FIT-IMA2Acad. year: 2020/2021
Series. The limit, continuity, partial derivatives and extrema of a function of several variables. Double and triple integrals. Differential equations. Analytical and numerical solutions of the initial problem.
Learning outcomes of the course unit
The ability to understand the basic problems of higher calculus and use derivatives, integrals and differential equations for solving specific problems.
Recommended optional programme components
Recommended or required reading
Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2019.
Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966.
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), McGraw-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.
Planned learning activities and teaching methods
Assesment methods and criteria linked to learning outcomes
Home assignments during the semester.
The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.
Language of instruction
The main goal of the course is to enhance the knowledge of calculus from the previous semester and explain the basic principles and methods of higher calculus. The emphasis is put on handling the practical use of these methods for solving specific problems.
Specification of controlled education, way of implementation and compensation for absences
Classes are not compulsory.
Type of course unit
26 hours, optionally
Teacher / Lecturer
- Number series.
- Power series.
- Fourier series. Fourier transform.
- Differential calculus of functions of several variables I: limit, continuity, partial derivatives, Schwarz theorem.
- Differential calculus of functions of several variables II: differential, tangent plane, Taylor polynomial.
- Differential calculus of functions of more variables III: local extrema, Hess matrix, Sylvester criterion,.
- Integral calculus of functions of several variables I: double integral, normal domain in plane, Fubini's theorem, change of variables.
- Integral calculus of functions of several variables II: triple integral, normal domain in space, Fubini's theorem.
- Integral calculus of functions of several variables III: change of variables in triple integral.
- Introduction to differential equations. Initial problem. Existence and uniqueness of a solution. Separable equation. Linear equation
- Numerical solution of differential equations of the first order.
26 hours, compulsory
Teacher / Lecturer
Problems discussed at numerical classes are chosen so as to complement suitably the lectures.
- Ima [.pdf] 5.29 MB
- Inm [.pdf] 2.79 MB
- Matematika_1_sbirka [.pdf] 462.58 kB
- Ism [.pdf] 1.92 MB
- Matematika_2_sbirka [.pdf] 589.26 kB
- Matematika_1b_sbirka [.pdf] 559.66 kB