1. komponenta

Lecture type	Total
Lectures	45
Exercises	30

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

COURSE AIMS AND OBJECTIVES:
In this course, students are introduced to the structure of the n-dimensional Euclidean space Rn (with emphasis on n = 2 or 3), continuous vector-valued functions of several real variables, differentiability, and the fundamental theorems of differential calculus for such functions, as well as multiple Riemann integrals (with emphasis on double and triple integrals) and line and surface integrals. The focus is on concepts and ideas, with minimal emphasis on proofs.

COURSE DESCRIPTION AND SYLLABUS:
1. Structure of the space Rn. Open and closed sets. Sequences in Rn, convergence, Bolzano-Weierstrass theorem in Rn.
2. Differential, partial derivatives, gradient. Directional derivative (derivative along a vector) and applications. Partial derivatives of composite and implicitly defined functions. Extrema of functions of several variables.
3. Multiple integrals. Fubini's theorem. Change of variables in double integrals. Polar coordinates. Line integrals. Green's theorem

1. Matematička analiza 3: Funkcije više varijabli, S. Kurepa, Matematička analiza 3: Funkcije više varijabli, 1981.
2. Matematička analiza 3, Š. Ungar, Tehnička knjiga, Zagreb, 2003.
3. Vector Calculus, M. Lovrić, Addison-Wesley Publ. Ltd., Don Mills, Ontario, 1997.
4. Calculus III, Undergraduate Texts in Mathematics, J. Marsden, A. Weinstein, Springer-Verlag, New York, 1985.
5. Vector Calculus, 5th ed., J. E. Marsden, A. Tromba,, W. H. Freeman, 2003.
6. Calculus: One and Several Variables, 10th ed., S. L. Salas, E. Hille, G. J. Etgen, J. Wiley & Sons, 2007.
7. A first Course in Calculus, 5th ed., S. Lang, Springer, 1986.
8. Zadaci i riješeni primjeri iz Matematičke analize, B. P. Demidovič i dr., Danjar d.o.o., Zagreb, 1995.

Enrollment :
Attended : Mathematical analysis 2

Examination :
Passed : Mathematical analysis 2

Mandatory course - Regular study - Mathematics Education