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Mathematics for Physicists I - NMAF041

Title:	Matematika pro fyziky I
Guaranteed by:	Laboratory of General Physics Education (32-KVOF)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Class:	Fyzika
Classification:	Physics > Mathematics for Physicists

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Annotation -

Last update: G_M (03.06.2004)

Third part of the basic course of mathematics for the students of physics (bachelor study). Follows the course MAF033, a simultaneously running course MAF034 is recommended.

Aim of the course -

Last update: T_KVOF (28.03.2008)

Third part of the basic course of mathematics for the students of physics (bachelor study). Follows the course MAF033, a simultaneously running course MAF034 is recommended.

Literature - Czech

Last update: G_F (07.01.2003)

Kopáček, J. a kol.: Matematika pro fyziky, díly III-V, skriptum MFF UK

Teaching methods - Czech

Last update: T_KVOF (28.03.2008)

přednáška + cvičení

Syllabus -

Last update: G_M (03.06.2004)

1. Metric and norm spaces:

Metric, norm, open and closed sets, closure, interior, boundary. Convergence, completeness, compactness, separability. BAnach and Hilbert spaces. Continuity and uniform continuity, Heine theorem. Continuous functions on a compact set. Contractive mapping. Banach fixed point theorem. Theorem on the solvability of ODE.

2. Functions of more than one variable:

Metrics and norms in Rn. Limit and continuity. Partial and directional derivatives, total differential. Exact differential equations. Chain rule, change of variables. Mean value theorem, Taylor series. Local and global extrema, Lagrange multipliers. Implicit functions.