Lecturer(s)


Petrášková Vladimíra, doc. RNDr. Ph.D.

Kobera Marek, Mgr. Bc. Ph.D.

Course content

1. Two and three  variable function.A limit of two and three  variable function. 2. Continuity of two and three  variable function 3. Partial derivative.Total differential, directional derivative 4. Tangent hyperplane. Relative extremes 5. Constrained extremes 6. Primitive functions (definition, properties). Proper integral. 7. Per partes and substitutions for proper integral. 8. Integration of rational function. 9. Riemannian integral, definition. 10. Inequality theorems. 11. Relation between improper and Riemannian integral. 12. Generalized Riemannian integral. 13. Applications, volumes and areas in space. 14. Application, curve length.

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming)

Learning outcomes

The theory of Riemannian integral. Generalized Riemannian integral. Applications. Differential calculus of two and three variable function.
The student will have a good grasp of the theory Riemann integral and the elements of differential calculus of two and three variable function.

Prerequisites

knowledge of the content of subject Calculus I

Assessment methods and criteria

Combined exam
active participation in colleges and tutorials, 2x written test

Recommended literature


Grossmann,S.,I.:. Calculus, Saunders College Publishing, 2001. Liberec, 1997.

Jarník, V.:. Diferenciální a integrální počet II., Academia, Praha 1976.

Jirásek,F. a kolektiv:. Sbírka řešených příkladů z matematiky II, SNTL, Praha 1989.
