Calculus B3

Garant předmětu:

Milan Krbálek

Lecturer:

Milan Krbálek

Tutor:

Martin Jex, Václav Klika, Martin Kovanda, Jan Kovář, Milan Krbálek

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:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• BS Matematické inženýrství - Aplikované matematicko-stochastické metody (compulsory elective course)
• BS Informatická fyzika (compulsory elective course)
• BS Aplikace softwarového inženýrství (compulsory course of the specialization)
• BS jaderné inženýrství B (compulsory course of the specialization)
• 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)