Course details

Mathematical Analysis

IMA Acad. year 2011/2012 Summer semester 5 credits

Current academic year

Limit and continuity, derivative of a function. Partial derivatives. Basic differentiation rules. Elementary functions. 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.

Guarantor

Krupková Vlasta, RNDr., CSc.

Language of instruction

Czech

Completion

Examination

Time span

  • 26 hrs lectures
  • 10 hrs exercises
  • 10 hrs pc labs
  • 6 hrs projects

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.

Prerequisite knowledge and skills

Secondary shool mathematics and the kowledge from Discrete Mathematics course.

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.

Syllabus of lectures

  1. Function of one variable, limit, continuity.
  2. Differential calculus of functions of one variable I: derivative, differential, Taylor theorem.
  3. Differential calculus of functions of one variable II: maximum, minimum, behaviour of the function.
  4. Integral calculus of functions of one variable I: indefinite integral, basic methods of integration.
  5. Integral calculus of functions of one variable II: definite Riemann integral and its application.
  6. Infinite number and power series.
  7. Taylor series.
  8. Functions of two and three variables, geometry and mappings in three-dimensional space.
  9. Differential calculus of functions of more variables I: directional and partial derivatives, Taylor theorem.
  10. Differential calculus of functions of more variables II: funcional extrema, absolute and bound extrema.
  11. Integral calculus of functions of more variables I: two and three-dimensional integrals.
  12. Integral calculus of functions of more variables II: method of substitution in two and three-dimensional integrals.

Syllabus of numerical exercises

The class work is prepared in accordance with the lecture.

Syllabus of computer exercises

Trained tasks are prepared to follow and complete study matter from lectures and seminar practice.

Progress assessment

Study evaluation is based on marks obtained for specified items. Minimimum number of marks to pass is 50.

Controlled instruction

Practice tasks: 25 points.
Homeworks: 15 points.
Semestral examination: 60 points.

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