PřF:F3712 Mathematics 3 - Course Information
F3712 Mathematics 3
Faculty of ScienceAutumn 2024
- Extent and Intensity
- 2/2/0. 4 credit(s) (plus extra credits for completion). Type of Completion: zk (examination).
In-person direct teaching - 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
- Thu 13:00–14:50 F3,03015, Fri 12:00–13:50 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
- 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), 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
- 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/autumn2024/F3712