Course details

Mathematical Analysis

IMA Acad. year 2003/2004 Summer semester 5 credits

Current academic year

The limit and the continuity of a function. The derivative. Partial derivatives. Basic differentiation rules. The chain rule. The elementary functions. Applications of derivatives. Extrema for functions (of one and of several variables). Indefinite integral. Techniques of integration. The Riemann (definite)integral. Multiple integrals. Applications of integrals. Infinite sequences and infinite series. Taylor polynomials. Fourier series. Functions of a complex variable. Their derivative. Integral with respect to a complex variable. The Laurent series. Differential equations (basic notions). Elements of operational calculus. The Laplace transform, applications to solving differential equatitions). The Z-transform and solving difference equations.

Details ...

Guarantor

Krupková Vlasta, RNDr., CSc.

Language of instruction

Czech

Completion

Credit+Examination

Time span

Department

Department of Mathematics (UMAT)

Subject specific learning outcomes and competences

The ability of orientation in the basic problems of higher mathematics and the ability to apply the basic methods. Solving problems in the areas cited in the annotation above by using basic rules. Solving these problems by using modern mathematical software.

Learning objectives

The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of computer science. The practical aspects of applications of these methods and their use in solving concrete problems (including the application of contemporary mathematical software in the laboratories) are emphasized.

Study literature

  • Brabec, B., Hrůza, B., Matematická analýza II, SNTL, Praha, 1986.
  • Švarc, S., kol., Matematická analýza I, PC DIR, Brno, 1997.
  • Krupková, V. Matematická analýza pro FIT, elektronický učební text, 2007.

Fundamental literature

  • Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993.
  • Fong, Y., Wang, Y., Calculus, Springer, 2000.
  • Ross, K.A., Elementary analysis: The Theory of Calculus, Springer, 2000.
  • Small, D.B., Hosack, J.M., Calculus (An Integrated Approach), Mc Graw-Hill Publ. Comp., 1990.
  • Thomas, G.B., Finney, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.
  • Zill, D.G., A First Course in Differential Equations, PWS-Kent Publ. Comp., 1992.

Progress assessment

Submission of projects (homework) in ruled terms.

Course inclusion in study plans

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