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### Fundamentals of mathematical analysis

 Code: 186321 ECTS: 10.0 Lecturers in charge: doc. dr. sc. Tomislav Berić - Lectures doc. dr. sc. Ana Prlić - Lectures Lecturers: Karmen Grizelj, mag. math. - Exercises Bruno Predojević, mag. math. - Exercises

### 1. komponenta

Lecture typeTotal
Lectures 60
Exercises 30
Description:
COURSE AIMS AND OBJECTIVES: In this course we address some of the delicate situations they have appeared in Differential and integral calculus 1 and 2. We introduce epsilon-delta terminology and use it for rigorous foundation of basic notions and theorems of mathematical analysis. The role of lectures is to introduce notions and to illustrate them by examples, while tutorials serve for adopting techniques for solving problems.

COURSE DESCRIPTION AND SYLLABUS:
1. Motivation: numbers, holes in Q, deceiving intuition.
2. Foundation of N, Z, C, Q and Rn, using competitions adopted during the first year.
3. Sequences in R, C, Rn. Convergence . Epsilon terminology.
4. Subsequences, boundness, monotonicity (in R). Bolzano - Weierstrass theorem for sequences in Rn.
5. Limits of functions. Continuity.
6. Open, closed, compact and connected sets in Rn.
7. Continuous functions on compact sets.
8. Derivative. Rolle's theorem.
9. Riemann's integral. Fundamental theorem.
10. Integrability of continuous functions. Lebesgue's theorem on riemann integrability.
11. Differential and derivative of functions of several variables.
12. Taylor formula for functions of several variables.
13. Implicite function theorem. Inverse function theorem.
14. Continuity and differentiability. Notion of curve.
Literature:
1. B. Guljaš: Osnove matematičke analize, skripta
2. Š. Ungar: Matematička analiza
3. S. Kurepa: Matematička analiza 3: Funkcije više varijabli
Prerequisit for:
Enrollment :
Passed : Differential and integral calculus 2
 4. semester Mandatory course - Regular study - Mathematics Education
Consultations schedule:

### Content

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

Link to the notices web page: http://www.pmf.unizg.hr/math/predmet/oma_b