PřF:F2712 Mathematics 2 - Course Information
F2712 Mathematics 2
Faculty of ScienceSpring 2025
- Extent and Intensity
- 4/3/0. 6 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
- Teacher(s)
- Mgr. Pavla Musilová, Ph.D. (lecturer)
- 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 - Prerequisites
- Grammar school mathematics, matter of Mathematics 1
- 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
- Applied Physics (programme PřF, B-AF, specialization Astrophysics)
- Applied Physics (programme PřF, B-AF, specialization Medical Physics)
- Biophysics (programme PřF, B-FY)
- Course objectives
- The discipline is a second part of Mathematics for students of bachelor studies of applied physics and non-physical programs. Its aim is to give students a knowledge and understanding of fundamental concepts of basic mathematical disciplines required for natural sciences and technical disciplines -- mathematical analysis, linear algebra and geometry, probability theory.
- Learning outcomes
- Absolving the discipline a student obtain following knowledge and skills:
understanding of the concept of linearity, ability of practical calculus in linear algebra and geometry (calculations with vectors and linear mappings in bases using matrix algebra solving eigenvalue problem)
skills in calculations using curvilinear coordinates
solving simple differential equations and systems of differential equations, and their use for applications in physics, geometry, technical disciplines, chemistry, etc
understanding of differential and integral calculus of n-variable functions
understanding of basic concepts of vector analysis and practical calculations including applications - Syllabus
- 1. Linear mapping of vector spaces, eigenvalue problem.
- 2. Basic of metric and topology spaces.
- 3. Ordinary differential equations of first order.
- 4. Ordinary differential equations of higer order.
- 5. Systems of ordinary differential equations.
- 6. Differential calculus of functions of n-variables.
- 7. Applications of differential calculus of functions of n-variables.
- 8. Mappings Euclidean spaces.
- 9. Coordinate systems.
- 10. Integral calculus of functions of n-variables - volume.
- 11. Integral calculus of functions of n-variables - curve integrals.
- 12. Integral calculus of functions of n-variables - surface integrals.
- 13. Differential oparators in physics.
- Literature
- required literature
- 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
- recommended literature
- KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia, 1997, 383 s. ISBN 8020000887. info
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009, 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. info
- not specified
- MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi III (Mathematics for understanding and praxis III). 1st ed. Brno: VUTIUM, VUT Brno, 2018, 1068 pp. ISBN 978-80-214-5503-0. info
- Teaching methods
- Lectures: theoretical explanation with practical examples
Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems, homeworks, tests - Assessment methods
- Teaching: lectures and exercises
Exam: written test (solving problems and test), oral exam - Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course is taught annually.
The course is taught: every week.
- Enrolment Statistics (Spring 2025, recent)
- Permalink: https://is.muni.cz/course/sci/spring2025/F2712