Course details

# Mathematical Analysis

IMA Acad. year 2015/2016 Summer semester 5 credits

Guarantor

Language of instruction

Completion

Time span

Assessment points

Department

Lecturer

Instructor

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: 15 points.

Semestral examination: 60 points.

Course inclusion in study plans