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
    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
The course is also listed under the following terms Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (recent)
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