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Mathematical analysis 2

Code: 21508
ECTS: 9.0
Lecturers in charge: izv. prof. dr. sc. Vjekoslav Kovač - Lectures
prof. dr. sc. Hrvoje Šikić - Lectures
Lecturers: doc. dr. sc. Igor Ciganović - Exercises
Tomislav Kralj - Exercises
doc. dr. sc. Snježana Lubura Strunjak - 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.
Load:

1. komponenta

Lecture typeTotal
Lectures 45
Exercises 60
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: To familiarize students with the basics of differential and integral calculus in R. Rigorous mathematical concepts are introduced.

COURSE DESCRIPTION AND SYLLABUS:
1. Derivative. Motivation (geometry, physics) and definition of derivative, connection between derivability and continuity, basic rules for differentiation, derivative of elementary functions. Rolle's and Lagrange's middle value theorem, monotony, local extremes. Derivatives of higher order, Taylor's middle value theorem, convex functions, inflection. Asymptotes, analysis of function flow and graph of function. Some applications. (5 weeks)
2. Integrals. Motivation (plane area, work done by a force) and definition of Riemann integral. Integrability, monotony and continuous functions. Primitive function, Newton - Leibniz formula. Substitution, partial integration, integration of rational functions. Improper integrals. (5 weeks)
3. Series. Definition, criteria of convergence. Power series, Taylor series. Uniform convergence, function series. (3 weeks)
Literature:
  1. S. Kurepa: Matematička analiza 1: Diferenciranje i integriranje
  2. S. Kurepa: Matematička analiza 2: Funkcije jedne varijable
  3. M. H. Protter, C. B. Morrey: A First Course in Real Analysis
Prerequisit for:
Enrollment :
Passed : Mathematical analysis 1
2. semester
Mandatory course - Mandatory studij - Mathematics
Consultations schedule:

Content

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