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Lecturer(s)
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Marek Jaroslav, Mgr. Ph.D.
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Rak Josef, RNDr. Ph.D.
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Course content
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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. The content of the course MATHEMATICS (II) are basic knowledge of the endless series, of the foundations of diferential and an integral number of functions of more variables, then the fundamental methods of solution of ordinary differential equations. An infinite series. Convergence and divergence, the convergence criteria, the alternating series, absolutely and relatively convergent series. Functional series, scope of convergence, the sum of the series. Power series, radius and interval of convergence. The Taylor series, and their use. Differential calculus of functions of more variables, limit. Partial derivatives and their geometrical meaning. The total differential of the function and its use. Partial derivative and total differentials of the higher orders. partial derivatives. Taylor theorem and its use. Implicit function and its derivative. The local extrema of functions of more variables, the method of least squares. Bound extremes, method of Lagrange multipliers. Absolute extremes and their determination. Derivative in the direction, the gradient, scalar field, divergence and rotation of a vector field. Ordinary differential equations. The concept of ordinary differential equations, the General and particular solution of differential equations. Cauchy problem. Homogeneous equation, linear differential equation, exact equation, the methods of their solution Elementary methods of solution of differential equations of higher orders by help of reduction, linear differential equations of second order with constant coefficients--method of variation of constants. Integral number of functions of more variables.Riemann multidimensional integral on a compact interval and measurable set, Fubini's theorem, the methods of calculation. Substitution. The transformation to polar, cylindric and spherical coordinates. Application of double and triple integral. Curve integral scalar and vector field. The basic characteristics of the curve integral. Aplications of integrals.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Projection, Skills training
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- 78 hours per semester
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Learning outcomes
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The subject Mathematics II 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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Prerequisites
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Standard mathematical knowns and skills of the mathematics of the middle schools and subjects IMAT1 and ILALG, which make possible to continue the differential and integral multivariable calculus.
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Assessment methods and criteria
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Written examination
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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Recommended literature
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Kolda, S. - Machačová, L. - Prachař, 0. Cvičebnice z Matematiky II. Pardubice, 2007. ISBN 80-7194-932-9.
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Kolda, S. - Machačová, L. Matematika II (skriptum). Pardubice, 2007. ISBN 80-7194-931-2.
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Machačová, Ludmila. Matematika : základy diferenciálního a integrálního počtu. Pardubice: Univerzita Pardubice, 2003. ISBN 80-7194-577-3.
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Prachař, O. - Cabrnochová, R. Průvodce předmětem MATEMATIKA I (třetí část). Pardubice, 2007. ISBN 80-7194-715-6.
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Prachař, Otakar. Průvodce předmětem matematika II.. Pardubice: Univerzita Pardubice, 2003. ISBN 80-7194-557-9.
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Prachař, Otakar. Průvodce předmětem matematika II.. Pardubice: Univerzita Pardubice, 2004. ISBN 80-7194-655-9.
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