Course details

# Mathematical Analysis

IMA Acad. year 2018/2019 Summer semester 6 credits

Guarantor

Deputy Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Fusek Michal, Ing., Ph.D. (DMAT FEEC BUT)

Hliněná Dana, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Krupková Vlasta, RNDr., CSc. (DMAT FEEC BUT)

Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Instructor

Fusek Michal, Ing., Ph.D. (DMAT FEEC BUT)

Hliněná Dana, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Krupková Vlasta, RNDr., CSc. (DMAT FEEC BUT)

Novák Michal, doc. RNDr., Ph.D. (DMAT FEEC BUT)

Šafařík Jan, Mgr. et Mgr., Ph.D. (BUT)

Vítovec Jiří, Mgr., Ph.D. (DMAT FEEC BUT)

Subject specific learning outcomes and competences

Learning objectives

Prerequisite kwnowledge and skills

Study literature

- Brabec B., Hrůza,B., Matematická analýza II, SNTL, Praha, 1986.
- Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997.
- Krupková, V. Matematická analýza pro FIT, electronical textbook, 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

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

Syllabus of numerical exercises

Syllabus - others, projects and individual work of students

- Limit, continuity and derivative of a function. Partial derivative. Derivative of a composite function.
- Differential of function of one and several variables. L'Hospital's rule. Behaviour of continuous and differentiable function. Extrema of functions of one and several variables.
- Primitive function and undefinite integral. Basic methods of integration. Definite one-dimensional and multidimensional integral.
- Methods for solution of definite integrals (Newton-Leibnitz formula, Fubini theorem).
- Indefinite number series. Convergence of series. Sequences and series of functions. Taylor theorem. Power series.

Progress assessment

Homeworks: 12 points.

Semestral examination: 60 points.

Course inclusion in study plans