Calculus A3

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Function sequences and series, foundation of topology, and differential calculus of several variables.

Requirements:

Basic Course of Calculus and Linear Algebra (in the extent of the courses 01MA1, 01MAA2, 01LA1, 01LAA2 held at the FNSP CTU in Prague).

Syllabus of lectures:

Function sequences and series: Pointwise and uniform convergence, interchange rules for limits, derivatives and integrals. Fourier's series, expansion of a function into trigonometrical series, tests for pointwise and uniform convergence of trigonometrical series, completeness of trigonometric system. Topology of normed linear space, compact, connected and complete sets, fixpoint theorem. Differential calculus of several variables: directional derivatives, partial and total derivatives, mean-value theorems, extremum, manifolds, constrained extrema.

Syllabus of tutorials:

Uniform convergence. Interchange rules. Expansion of a function into trigonometrical series.

Directional derivative. Total derivative. Local extrema.

Study Objective:

To acquaint the students with the properties of function sequences and series, expansion of a function into trigonometrical series, with an introduction to the topology, and with foundation of differential calculus of several variables.

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)