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Lecturer(s)
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Horváth Pavel, RNDr. Ph.D.
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Havelková Martina, Mgr.
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Course content
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1. Linear algebra: Vectors, matrices, determinants, systems of linear equations (the Frobenius's Theorem and the Cramer's Rule). 2. Fundamentals of analytic geometry in plane and space. 3. Fundamentals of integral calculus: Indefinite integral, the Riemann integral, application in determination of curve length, area, surface and volume of a revolution solid. 4. Applications of differential and integral calculus in physics. 5. Functions of two variables: Partial derivative, differential. 6. Introduction to differential equations: First order ordinary differential equations. 7. Use of the software MATHEMATICA for selected themes - exercises.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming)
- Attendace
- 26 hours per semester
- Preparation for the Course Credit
- 4 hours per semester
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Learning outcomes
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Acquire the basic knowledge of mathematical analysis, linear algebra and geometry focused on physics applications.
Knowledge. Explain fundamental principles of integral calculus, differential calculus of functions of two variables, linear algebra and geometry. Apply knowledge on solutions of problems of mathematical analysis, algebra and geometry for physicists.
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Prerequisites
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Prior knowledge of the introductory course of the mathematical analysis.
SLO/PMF1
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Assessment methods and criteria
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Student performance
Colloquium: participation in the proseminar, passing a written test.
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Recommended literature
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BRABEC J., MARTAN F., ROZENSKÝ Z. (1989). Matematická analýza 1. SNTL, Praha.
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KOPÁČEK J. (2007). Matematická analýza nejen pro fyziky (II). Matfyzpress, Praha.
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KOPÁČEK J. (2004). Matematická analýza nejen pro fyziky (I). Matfyzpress, Praha.
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KOPÁČEK J. (2006). Příklady z matematiky nejen pro fyziky (II). Matfyzpress, Praha.
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KOPÁČEK J. (2005). Příklady z matematiky nejen pro fyziky (I). Matfyzpress, Praha.
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KVASNICA J. (2004). Matematický aparát fyziky. Academia, Praha.
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POLÁK J. (1995). Přehled středoškolské matematiky. Prometheus, Praha.
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REKTORYS K. (1995). Přehled užité matematiky I a II. Prometheus, Praha.
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RUSKEEPÄÄ H. (2009). Mathematica navigator - Mathematics, Statistics, and Graphics. Academic Press, London.
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