1. komponenta

Lecture type	Total
Lectures	60
Exercises	45

* Load is given in academic hour (1 academic hour = 45 minutes)

COURSE AIMS AND OBJECTIVES:
At the beginning the students are introduced to number series and power series, and later to differential and integral calculus of vector functions of several real variables. The attention is focused on situation where one can see things, i.e. to function from R to R2 and R3, and to real functions of two and three real variables. Again we are not using the epsilon-delta technique, and the emphasis is put on the ideas and not on the quantity and technical trickery.

COURSE DESCRIPTION AND SYLLABUS:
1. Taylor's formula.
2. Series, convergence, absolute convergence.
3. Convergence tests.
4. Power series.
5. Basic notions in Rn.
6. Derivative of vector functions, arc length..
7. Functions of several variables, partial derivatives, gradient. Directional derivative and applications
8. Chain rule and implicit functions. Extrema of functions of several variables.
9. Multiple integrals. Fubini's theorem.
10. Change of variables in double integral. Polar coordinates.
11. Line integrals. Green's theorem.
12. Scalar and vector fields.
13. Divergence. Gauss' theorem
14. Curl. Stokes' theorem

1. Matematička analiza 3: Funkcije više varijabli, S. Kurepa, Tehnička knjiga, Zagreb, 1981.
2. Matematička analiza, Š. Ungar, Tehnička knjiga, Zagreb, 2003.
3. A first Course in Calculus, 5th edition, S. Lang, Springer Verlag, 1986.
4. Vector Calculus, M. Lovrić, Addison - Wesley Publ, 1997.

Mandatory course - Regular study - Mathematics and Physics Education