Calculus A4
Code  Completion  Credits  Range  Language 

01MAA4  Z,ZK  10  4+4  Czech 
 Course guarantor:
 František Štampach
 Lecturer:
 František Štampach
 Tutor:
 Monika Balázsová, Pavel Strachota, František Štampach
 Supervisor:
 Department of Mathematics
 Synopsis:

Integration of functions of several variables, measure theory, foundation of differential and integral calculus on manifolds and complex analysis.
 Requirements:

Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA23, 01LA1, 01LAA2 held at the FNSP CTU in Prague).
 Syllabus of lectures:

Lebesgue integral: Daniel?s construct, interchange rules, measurable sets and measurable functions. Fubini's theorem, theorem on changing variables. Parametrical integrals: Interchange theorems, Gamma and Beta functions. Differential forms: conservative, exact and closed form and their relations, potential. Line and surface integral: Green's, Gauss' and Stokes' theorem. Complex analysis: analytic functions, Cauchy's theorem, Taylor's expansion, Laurent's expansion, singularities, residue theorem.
 Syllabus of tutorials:

Smooth manifolds. Constrained extrems. Differential forms. Lebesgue integral in several variables. Use of Fubini's theorem and theorem on changing variables. Use of Gamma and Beta functions for computation of integrals. Computation of integrals
 Study Objective:

To acquaint the students with foundations of Lebesgue integration and with foundations of complex analysis and its use in applications.
 Study materials:

Key reference: W.H.Fleming,Functions of Several Variables, AddisonWesley, Reading, MA, 1966.
Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis  An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009
 Note:
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: