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### Differential and integral calculus 2

 Code: 201719 ECTS: 8.0 Lecturers in charge: prof. dr. sc. Eduard Marušić-Paloka - Lectures izv. prof. dr. sc. Vjekoslav Kovač - Lectures Lecturers: doc. dr. sc. Matko Ljulj - Exercises dr. sc. Martina Stojić - Exercises
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### 1. komponenta

Lecture typeTotal
Lectures 60
Exercises 45
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
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
Literature:
1. S. Kurepa: Matematička analiza 3: Funkcije više varijabli
2. Š. Ungar: Matematička analiza
3. S. Lang: A first Course in Calculus, 5th edition
4. M. Lovrić: Vector Calculus
Prerequisit for:
Enrollment :
Passed : Differential and integral calculus 1
 3. semester Mandatory course - Regular study - Mathematics and Physics Education
Consultations schedule:
• doc. dr. sc. Matko Ljulj:

Summer term 22/23:  Friday 10-12h (registration by e-mail obligatory)

Location: 312

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