F1711 Mathematics 1

Faculty of Science
Autumn 2023
Extent and Intensity
3/3/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Mgr. David Linhart (seminar tutor)
Guaranteed by
Mgr. Pavla Musilová, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Contact Person: Mgr. Pavla Musilová, Ph.D.
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Fri 9:00–11:50 F3,03015
  • Timetable of Seminar Groups:
F1711/01: Fri 12:00–14:50 F3,03015, D. Linhart
Prerequisites
Grammar school mathematics
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
Students obtain basic knowledge of linear algebra, mathematical analysis and statistics. After absolving the course a student is able to practically solve systems of linear equations,and he/she gains practical skills in basic calculus in mathematical analysis (derivations and integrals of one variable functions). Finally, he can made standard calculations of probabilities and treatment of measurement data.
Learning outcomes
After absolving the course a student is able to:
- solve systems of linear equations,
- compute with matrixs,
- solve geometrical problems in vector spaces,
- compute limits of one variable function,
- compute derivatives and integrals of one variable function,
- apply methods of differential and integral calculus for solving practical problems,
- compute with probablity,
- statistically process a measurment,
Syllabus
  • 1. Linear algebra - systems of linear equation,
  • 2. Algebra - real and complex nubers,
  • 3. Linear algebra - matrix calculus,
  • 4. Linear algebra - vector calculus,
  • 5. Analysis - functions of one real variable,
  • 6. Analysis - limits of functions, continuous funkction,
  • 7. Analysis - derivatives,
  • 8. Analysis - application of differencial calculus,extremal problems, Taylor series
  • 9. Analysis - sequences, limits of sequences,
  • 10. Analysis - integral calculus of one variable function,
  • 11. Analysis - application of integral calculus,
  • 12. Probability and combinatorics,
  • 13. Statistics.
Literature
    required literature
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis). Brno: VUTIUM, 2006, 281 pp. Vysokoškolské učebnice. ISBN 80-214-2914-3. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
  • MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika II pro porozumění i praxi (Mathematics II for understanding and praxis). první. Brno: VUTIUM (Vysoké učení technické v Brně), 2012, 697 pp. ISBN 978-80-214-4071-5. info
Teaching methods
Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems.
Assessment methods
Lectures and seminars. Requirements see www.physics.muni.cz/~pavla/teaching.php
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Teacher's information
http://physics.muni.cz/~pavla/teaching.php
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, spring 2012 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2023, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2023/F1711