CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

# Calculus B3

Code Completion Credits Range Language
01MAB3 Z,ZK 7 2+4 Czech
Lecturer:
Milan Krbálek (guarantor)
Tutor:
Milan Krbálek (guarantor), Jitka Kostková, Pavel Strachota, Kateřina Škardová
Supervisor:
Department of Mathematics
Synopsis:

The course is devoted to functional sequences and series, theory of ordinary differential equations, theory of quadratic forms and surfaces, and general theory of metric spaces, normed and prehilbert?s spaces.

Requirements:

Basic course of Calculus a Linear Algebra (in the extent of the courses 01MA1, 01MAB2, 01LA1, 01LAB2 held at the FNSPE CTU in Prague).

Syllabus of lectures:

1. Functional sequences and series - convergence range, criteria of uniform convergence, continuity, limit, differentiation and integration of functional series, power series, Series Expansion, Taylor?s theorem. 2. Ordinary differential equations - equations of first order (method of integration factor, equation of Bernoulli, separation of variables, homogeneous equation and exact equation) and equations of higher order (fundamental system, reduction of order, variation of parameters, equations with constant coefficients and special right-hand side, Euler?s differential equation). 3. Quadratic forms and surfaces - regularity, types of definity, normal form, main and secondary signature, polar basis, classification of conic and quadric 4. Metric spaces - metric, norm, scalar product, neighborhood, interior and exterior points, boundary point, isolated and non-isolated point, boundary of set, completeness of space, Hilbert?s spaces.

Syllabus of tutorials:

1. Functional sequences. 2. Functional series. 3. Power series 4. Solution of differential equations. 5. Quadratic forms. 6. Quadratic surfaces. 7. Metric spaces, normed and Hilbert?s spaces.

Study Objective:

Knowledge: Investigation of uniform convergence for functional sequences and series. Solution of differential equations. Classification of quadratic forms and surfaces. Classification of points of sets. Skills: Individual analysis of practical exercises.

Study materials:

Key references:

[1] Robert A. Adams, Calculus: A complete course, 1999,

[2] Thomas Finney, Calculus and Analytic geometry, Addison Wesley, 1996

Recommended references:

[3] John Lane Bell: A Primer of Infinitesimal Analysis, Cambridge University Press, 1998

Media and tools: MATLAB

Note:
Time-table for winter semester 2019/2020:
Time-table is not available yet
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-04-05
For updated information see http://bilakniha.cvut.cz/en/predmet10379505.html