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Lecturer(s)
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Kopal Stanislav, doc. RNDr. Ph.D.
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Breitfelder Ondřej, Mgr.
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Čižmář Jiří, doc. Ing. Ph.D.
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Pinte Jan, RNDr. Ph.D.
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Vávrová Miroslava, RNDr.
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Valentová Ivana, doc. Ing. Ph.D.
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Course content
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Week 1: Primitive functions and indefinite integral. Week 2: Calculating the integral (per-partes, integration by substitution). Week 3: Definite integral and its application. Week 4: Matrices - basic concepts, operations with matrices, rank of a matrix. Week 5: Systems of linear algebraic equations - matrix notation, existence of solutions, Gaussian elimination method, inverse matrices Week 6: Linear vector space - linear dependence and independence of LVS elements, bases and dimensions of LVS Week 7: Determinant - calculation, use in solving a system of linear algebraic equations Week 8: Eigenvalues and eigenvectors of a matrix, Jordan canonical form of a matrix. Week 9: Ordinary differential equations of the 1st order, nonlinear, linear. Formulation of the initial value problem. Week 10: Methods of solving ODEs of the 1st order: direct integration, separation, variation of parameters. Week 11: Higher order linear differential equations - homogeneous, nonhomogeneous, with constant coefficients. Characteristic equation method. Week 12: Variation of parameters. Estimate of the particular integral. Week 13: Systems of the 1st order differential equations.
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Learning activities and teaching methods
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Interactive lecture, Lecture with practical applications, Practicum
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Contact hours
- 52 hours per semester
- Preparation for an examination (30-60)
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| identify logical symbols, statements and quantifiers |
| describe continuous and inverse functions |
| describe a limit of a function of one real variable |
| describe a derivative of a function of one real variable |
| Skills |
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| draw graphs of elementary functions |
| compute a limit of a function of one real variable |
| differentiate a function of one real variable |
| solve simple systems of equations |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| define an indefinite integral and a primitive function |
| define a definite integral and integral sums |
| explain the concept of vector, matrix |
| characterize eigenvalues and eigenvectors of matrices |
| formulate initial value problem for ordinary differential equations of the first order |
| formulate initial and boundary value problems for ordinary differential equations of the second order |
| Skills |
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| find the primitive function use integral calculus methods |
| calculate the determinant and the inverse matrix |
| solve systems of linear algebraic equations |
| determine eigenvalues and eigenvectors of matrices |
| solve an ordinary differential equation of the first order by the method of separation of variables |
| solve homogeneous and nonhomogeneous linear ODEs of higher order with constant coefficients |
| Competences |
|---|
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
|---|
| Interactive lecture |
| Practicum |
| Skills |
|---|
| Practicum |
| Lecture with visual aids |
| One-to-One tutorial |
| Task-based study method |
| Competences |
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| Lecture |
| Practicum |
| Task-based study method |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
| Skills |
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| Written exam |
| Test |
| Skills demonstration during practicum |
| Competences |
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| Oral exam |
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Recommended literature
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A. Kufner. Obyčejné diferenciální rovnice. 1993. ISBN 80-7082-106-X.
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P. Drábek, S. Míka. Matematická analýza II. Plzeň, 2010. ISBN 978-80-7082-977-6.
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P. Drábek, S. Míka. Matematická analýza I. Plzeň, 2003. ISBN 80-7082-978-8.
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Teschl, Gerald. Ordinary differential equations and dynamical systems. Providence : American Mathematical Society, 2012. ISBN 978-0-8218-8328-0.
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Tesková, Libuše. Lineární algebra. 3. vyd. Plzeň : Západočeská univerzita, 2010. ISBN 978-80-7043-966-1.
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Watkins, David S. Fundamentals of matrix computations. 2nd ed. New York : John Wiley & Sons, 2002. ISBN 0-471-21394-2.
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