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Lecturer(s)
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Černá Dana, doc. RNDr. Ph.D.
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Course content
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Lectures: 1. Improper integral. 2. Infinite number series - basic concepts, partial sums, the sum of series. 3. Absolute convergence, tests for convergence. 4. Vector space, basis, dimension. 5. Determinant, eigenvalues, and eigenvectors. 6. Euclidean space, multivariable functions - basic concepts, limits, continuity. 7. Partial derivatives, the chain rule, total differentials, tangent plane, gradient, and directional derivative. 8. Partial derivatives and higher-order total differential, Taylor polynomial. 9. Relative and constrained extrema of multivariable functions. 10. Absolute extrema of multivariable functions. 11. Ordinary differential equations - existence and uniqueness, slope field, separation of variables. 12. Differential equations with homogeneous functions, Bernoulli differential equation, a variation of constant for first-order linear differential equations, applications. 13. Linear differential equations of n-th order - the structure of the solution, characteristic equation, the method of undetermined coefficients. 14. Time reserve, revision. Materials are available in the course KMD/MP2-M in the e-learning portal TUL.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing), Self-study (text study, reading, problematic tasks, practical tasks, experiments, research, written assignments)
- Class attendance
- 56 hours per semester
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Learning outcomes
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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, numerical mathematics and linear algebra.
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Prerequisites
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Secondary school mathematics, knowledge of MP1-M.
KMA/MC2-M
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Assessment methods and criteria
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Written exam
Exam: written exam, consists of the practical examples and the theoretical part. It is necessary to pass the credit from the subject MC2-M prior to the exam.
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Recommended literature
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Brabec, J. - Hrůza, B.:. Matematická analýza II. Praha, 1986.
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Brabec, J.:. Matematická analýza II. Praha, 1979.
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Budinský, B. - Charvát, J.:. Matematika II. Praha, 1999.
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Ivan, J.:. Matematika 1; 2. Bratislava/Praha, 1989.
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Jacob, B.:. Linear Functions and Matrix Theory. Springer ? Verlag, 1995.
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Kopáčková, A.:. Studijní materiály zveřejněné na e-learningovém portále fakulty https://elearning.fm.tul.cz. 2019.
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Mezník, I. , Karásek, J., Miklíček, J.:. Matematika I pro strojní fakulty. SNTL, Praha, 1992.
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Nagy, J.:. Elementární metody řešení obyčejných diferenciálních rovnic. Praha, 1978.
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Nekvinda, M. aj.:. Matematika II. [Skripta TU]. Liberec, TUL, 2002.
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Nekvinda, M.- Říhová, H. - Vild, J.:. Matematické oříšky II. TU Liberec, 2002.
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Nešetřil, J. ? Matoušek, J.:. Kapitoly z diskrétní matematiky. Praha, Karolinum, 2000.
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Rektorys K. a další:. Přehled užité matematiky I, II, Prometheus 1995..
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