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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2018/2019

Calculus A4

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Code Completion Credits Range Language
01MAA4 Z,ZK 10 4+4 Czech
Lecturer:
Leopold Vrána (guarantor)
Tutor:
Radek Fučík, Jan Vybíral
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, 01MAA2-3, 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, Addison-Wesley, Reading, MA, 1966.

Recommended references: Mariano Giaquinta, Giuseppe Modica, Mathematical Analysis - An Introduction to Functions of Several Variables, Birkhäuser, Boston, 2009

Note:
Time-table for winter semester 2018/2019:
Time-table is not available yet
Time-table for summer semester 2018/2019:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2019-06-20
For updated information see http://bilakniha.cvut.cz/en/predmet11328205.html