Mathematical analysis II

Grading of the course requires grading of the following courses:

Calculus 1 (01MA1)

Lecturer:

Edita Pelantová (gar.)

Tutor:

Edita Pelantová (gar.), Jiří Mikyška, Severin Pošta

Supervisor:

Department of Mathematics

Synopsis:

The subject is devoted mainly to the integral calculus of the real functions with one real variable and to the theory of the number series and the power series.

Requirements:

Succesfull completion of the course Mathematical analysis I, i.e. familiarity with differential calculus.

Syllabus of lectures:

Continuation of differential calculus: the l´Hospital rule, Taylor´s Polynomials, Taylor´s formula; Theory of integrals: primitives, definite integral (Riemann definition), techniques of integration and application of integrals; Infinite series: criteria of convergence, operations on series, absolute and conditional convergence, real and complex power series, the Cauchy-Hadamard theorem, expansion of function into power series, summation of infinite series.

Syllabus of tutorials:

Content of excercises consists in solving problems with emphasis on using theoretical results. The domains of problems: evaluation fo limits by the l´Hospital rule, uniform continuity, approximation of function by the Taylor polynomial, technics for determination of primitive functions, evaluation of volumes and areas, expansion of function into a power series

Study Objective:

Acquired knowledge: a rigorous construction of integral, to focus on properties of power series.

Acquired skills: application of the theoretical results in geometry, discrete mathematics and in physics.

Study materials:

Obligatory:

[1] E. Pelantová: Matematická analýza II, skriptum ČVUT, 2007

[2] E.Pelantová, J.Vondráčková: Cvičení z matematické analýzy - Integrální počet a řady, skriptum ČVUT 2006

Optional:

[3] I. Černý, M. Rokyta: Differential and Integral Calculus of One Real Variable, Karolinum, Praha 1998

[4] I.Černý, Úvod do inteligentního kalkulu I, Academia 2005

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

Time-table is not available yet

The course is a part of the following study plans: