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PřF:F3712 Mathematics 3 - Course Information

## F3712 Mathematics 3

**Faculty of Science**

Autumn 2022

**Extent and Intensity**- 2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).

Taught in person. **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 8:00–9:50 F1,01014, Wed 16:00–17:50 F3,03015
**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 knowldege about algebraic structures

-work with vector spaces, scalar product, linear mappings and tensors.

-compute spectral representation of normal operators

-have basic knowledge about metric spaces and Banach spaces, **Syllabus**- 1. Series of numbers,
- 2. Series of functions,
- 3. Fundamentals of spectral Analysis,
- 4. Basics of integral transformations and distributions,
- 5. Algebraic structures, group, ring, field, vector space.
- 6. Linear mappings, kernel, image, eigenvalues and eigenvectors, diagonal representation.
- 7. Scalar products, unitary spaces.
- 8. Linear operators in unitary spaces, spectral representation.
- 9. Linear algebra - tensors.
- 10. Metric spaces, Banach and Hilbert spaces,

**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), 2012. 697 pp. ISBN 978-80-214-4071-5. info

*required 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

*recommended literature***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

- Enrolment Statistics (recent)

- Permalink: https://is.muni.cz/course/sci/autumn2022/F3712