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### Differential and integral calculus 1

 Code: 93075 ECTS: 9.0 Lecturers in charge: prof. dr. sc. Eduard Marušić-Paloka - Lectures izv. prof. dr. sc. Ivica Nakić - Lectures Lecturers: Luka Cigler, mag. math. - Exercises dr. sc. Matko Ljulj - Exercises English level: 1,0,0 All teaching activities will be held in Croatian. However, foreign students in mixed groups will have the opportunity to attend additional office hours with the lecturer and teaching assistants in English to help master the course materials. Additionally, the lecturer will refer foreign students to the corresponding literature in English, as well as give them the possibility of taking the associated exams in English.

### 1. komponenta

Lecture typeTotal
Lectures 60
Exercises 45
Description:
COURSE AIMS AND OBJECTIVES:
The students are introduced to basic ideas of the differential and integral calculus of real function of a real variable. The epsilon-delta terminology is not being used, but, except for some basic facts and theorems which are only stated and well illustrated, the rest is done with adequate rigour. The emphasis is put on the ideas and not on the quantity, artificial examples and technical trickery.

COURSE DESCRIPTION AND SYLLABUS:
1. Limits and the derivative.
2. The chain rule, higher-order derivatives, implicit differentiation.
3. Sine and cosine: graphs, addition formulas.
4. Sine and cosine: derivative, basic limits, polar coordinates.
5. Extrema, mean value theorem.
6. Graphical behaviour of functions and curve sketching.
7. Inverse functions, inverse trigonometric functions.
8. Exponential and logarithmic function.
9. Antiderivative ("indefinite integral").
10. Continuous functions, area, integral ("definite integral").
11. Integration rules and the Fundamental Theorem of Calculus.
12. Integration techniques.
13. Some important integrals and applications to areas and volumes.
14. Arc length and some applications of integrals in physics.
Literature:
1. S. Kurepa: Matematička analiza 1: Funkcije jedne varijable
2. S. Kurepa: Matematička analiza 2: Diferenciranje i integriranje
3. S. Lang: A first Course in Calculus, 5th edition
Prerequisit for:
Enrollment :
Passed : Introduction to mathematics
 2. semester Mandatory course - Regular study - Mathematics and Physics Education
Consultations schedule:
• dr. sc. Matko Ljulj:

Monday, 12-14h (registration by e-mail obligatory)

Location: 312

### Content

Link to the course web page: https://web.math.pmf.unizg.hr/nastava/dir