Czech

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Institute of Mathematics and Descriptive Geometry (MAT)

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Angl. stejne jako AD4

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Lectures

1. Definition of double integral, its basic properties. Calculus of double integral.
2. Transformation of double integral, its geometrical and physical interpretation.
3. Definition of double integral, its basic properties. Calculus of double integral.
4. Transformation of double integral, its geometrical and physical interpretation.
5. Application of double and triple integral.

6. A (curved) line, methods of settings in R2 and R3. Line integral in a scalar field (definition, properties, calcuclus and applications).
7. Vector field. Line integral in a vector field definition, properties, calcuclus and applications).
8. Green theorem and its application (area of R2-domain). Divergence and rotation of a vector field.
9. Independence of line integral of its integration path.

10. Infinite series of real numbers and functions. Convergence of series of numbers.
11. Region of convergence of function series. Orthogonal series, Fourier series.
12. Fourier series on an arbitrary bonded interval, periodic extension of a function. Sine and cosine series.
13. Applications of Fourier series.

Seminars

1. Quadratic surfaces in R2. Integral calculus of function of 1 variable – repetition.
2. Calculus of double integral.
3. Transformation of double integral, its geometrical and physical interpretation.
4. Calculus of triple integral.
5. Transformation of triple integral, its geometrical and physical interpretation.
6. Applications of double and triple integrals.

7. Calculus of line integral in a scalar field and its applications (length of a part of curved line, area of a part of cone surface, mass, static moments, moments of inertia related to given axes).
8. Calculus of line integral in a vector field and its applications.
9. Green theorem and its application.
10. Independence of a line integral of its integration path. Test.

11. Convergence of series of real numbers (geometrical series, limit d’Alembert and integral series).
12. General Fourier series.
13. Sine and cosine series. Credits.

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Angl. stejne jako AD4

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

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Not applicable.

S.LANG: Calculus of several variables. Springer Verlag, New York 1988
Veverka J.: Matematika II-3: Nekonečné řady. CERM Brno 1998

DANĚČEK J., DLOUHÝ O.: Integrální počet II. CERM Brno 2000
REKTORYS K. a kol.: Přehled užité matematiky I. Prometheus Praha 1995
ŠKRÁŠEK J., TICHÝ Z.: Základy aplikované matematiky II. SNTL Praha 1986