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Lecturer(s)
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Caletka Tomáš, RNDr. CSc.
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Hrabáček Vítězslav, Ing. Ph.D.
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Brada Pavel, Ing. Ph.D.
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Course content
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Week 1: Functions of more variables and their properties (recapitulation). Week 2: Differential calculus of functions of more variables, partial derivatives, gradient. Week 3: Higher order partial derivatives. Chain rule, derivatives of implicit functions. Week 4: Fundamental optimization probles in Rn. Stationary points, local extrema. Week 5: Double integral, Fubini theorem. Methods to computation. Week 6: Change of variables in a double integrals Week 7: Triple integral, methods to computation. Change of variables. Week 8-9: Vector functions of one scalar variable. Week 10-11: Introduction to partial differential equations. Formulation of fundamental problems. Week 12: Classification of basic types of partial differential equations. Week 13: Recapitulation
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Learning activities and teaching methods
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Interactive lecture, Lecture with practical applications, Practicum
- Contact hours
- 52 hours per semester
- Preparation for formative assessments (2-20)
- 20 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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| There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M2S. |
| Skills |
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| 1. To use integral calculus in one dimension with application to real world problems. 2. To expand function into Taylor or Fourier series. 3. To formulate basic initial and boundary value ordinary differential equations. 4. To solve first order ODE and systems of first order ODE's. 5. To solve higher order linear ODE's with constant coefficients. 6. To apply differential equations and knowledge of their solutions to real world problems. 7. To use functions of several real variables. 8. To use basic concepts in differential calculus of several real variables (partial derivatives, gradient) |
| Competences |
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| N/A |
| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| By the end of the course, a successful student should be able to: 1. Compute directional and partial derivatives of functions of more variables; 2. Formulate basic min/max problems and solve them using differential calculus; 3. Evaluate double and triple integrals; 4. Work with curves and vector functions; 5. Formulate fundamental problems for partial differential equations; 6. Classify basic types of partial differential equations. |
| Skills |
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| 1. To calculate directional derivatives and partial derivatives of functions of several real variables. 2. To solve basic min-max problems. 3. To compute double and triple integrals. 4. To use curves and vector functions. 5. To formulate basic problems governed by partial differential equations. 6. To classify basic types of PDE's. |
| Competences |
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| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Interactive lecture |
| Practicum |
| Skills |
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| Lecture supplemented with a discussion |
| Practicum |
| Interactive lecture |
| Competences |
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| Seminar |
| Lecture supplemented with a discussion |
| Interactive lecture |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
| Skills |
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| Skills demonstration during practicum |
| Combined exam |
| Competences |
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| Combined exam |
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Recommended literature
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Brabec, Jiří; Hrůza, Bohuslav. Matematická analýza II. Praha : SNTL, 1986.
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Drábek, Pavel; Míka, Stanislav. Matematická analýza II. 3. nezm. vyd. Plzeň : ZČU, 1999. ISBN 80-7082-528-6.
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Ivan, Ján. Matematika 2. 1. vyd. Bratislava : Alfa, 1989. ISBN 80-05-00114-2.
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Jana Musilová a Pavla Musilová. Matematika II/1. Brno, 2012. ISBN 978-80-214-4071-5.
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Jana Musilová a Pavla Musilová. Matematika II/2. Brno, 2012. ISBN 978-80-214-4071-5.
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Jirásek, František; Vacek, Ivan; Čipera, Stanislav. Sbírka řešených příkladů z matematiky II. 1. vyd. Praha : SNTL, 1989.
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