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Applied mathematical analysis

Code: 36937
ECTS: 7.0
Lecturers in charge: doc. dr. sc. Marko Radulović - Lectures
Lecturers: Ivan Puljiz, mag. math. - Exercises
doc. dr. sc. Marko Radulović - 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 30
Exercises 30
* Load is given in academic hour (1 academic hour = 45 minutes)
Description:
COURSE AIMS AND OBJECTIVES: The goal of this course is to develop competences of students to apply techniques of differential and integral calculus on solving ordinary differential equations and some typical problems of numerical mathematics. In the first part we study ordinary differential equations. We emphasize examples of differential equations that model some real life situations, formulate the problem, and solve some simple examples. The second part is devoted to numerical methods for determination of zeros of some functions (in particular polynomials), interpolation, numerical integration and numerical methods for ordinary differential equations. During the lectures we introduce new notions and illustrate them by examples, while on tutorials students adopt methods and techniques for solving problems. In particular they implement numerical methods using computers.

COURSE DESCRIPTION AND SYLLABUS:
1. Ordinary differential equations. Motivation.
2. Existence and uniqueness of the solution.
3. Differential equations of first order. Real world examples.
4. Separeble equations. Examples.
5. Special types of equations (Bernoulli, Ricatti)
6. Linear equations.
7. Implicit equations.
8. Explicit computations in R. The idea of approximation. Motivation.
9. Solving nonlinear equations. Method of iterations.
10. Newton's method.
11. Method of secants.
12. Interpolation. Basic ideas of polynomial interpolation.
13. Numerical integration.
14. Introduction to numerical methods for ODE's
Literature:
  1. M. Alić: Obične diferencijalne jednadžbe
  2. K. E. Atkinson: An Introduction to Numerical Analysis
  3. W. E. Boyce, R. C. DiPrima: Elementary Differential Equations and Boundary Value Problems, 7th edition
  4. A. Gray, M. Mezzino, M. A. Pinsky: Introduction to Ordinary Differential Equations with Mathematica
  5. V. Hari i dr: Numerička analiza: osnovni udžbenik
  6. E. Suli, D. Mayers: Introduction to Numerical Analysis
5. semester
Mandatory course - Regular study - Mathematics Education
Consultations schedule:

Content

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