Course detail
Mathematics 2 (G)
FAST-BAA009Acad. year: 2023/2024
Primitive function, indefinite integrals, properties of indefinite integrals, overview of basic indefinite integrals, methods of integration. Integrating rational functions, trigonometric functions, selected types of irrational functions.
Newton integral, its properties and calculation. Defining the Riemann integral. Applications of the definite integral in geometry and physics.
Real two- and more-functions, composite functions. Limit of a function, continuous two- and more functions. Theorems on continuous functions. Partial derivatives of composite functions, higher-order partial derivatives. Transformations of differential expressions. Total differential of a function. Higher-order total differentials. Taylor polynomials of two-functions. Local maxima and minima of two-functions. One-functions defined implicitly. A two-function defined implicitly. Global maxima and minima. Finding global maxima and minima using realtive maxima and minima. Scalar field and its levels. Directional derivative of a scalar function, gradient. Tangent and normal plane to a 3D Curve. Tangent plane and normal to a surface defined implicitly.
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Number of ECTS credits
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Department
Entry knowledge
Formulas used to calculate indefinite and definite integrals, and the basic integration methods.
Rules for evaluation and completion of the course
Aims
They should acquaint themselves with the basics of calculus of two- and more-functions, including partial derivatives, implicit functions, understand the geometric interpretation of the total differential. Learn how to find local and glogal minima and maxima of two-functions, calculate directional derivatives.
Students will known methods of solving undefinite and definite integrals and will be able to use methods successfully to important applied problems. Except this students will understand basic calculus of functions of several variables and its application to analysis of behavior of functions in three-dimenesional space.
Study aids
Prerequisites and corequisites
Basic literature
Daněček Josef, Dlouhý Oldřich, Přibyl Oto. Matematika I, Modul 8, Určitý integrál, Brno, VUT, FAST, Studijní opora, 2004 (CS)
Dlouhý Oldřich, Tryhyk Václav. Matematika I, Modul BA01_M09, GA04_M03, Reálná funkce dvou a více proměnných-I, Brno, VUT, FAST, Studijní opora, 2004 (CS)
Dlouhý Oldřich, Tryhyk Václav. Matematika II, Modul BA01_M10, GA04_M04, Reálná funkce dvou a více proměnných-II, Brno, VUT, FAST, Studijní opora, 2004 (CS)
Recommended reading
Klaus Weltner, S. T. John, Wolfgang J. Weber, Peter Schuster, Jean Grosjean. Mathematics for Physicists and Engineers: Fundamentals and Interactive Study Guide, Springer, 2023. (EN)
Classification of course in study plans
- Programme BPC-GK Bachelor's 1 year of study, summer semester, compulsory
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