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.
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
Wed 8:00–9:50 F1,01014, Wed 16:00–17:50 F3,03015
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,
  • 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,
    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
Further comments (probably available only in Czech)
Study Materials
Teacher's information
The course is also listed under the following terms Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2022/F3712