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Vyučující
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Marek Jaroslav, Mgr. Ph.D.
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Cvejn Jan, doc. Ing. Ph.D.
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Obsah předmětu
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The aim of the course is to equip students with the mathematical apparatus that serves other scopes to various applications. The student should understand the basic concepts to be able to define them, to know the important sentences, to be able to use the mathematical apparatus, in order to be able to formulate and solve the specific problems of mathematical science. 1. Number series. Series with non-negative terms. Alternating series. Absolutely and non-absolutely convergent series. 2. Power series. Taylor and Maclaurin series. Applications in integral calculus. 3. Vectors, matrices and tensors. Properties of matrices. Matrix operations. Linear and quadratic forms. 4. Solving systems of linear equations. Matrix determinant. Gauss elimination method. Cramer's rule. 5. Inverse matrices. Eigenvalues and vectors. Sylvester's criterion. 6. Limit and continuity of functions of several variables. Total differentials of higher orders. Taylor's theorem and its application. 7. Local and global extrema of functions of several variables. Bound extrema, substitution method, Lagrange multiplier method, Jacobian method. 8. Derivative in a given direction, nabla operator, gradient of a scalar field, divergence and rotation of a vector field. 9. Advanced parts of differential calculus. Mean value theorems. Implicit functions and their derivatives. 10. Advanced parts of integral calculus of functions of one variable. Special substitutions. 11. Ordinary differential equations. General and particular solutions. Cauchy's problem. Separation of variables. Homogeneous and inhomogeneous linear differential equations of the first order. Method of variation of constants. 12. Advanced parts of integral calculus of functions of several variables. Transformation of variables. Double and triple integrals. Curve integral. Applications.
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Studijní aktivity a metody výuky
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Monologická (výklad, přednáška, instruktáž), Projekce, Nácvik dovedností
- Kontaktní výuka
- 52 hodin za semestr
- Příprava na zkoušku
- 40 hodin za semestr
- Domácí příprava na výuku
- 50 hodin za semestr
- Příprava na zápočet
- 38 hodin za semestr
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Výstupy z učení
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The subject Mathematics 2 includes the following topics: infinite sequences, infinite series, power sets mappings, a differential and integral calculus of functions of more real variables, vector functions, differential equations.
Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.
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Předpoklady
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Standard mathematical knowns and skills of the mathematics of the middle schools and subjects ZMAT1 and ZLALG, which make possible to continue the differential and integral multivariable calculus.
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Hodnoticí metody a kritéria
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Písemná zkouška
Credit requirements: active participation in seminars with at most three hours absent, and at least 50% success in written test. The course is completed by written exam, at least 55% of success is required. An oral form of the exam is optional, upon a student's request.
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Doporučená literatura
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ABADIR, Karim M. a MAGNUS, Jan R. Matrix algebra. Econometric exercises, 1. New York: Cambridge University Press, 2005. ISBN 978-0-521-53746-0.
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AYRES, Frank a MENDELSON, Elliott. Schaum's outline of calculus. 6th ed. Schaum's outline series. New York: McGraw-Hill, 2013. ISBN 978-0-07-179553-1.
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FRIEDBERG, Stephen H.; INSEL, Arnold J. a SPENCE, Lawrence E. Linear algebra. 4th ed. Upper Saddle River: Pearson Education, 2003. ISBN 978-0-13-008451-4.
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