Mathematics III

English Programme

Course title: Mathematics III

About the course

The course is organized in 14 hundred-and-fifty-minute lectures and 28 hundred-minute seminars.

The curriculum and teaching is supervised by: Prof. RNDr. Josef Šlapal, CSc.

Curriculum summary

At the beginning of the course, students will learn the basics of series - number series, power series, Taylor series, and Fourier series, focussing on the convergence tests, and expansions of functions into Taylor and Fourier series. In the second part of the course, the topic will be differential equations including initial and boundary problems in ordinary and partial differential equations. Also systems of linear differential equations will be investigated. The last two lectures will be dealing with selected numerical methods of solution of partial differential equations.

Syllabus: Math3

Examinations, assessment of results: Examinations

Literature:

Lasser, R.: Introduction to Fourier Series, Marcel Dekker, Inc., New York, 1996

Voxman, W.L., Goetschel, R.H.: Advanced Calculus, Marcel Dekker, Inc., New York, 1981.

Robinson, J.C.: An Introduction to Ordinary Differential Equations, Cambridge University Press, 2004

Lectures for downloading:

FourierSeries.doc, FunctionalSeries.ppt, LinearDEConstCoeff.ppt, FirstOrderLinearDE.ppt, MatrixFunctions.pdf, NumericalSolutions.ppt, OrdinaryDE.ppt, SeparateVariables.ppt, PowerSeries.ppt, SequenceBasics.ppt, SequenceLimits.ppt, EulerNumber.ppt, SeriesBasics.ppt, ConvergenceTests.ppt, SeriesProperties.ppt, TaylorSeries.ppt