Czech

Not applicable.

Institute of Mathematics and Descriptive Geometry (MAT)

Methods of solving indefinite and definite integrals.
Main applications of definite integrals.
Basic calculus of functions of several variables.
Total differential of function of several variables.
Local and global extreme of functions of two variables.
Computation of directional derivatives of functions of several variables.

Basics of the theory of one-functions(limit, continuous functions, graphs of functions, derivative, sketching the graph of a function).
Formulas used to calculate indefinite and definite integrals, and the basic integration methods.

Not applicable.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations – lectures, seminars.

Abilities leading to successful solution of some typical classes of differential equations as well as necessary theoretical knowledge and its application will be positively estimated.
The final evaluation (examination) depends on assigned points (0-100 points), 30 points is maximum points which can be assigned during seminars. Final examination is in written form (estimated by 0-70 points ).

1. Integrating a rational function.
2. Integrating a trigonometric function.
3. Integrating selected types of irrational functions. Newton integral, its properties and calculation. Riemann integral.
4. Geometric and physical applicetions of calculus.
5. Real two- and more-function, composite function. Limit and continuous two- and more-functions.
6. Partial derivative, partial derivative of a composite function, higher-order partial derivatives. Transformations of differential expressions.
7. The total differential of a function. Higher-order total differentials. Taylor polynomial of a two-function. Local maxima and minima of two-functions.
8. Function defined implicitly. Two-function defined implicitly.
9. Global maxima and minima. Simple problems in global maxima and minima on teh basis of relative maxima and minima. Scalar field and its levels. Directional derivative of a scalar function, gradient.
10. Tangent and normal plane to a 3D curve. Tanget plane and normal to a surface defined explicitly.

Not applicable.

After the course, the students should understand the principles of integration of some more sophisticated elementary functions, some of the applications of teh definite integral.
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.

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

Not applicable.

Not applicable.

Daněček, J., Dlouhý, O., Přibyl, O.: Matematika I, Modul 7, Neurčitý Integrál. CERM - studijní opora v intranetu i tištěný text, 2007. (CS)
Daněček, J., Dlouhý, O., Přibyl. O.: Matematika I, Modul 8, Určitý Integrál. CERM - studijní opora v intranetu i tištěný text, 2007. (CS)
HŘEBÍČKOVÁ, J., SLABĚŇÁKOVÁ, J., ŠAFÁŘOVÁ, H.: Sbírka příkladů z matematiky II. CERM, 2008. (CS)
Larson R., Hostetler R.P., Edwards B.H.: Calculus (with Analytic Geometry). Brooks Cole, 2005. (EN)
TRYHUK, V., DLOUHÝ, O.: Matematika I, Diferenciální počet funkcí více reálných proměnných. CERM - studijní opora v intranetu i tištěný text, 2004. (CS)

Not applicable.