PřF:F1110 Linear algebra and geometry - Course Information

F1110 Linear algebra and geometry

Extent and Intensity

2/2. 4 credit(s) (plus 2 credits for an exam). Type of Completion: zk (examination).

Teacher(s)

prof. RNDr. Jana Musilová, CSc. (lecturer)
Mgr. Pavla Musilová, Ph.D. (seminar tutor)

Guaranteed by

prof. RNDr. Michal Lenc, Ph.D.
Department of Theoretical Physics and Astrophysics – Physics Section – Faculty of Science

Timetable

Wed 10:00–11:50 F1 6/1014

• Timetable of Seminar Groups:

F1110/01: Tue 13:00–14:50 F4,03017, P. Musilová
F1110/02: Thu 11:00–12:50 F4,03017, P. Musilová

Prerequisites

Secondary school mathematics

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives

The first part of the fundamental course of linear and multilinear algebra and geometry for physicist. As the linear algebra and geometry are key mathematical tools for most physical theories, the aim of the discipline is to give students a sufficiently deep understanding of their concepts: Vector spaces and subspaces, linearity, linear mapping, practical calculus of matrices, and solving systems of linear equations.  

Absolving the discipline students obtain following knowledge and practical skills:

* Understanding of the concept of a matrix and practical skills with calculus of matrices.
* Practical skills in solving systems od linear equations.
* Understanding of basic algebraic structures necessary for the concept of a vector space, understanding of the concept of vector space and subspace and the concept of linearity.
* Understanding of the theory of systems of linear equations in the context of vecor spaces and subspaces.

Syllabus

• 1. Matices, calculus of matrices, rank of a matrix, Gauss elimination.
• 2. Determinant of a matrix, inverse matrix.
• 3. Solving systems of linear equations.
• 4. Algebraic structures with one and two operatios, groups, rings, fields.
• 5. Vector spaces, linear dependent and linear independent systems of vectors.
• 6. Base, dimension, transformations of bases.
• 7. Vector subspaces.
• 8. Vector subspaces generated by a system of vectors, intersection of vector spaces, complement.
• 9. Examples of vector spaces and subspaces.
• 10. Systems of linear equations and vector spaces.
• 11. Linear mapping, vector spaces connected with a linear mapping.
• 12. Representation of a linear mapping in bases, transformations of bases.
• 13. Dual space, dual basis.
• 14. Applications, examples.

Literature

• STRANG, Gilbert. Introduction to linear algebra. Online. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, 2009. ix, 574. ISBN 9780980232721. [citováno 2024-04-23] info
• MUSILOVÁ, Jana and Demeter KRUPKA. Lineární a multilineární algebra. Online. 1. vyd. Praha: Státní pedagogické nakladatelství, 1989. 281 s. [citováno 2024-04-23] info
• MUSILOVÁ, Jana and Pavla MUSILOVÁ. Matematika pro porozumění i praxi I (Mathematics for understanding and praxis I). Online. Vydání druhé, doplněné. Brno: VUTIUM, VUT Brno, 2009. 339 pp. Vysokoškolské učebnice. ISBN 978-80-214-3631-2. [citováno 2024-04-23] info
• SLOVÁK, Jan. Lineární algebra. Online. Učební texty. Brno: Masarykova univerzita, 1998. 138 pp. elektronicky dostupné na www.math.muni.cz/~slovak. ISBN nemá. [citováno 2024-04-23] 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, exercises.
Exam: written test (consisting of two parts: (a) solving problems, (b) test), oral part.

Language of instruction

Czech

Follow-Up Courses

• F2182 Linear and multilinear algebra
• F3063 Integration of forms

Further comments (probably available only in Czech)

Study Materials
The course is taught annually.

• Enrolment Statistics (Autumn 2011, recent)
  
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