|
Lecturer(s)
|
-
Břehovský Jiří, Mgr. Ph.D.
-
Černá Dana, doc. RNDr. Ph.D.
|
|
Course content
|
Lectures: 1. Infinite series, tests for convergence, absolute convergence. 2. Introduction to metric spaces, multivariable functions. 3. Continuity and limits of multivariable functions. 4. Partial derivatives, total differentials, the chain rule, directional derivatives. 5. Taylor's formula, implicit functions. 6. Repetition. 7. Relative extrema of multivariable functions. 8. Constrained and absolute extrema of multivariable functions. 9. First-order ordinary differential equations, existence and uniqueness of solutions. 10. Second-order ordinary differential equations with constant coefficients. 11. Introduction to numerical solution methods for first-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. 14. Repetition. Practice: 1. Repetition of integration. 2. Infinite series, tests for convergence, absolute convergence. 3. Infinite series, metric spaces, multivariable functions. 4. Continuity and limits of multivariable functions. 5. Partial derivatives, total differentials, the chain rule, directional derivatives. 6. Taylor's formula, implicit functions. 7. Repetition. 8. Relative extrema of multivariable functions. 9. Constrained and absolute extrema of multivariable functions. 10. Solution methods for first-order ordinary differential equations. 11. Solution methods for second-order ordinary differential equations. 12. Introduction to multiple integrals, Fubini's theorem. 13. Substitutions in multiple integrals. 14. Repetition.
|
|
Learning activities and teaching methods
|
Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments), Written assignment presentation and defence
- Class attendance
- 70 hours per semester
- Home preparation for classes
- 70 hours per semester
|
|
Learning outcomes
|
The subject focuses on an introduction to differential calculus of functions of more (especially two) real variables and basics of differential equations. Selected topics of linear algebra are included.
Mastering essentials of differential calculus of function of more (especially two) real variables, ordinary differential equations, essentials of number series and numerical mathematics.
|
|
Prerequisites
|
Secondary school mathematics, knowledge of MA1*M.
|
|
Assessment methods and criteria
|
Written exam
Credit: Active participation on seminars and written tests. Exam: written exam, consists of the practical examples and the theoretical part. The evaluation on seminars will be taken into account in the exam.
|
|
Recommended literature
|
-
Brabec, J. - Hrůza, B.:. Matematická analýza II. Praha, 1986.
-
Brabec, J.:. Matematická analýza II. Praha, 1979.
-
Budinský, B. - Charvát, J.:. Matematika II. Praha, 1999.
-
Ivan, J.:. Matematika 1; 2. Bratislava/Praha, 1989.
-
Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
-
Nagy, J.:. Elementární metody řešení obyčejných diferenciálních rovnic. Praha, 1978.
-
Nekvinda, M. aj.:. Matematika II. [Skripta TU]. Liberec, TUL, 2002.
-
Nekvinda, M.- Říhová, H. - Vild, J.:. Matematické oříšky II. TU Liberec, 2002.
-
Rektorys K. a další:. Přehled užité matematiky I, II, Prometheus 1995..
|