Course detail

# Mathematics 2

FAST-BA002Acad. year: 2022/2023

Antiderivative, indefinite integral, its properties and methods of calculation. Newton integral, its properties and calculation. Definition of Riemann integral. Applications of integral calculus in geometry and physics - area of a plane figure, length of a curve, volume and surface of a rotational body, static moments and the centre of gravity.

Functions in two and more variables. Limit and continuity, partial derivatives, implicit function, total differential, Taylor expansion, local minima and maxima, relative maxima and minima, maximum and minimum values of a function; directional derivative, gradient. Tangent to a 3-D curve, Tangent plane and normal to a surface.

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Course curriculum

2. Integrating rational functions.

3. Integrating trigonometric functions. Integrating irrational functions.

4. Newton and Riemann integral and their properties.

5. Integration methods for definite integrals. 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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Basic literature

Jirásek, F., Čipera, S., Vacek, M., Sbírka řešených příkladů z matematiky I, SNTL Praha 1986. (CS)

Recommended reading

Classification of course in study plans

- Programme B-P-C-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory

- Programme B-K-C-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory

- Programme B-P-C-MI (N) Bachelor's
branch MI , 1 year of study, summer semester, compulsory

- Programme B-P-E-SI Bachelor's
branch VS , 1 year of study, summer semester, compulsory

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