Mathematical Analysis 1
IMA1 Acad. year 2020/2021 Summer semester 4 credits
Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.
Language of instruction
Subject specific learning outcomes and competences
The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.
The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.
Why is the course taught
Fundamentals of calculus are a necessary part of a study at a technical university because virtually all technical and physical subjects employ the concepts of a derivative and integral.
- Discrete Mathematics (IDM)
Prerequisite kwnowledge and skills
Secondary school mathematics.
- Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2013. (in Czech).
- Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (in Czech).
- 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.
Syllabus of lectures
- The concept of a function of a real variable, properties of functions and basic operations with functions.
- Elementary functions of a real variable.
- Complex numbers. Functions of a complex variable.
- Limit of a sequence. Limit and continuity of a function.
- Differential calculus of functions of one variable. Derivative at a point, derivative in an interval, a differential of a function. Numerical differentiation.
- Second derivative. Extrema of a function.
- Graph properties.
- Taylor theorem. Approximation of functions.
- Newton and Lagrange interpolation.
- Numerical solutions of nonlinear equations.
- Integral calculus of functions of one variable. Indefinite integral, basic methods of integration.
- Definite Riemann integral, its applications.Numerical integration.
- Improper integral.
Syllabus of numerical exercises
Problems discussed at numerical classes are chosen so as to complement suitably the lectures.
Written tests during the semester (maximum 30 points).
Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.
At least 10 points from the tests during the semester.
Course inclusion in study plans