1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

* Load is given in academic hour (1 academic hour = 45 minutes)

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

Enrollment :
Passed : Fundamentals of mathematical analysis
Passed : Linear algebra 2

Izborni matematički predmet 4 - Regular study - Mathematics and Physics Education