|
Lecturer(s)
|
-
Fürst Tomáš, RNDr. Ph.D.
-
Tomeček Jan, doc. RNDr. Ph.D.
-
Ludvík Pavel, RNDr. Ph.D.
|
|
Course content
|
1. Lebesgue measure and integral. 2. Limits, sums and differentiation after the integral sign. 3. Fubini's Theorem and integration by substitution. 4. Curve integrals and potential. 5. Surface integrals. 6. Gauss-Ostrogradsky's, Green's and Stokes' Theorems. 7. Introduction to the calculus of variation
|
|
Learning activities and teaching methods
|
|
Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
|
|
Learning outcomes
|
Understand the fundamentals of the integral calculus of functions of several variables (with an emphasis on the Lebesgue integral), line and surface integrals, and the calculus of variations.
Comprehention Develop an understanding of the Lebesgue integral, its properties, and its consequences. Understand the meaning and applications of line and surface integrals. Grasp the underlying ideas of the calculus of variations.
|
|
Prerequisites
|
Differential calculus of functions of several variables and integral calculus of functions of one variable.
KMA/MA2
|
|
Assessment methods and criteria
|
Oral exam, Written exam
Combination of a written and oral exam. To obtain credit, active participation in exercises is required as well as successful completion of the credit tests.
|
|
Recommended literature
|
-
Černý, R., Pokorný, M. (2023). Základy matematické analýzy pro studenty fyziky 3. Praha.
-
Kopáček, J. (2007). Matematická analýza nejen pro fyziky (III). Praha.
-
Kopáček, J. (2015). Matematická analýza nejen pro fyziky (II). Praha.
-
Kopáček, J. (2006). Příklady z matematiky nejen pro fyziky III. Praha.
-
R. Feynman. (2005). The Feynman Lectures on Physics.
-
Stewart, J. (2015). Multivariable Calculus. Brooks Cole.
|