Load:

1. komponenta
Lecture type  Total 
Lectures 
30 
Exercises 
30 
* Load is given in academic hour (1 academic hour = 45 minutes)

Description:

By the successful passing of the exam Mathematics 2, a student will be able to:
1. Accomplish basic vector calculus operations (addition and multiplication of vectors by scalars, dot, cross and mixed vector product)
2. Handle basic operations with square matrices (addition, multiplication, calculating of the determinant)
3. Detect problems which are reduced to solving systems of linear equations and writing down such systems
4. Solving systems of linear equations using Gauss elimination method
5. Analyze ordinary differential equations using direction fields and numerical methods (Euler method)
6. Solve the basic types of ordinary differential equations
7. Transfer a basic problem of biological, chemical or physical origin in a mathematical form as a Cauchy (or initial) problem and solve it.
The content of the course:
Lectures:
1. Vectors in threedimensional space
2. Addition of vectors and multiplication by a scalar. Dot, cross and mixed vector product.
3. The notion of a matrix; addition and multiplication of matrices. The determinants.
5. The Cramers's rule. Discussion of the solutions. Applications.
6. Ordinary differential equations. Motivation.
7. Direction fields. Numerical methods.
8. Linear ordinary differential equations.
9. Autonomous equations. Population dynamics.
10. Basic types of differential equations.
11. Methods of solving linear differential equations with constant coefficients.
12. Application of ODE's in solving basic biological, physical or chemical problems.
Exercises:
1. Operations with vectors in threedimensional space
2. Matrix operations and calculations of determinants.
3. Problems with systems of linear equations.
4. Solving systems of linear equations using Gauss elimination method
6. Motivational problems for studying ordinary differential equations.
7. Drawing the direction fields and using numerical methods.
8. Solving linear ordinary differential equations.
9. Examples of autonomous equations and modeling the population dynamics.
10. Solving the basic types of ordinary differential equations and applications.

Literature:

 Boyce, DiPrima: Elementary differential equations, Wiley, 2004.
Elezović, Linearna algebra, Element, 2006.
prezentacija na web stranici http://web.math.pmf.unizg.hr/~hanmar/Matematika2/skripta2.pdf
