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Lecturer(s)
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Fuciman Marcel, Mgr. Ph.D.
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Course content
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Content of lectures: Mathematical theory of below mentioned parts of maths and examples of its use in physical problems: 1. Partial derivatives, total differential, local and global extrema 2. Gradient vector, directional derivative, curl operator, Lagrange multipliers 3. Coordinate systems, coordinate transformation, Lamé coeffitients 4. Double and triple integrals, Fubini's theorem 5. Line integrals, (in)dependence of path, Green's theorem 6. Some topics in vector calculus (vector calculus identities, divergence theorem, Stokes' theorem 7. System of first-order linear differential equations 8. Calculus of variations (Fermat's principle, action principle) 9. Some topics in probability and statistics (binomial, Poisson, Gaussian and Student's t-distribution) Content of practicals: Students actively solve mathematical and physical problems connected to topics discussed in corresponding lectures.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Practical training
- Class attendance
- 39 hours per semester
- Preparation for exam
- 11 hours per semester
- Preparation for credit
- 15 hours per semester
- Preparation for classes
- 12 hours per semester
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Learning outcomes
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Provision of mathematical readiness for courses of Physics III and IV, Theoretical Mechanics, Quantum Mechanics etc., aiming on practical abilities to solve mathematical part of problems in physics.
Student will intensify her/his knowledge of selected parts of mathematics and above all exercise solving of mathematical problems (including application on problems in physics) with relation to courses of Physics III to IV (Fyzika III to IV) and other courses with physics theme. (QM, Theoretical Physics etc.)
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Prerequisites
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The course follows up the course Mathematics for physicists I (Matematika pro fyziky I) and that course is a prerequisite for successful graduation from this course.
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Assessment methods and criteria
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Written examination
Student will graduate from the course by taking written test (solving of mathematical problems) with minimal success rate 60% (i.e. for mark 3).
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Recommended literature
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Daniel Turzík a kol.: Matematika II ve strukturovaném studiu, VŠCHT Praha 2005.
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J. B. Fraleigh: Calculus with Analytic Geometry, Addison-Wesley 1990.
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Karel Rektorys a kol.: Přehled užité matematiky I a II, Prometheus 2010.
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Mary L. Boas: Mathematical Methods in the Physical Sciences, 2006 John Wiley & Sons, Inc..
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Zuzana Došlá, Petr Liška: Matematika pro nematematické obory s aplikacemi v přírodních a technických vědách, Grada publishing 2014.
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