Calculus A4

Garant předmětu:

Lecturer:

Tutor:

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Matematické modelování (compulsory course of the specialization)
• BS Matematické inženýrství - Matematická fyzika (compulsory course of the specialization)
• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Dozimetrie a aplikace ionizujícího záření (compulsory elective course)
• BS Experimentální jaderná a částicová fyzika (compulsory elective course)
• BS Inženýrství pevných látek (compulsory elective course)
• BS Diagnostika materiálů (compulsory elective course)
• BS Fyzika a technika termojaderné fúze (compulsory elective course)
• BS Fyzikální elektronika (compulsory elective course)