 M2,01021
  • Timetable of Seminar Groups:
M4190/01: Mon 19. 2. to Sun 26. 5. Wed 10:00–11:50 M2,01021, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2023
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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, 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 M4,01024
  • Timetable of Seminar Groups:
M4190/01: Tue 14:00–15:50 M2,01021, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2022
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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, 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 M2,01021
  • Timetable of Seminar Groups:
M4190/01: Wed 10:00–11:50 M6,01011, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2021
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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
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. Mon 16:00–17:50 online_M4
  • Timetable of Seminar Groups:
M4190/01: Mon 1. 3. to Fri 14. 5. Wed 10:00–11:50 online_M5, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
    recommended literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
    not specified
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class (both online).
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge), both presumably online. At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2020
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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 M4,01024
  • Timetable of Seminar Groups:
M4190/01: Wed 8:00–9:50 M6,01011, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && ( M1100 Mathematical Analysis I || M1100F Mathematical Analysis I ))|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. This covers both the theory of local invariants and also global properties of curves and surfaces.
Learning outcomes
At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curvatures. Covariant derivative, intrinsic and extrinsic geometry of surfaces. Gauss-Bonnet theorem.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Two hours of lectures and two hours of problem class.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, 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. Mon 12:00–13:50 M6,01011
  • Timetable of Seminar Groups:
M4190/01: Mon 18. 2. to Fri 17. 5. Tue 16:00–17:50 M5,01013, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 16:00–17:50 M4,01024
  • Timetable of Seminar Groups:
M4190/01: Thu 14:00–15:50 M4,01024, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, 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. Mon 14:00–15:50 M2,01021
  • Timetable of Seminar Groups:
M4190/01: Mon 20. 2. to Mon 22. 5. Tue 16:00–17:50 M3,01023
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M4190/01: Tue 16:00–17:50 M3,01023, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 16:00–17:50 M4,01024
  • Timetable of Seminar Groups:
M4190/01: Thu 16:00–17:50 M3,01023, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M4190/01: Tue 16:00–17:50 M4,01024, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the Euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental form of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
Lectures and exercises.
Assessment methods
Exam written (focused on computation) and oral (focused on theoretical knowledge). At least 50% of the writen exam and at least basic theoretical knowledge on the oral exam is needed to pass.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 12:00–13:50 M5,01013
  • Timetable of Seminar Groups:
M4190/01: Thu 14:00–15:50 M4,01024, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
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 M2,01021
  • Timetable of Seminar Groups:
M4190/01: Thu 14:00–15:50 M2,01021, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 M3,01023
  • Timetable of Seminar Groups:
M4190/01: Wed 16:00–17:50 M2,01021, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2010
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
M4190/01: Wed 16:00–17:50 M5,01013, J. Šilhan
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2009
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Martin Čadek, CSc. (lecturer)
doc. RNDr. Jiří Vanžura, CSc. (lecturer)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 9:00–10:50 M3,01023
  • Timetable of Seminar Groups:
M4190/01: Wed 10:00–11:50 MP1,01014, L. Viskotová
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Assessment methods
Lectures and exercises. Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2008
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Vanžura, CSc. (lecturer), doc. RNDr. Martin Čadek, CSc. (deputy)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 9:00–10:50 N41
  • Timetable of Seminar Groups:
M4190/01: Thu 8:00–9:50 M3,04005 - dříve Janáčkovo nám. 2a, L. Viskotová
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2007
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Vanžura, CSc. (lecturer), doc. RNDr. Martin Čadek, CSc. (deputy)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Timetable
Tue 9:00–10:50 N41
  • Timetable of Seminar Groups:
M4190/01: Mon 16:00–17:50 M3,04005 - dříve Janáčkovo nám. 2a, L. Viskotová
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2006
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Vanžura, CSc. (lecturer), doc. RNDr. Martin Čadek, CSc. (deputy)
doc. Mgr. Lenka Zalabová, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Martin Čadek, CSc.
Timetable
Tue 9:00–10:50 N41
  • Timetable of Seminar Groups:
M4190/01: Thu 13:00–14:50 U1
Prerequisites
M2110 Linear Algebra II && M1100 Mathematical Analysis I
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Assessment methods (in Czech)
Započet ze cvičení bude udělen za aktivní účast (maximálně 3 absence) nebo v odůvodněných případech za úspěšné zvládnutí zápočtové písemky na konci semestru.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2005
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivan Kolář, DrSc. (lecturer)
doc. Mgr. Lenka Zalabová, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Timetable
Wed 10:00–11:50 N41
  • Timetable of Seminar Groups:
M4190/01: Tue 16:00–17:50 UM, L. Zalabová
Prerequisites
M2110 Linear Algebra II && M1100 Mathematical Analysis I
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2004
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivan Kolář, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Timetable of Seminar Groups
M4190/01: No timetable has been entered into IS. I. Kolář, Rozvrhově doporučeno 2;M
Prerequisites
M2110 Linear Algebra II && M1100 Mathematical Analysis I
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Diffrential Geometry of Curves and Surfaces

Faculty of Science
Spring 2003
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivan Kolář, DrSc. (lecturer)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Timetable of Seminar Groups
M4190/01: No timetable has been entered into IS. I. Kolář
Prerequisites
M2110 Linear Algebra II && M1100 Mathematical Analysis I
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas results of the differential geometry of curves and surfaces in the euclidean tree - space is presented.
Syllabus
  • Parametric expressions and aquations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis 3
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

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. Mgr. Josef Šilhan, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Martin Čadek, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis III
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented. At the end of this course, students should be able to apply differential geometry in mathematical analysis and applied mathematics.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Literature
  • KOLÁŘ, Ivan and Lenka POSPÍŠILOVÁ. Diferenciální geometrie křivek a ploch. Elportál. Brno: Masarykova univerzita, 2008. ISSN 1802-128X. URL info
  • GRAY, Alfred. Modern differential geometry of curves and surfaces with mathematica. 2nd ed. Boca Raton: CRC Press, 1997, xxiv, 1053. ISBN 0-8493-7164-3. info
Teaching methods
lectures and exercises.
Assessment methods
Exam written and oral.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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.

M4190 Differential Geometry of Curves and Surfaces

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Jiří Vanžura, CSc. (lecturer), doc. RNDr. Martin Čadek, CSc. (deputy)
RNDr. Lenka Viskotová, Ph.D. (seminar tutor)
doc. RNDr. Martin Čadek, CSc. (assistant)
Guaranteed by
prof. RNDr. Ivan Kolář, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivan Kolář, DrSc.
Prerequisites
( M2110 Linear Algebra II && M1100 Mathematical Analysis I )|| M3501 Mathematical Analysis III
The basic knowledge of the differential and integral calculus and analytic geometry is expected.
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
A rounded survey of the main ideas and results of the differential geometry of curves and surfaces in the euclidean three-space is presented.
Syllabus
  • Parametric expressions and equations of curves and surfaces. Contact of two curves and of a curve with a surface. Arc of a curve, Frenet frame, curvature and torsion of spacial curves. Envelops. The first and the second fundamental from of a surface, mean and Gauss curva- tures. Inner geometry of surfaces.
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
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, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, 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)