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Fundamentals of mathematical analysis

Code: 186321
ECTS: 10.0
Lecturers in charge: doc. dr. sc. Ana Prlić
Lecturers: doc. dr. sc. Ana Prlić - Exercises
dr. sc. Lucija Validžić - Exercises

1. komponenta

Lecture typeTotal
Lectures 60
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
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.

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.
Prerequisit for:
Enrollment :
Attended : Differential and integral calculus 2

Examination :
Passed : Differential and integral calculus 2
4. semester
Mandatory course - Regular study - Mathematics Education
Consultations schedule:


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