Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

Students will achieve the subject's objectives. They will get an understanding of the basics of integral calculus of functions of one variable, know how to integrate elementary functions and apply these (length of a curve, volume and surface area of a rotational body, static momentums and centre of gravity). Students will acquaint themselves with the basic concepts of the calculus of functions of two and more variables. They will be able to calculate partial derivatives of functions of several variables. They will get an understanding of the total differential of a function and its geometrical meaning. They will also learn how to find local and global minima and maxima of two-functions. They will get acquainted with directional derivatives of functions of several variables and their calculation.

Basics of linear algebra, vector calculus and analytical geometry in E3. Basic notions of the theory of functions of one variable, derivatives of elementary functions.

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1. Antiderivative, indefinite integral and their properties. Integration by parts and using substitutions.
2. Integrating rational functions. Integrating trigonometric functions.
3. Integrating trigonometric functions. Integrating irrational functions.
4. Newton and Riemann integral and their properties.
5. Integration methods for definite integrals. Geometric applications of the definite integral.
6. Geometric and engineering applications of the definite integral.
7. Real function of several variables. Basic notions, composite function. Limits of sequences, limit and continuity of two-functions.
8. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Total differential of a function, higher-order total differentials.
9. Taylor polynomial of a function of two variables. Local maxima and minima of functions of two variables.
10. Function in one variable defined implicitly. Function of two variables defined implicitly.
11. Some theorems of continuous functions, relative and global maxima and minima.
12. Tangent to a 3-D curve, Tangent plane and normal to a surface.
13. Scalar field, directional derivative, gradient.

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Understand and know how to integrate elementary functions, understand some applications of the definite integral (length of a curve, volume and surface area of a rotational body, static momentums and centre of gravity). Students should acquaint themselves with the basic concepts of calculus of two and more-functions. They should be able to calculate partial derivatives, acquaint themselves with the concept of an implicit function. To understand the geometric interpretation of the total differential of a function. Learn how to find local and global minima and maxima of two-functions. To learn about the directional derivative and its calculation.

Extent and forms are specified by guarantor’s regulation updated for every academic year.

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Lang, S.: Calculus of several variables. Springer Verlag, New York, 1988. (EN)
Stein, S. K.: Calculus and analytic geometry. New York, 1989. (EN)

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