F3712 Mathematics 3

Faculty of Science
Autumn 2020
Extent and Intensity
2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
Taught partially online.
Teacher(s)
Mgr. Pavla Musilová, Ph.D. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)
Guaranteed by
Mgr. Pavla Musilová, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Supplier department: Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science
Timetable
Wed 14:00–15:50 Fs1 6/1017
  • Timetable of Seminar Groups:
F3712/01: Thu 11:00–12:50 Fs1 6/1017, P. Musilová
Prerequisites
Grammar school mathematics, matter of Matematics 1 and Matematics 2
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The discipline is a third 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.
Learning outcomes
Student will after absolving this course:
-be able to work with series of numbers and functions,
-understand basics of spectral analysis,
-have basic knowledge about Fourier's transformation and distributions,
-have basic knowledge about metric spaces and Banach spaces,
-solve some simply partial differential equations using the Fourier's method,
-be able to apply integral calculus of n-variable functions,
-work with normal matrixs and operators,
-work with tensors.
Syllabus
  • 1. Series of numbers,
  • 2. Series of functions,
  • 3. Fundamentals of spectral Analysis,
  • 4. Basics of integral transformations and distributions,
  • 5. Metric spaces, Banach and Hilbert spaces,
  • 6. Basics of solving some simply partial differential equations,
  • 7. Integral calculus of n-variable functions - volume,
  • 8. Integral calculus of n-variable functions - flows,
  • 9. Integral calculus of n-variable functions - Stoke's theorem,
  • 10. Linear algebra - normal operators,
  • 11. Linear algebra - Jordan's normal matrix,
  • 12. Linear algebra - tensors,
  • 13. Applications.
Literature
    required literature
  • Musilová, Jana a Pavla Musilová, Matematika pro porozumění a praxi III. Vutium Brno 2018, ISBN 978-80-214-5503-0.
  • 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). 697 pp. ISBN 978-80-214-4071-5. 2012. info
    recommended literature
  • KVASNICA, Jozef. Matematický aparát fyziky. Vyd. 2., opr. Praha: Academia. 383 s. ISBN 8020000887. 1997. 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. 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. 2009. 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)
Study Materials
Teacher's information
http://www.physics.muni.cz/~pavla/teaching.php
The course is also listed under the following terms Autumn 2018, Autumn 2019, autumn 2021, Autumn 2022, Autumn 2023.
  • Enrolment Statistics (Autumn 2020, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2020/F3712