1. komponenta

Lecture type	Total
Lectures	30
Exercises	30

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

COURSE OBJECTIVES:
To introduce students to modern methods in numerical analysis, in the area of ordinary
differential equations (ODE), with an emphasis on their practical solution on computers.

COURSE CONTENT:
Initial value problem for ODE, existence and uniqueness of the solution. Euler-Cauchy
method, single step methods, Taylor method, Runge-Kutta methods with fix and variable
step size, variable-order method. Multistep methods, stiff equations. Boundary value
problems for ODE, shooting method. Direct and iterative methods for solving linear
systems of equations.

LEARNING OUTCOMES:
After the successful completion of the subject Numerical methods in physics, the
student will be able to:
1. express the basic definition and theorems associated with the ordinary and
partial differential equations, as well as with the approximation methods;
2. differentiate the methods for solving initial and boundary value problems
for ordinary and partial differential equations;
3. choose and apply the correct approximation methods for the given problem;
4. derive an analogous approximation method with certain properties;
5. analyze a given approximation method;
6. write a simple computer program for solving a given problem.

LEARNING MODE:
Following lectures, study of notes and literature, analysis of examples and
practicing, analysis of methods and practicing, analysis of computer programs
and the results obtained by solving problems on the computer and practicing.

TEACHING METHODS:
Lectures; solving examples; analysis of the methods; presentation of the
computer programs and their results.
METHODS OF MONITORING AND VERIFICATION:
Written exam through midterm exams; writing and presenting programming
assignments; oral exam.
TERMS FOR RECEIVING THE SIGNATURE:
Regular attendance to the lectures, and achievement of minimal 17 points out of 56 on
mid-term exams
EXAMINATION METHODS:
Grading components:
1. Two mid-term exams, 28 points each (together 56 points)
2. One programming assignment, 24 points
3. Final exam, 20 points
Mid-term exams
1. During the semester, students write two mid-term exams. Mid-term exams include
also some theoretical questions.
2. Minimal condition for passing the exam is achievement of 17 points.
3. For students who were not able to achieve the minimal number of points, one makeup
mid-term exam will be organized, which includes material of the whole semester.
Maximum number of points on the makeup exam is 56. Minimal condition for passing
this exam is achievement of 17 points. For students who approach the makeup mid-term
exam, the points from the regular mid-term exams are reset.
Programming assignment
1. During the semester, one individual programing assignment is set, which must be
solved within the time limit, which will be announced on the web page of the course.
Each assignment, in principle, includes a solution implemented in F90/F95, and is
explained to the lecturer.
2. Minimal condition for passing is achievement of 10 points.
Final exam
1. Final exam consists of an oral exam in front of the lecturer, which includes the
material of the whole course, and may include some tasks and test of the practical
knowledge on the computer.
2. The students who have passed the mid-term exams and the programming assignment
may approach the final exam.
Final grade
Minimal number of points for passing grade is 45. The final grade is determined by the
following table:

Points Grade
45-59 2
60-74 3
75-89 4
>90 5

1. COMPULSORY LITERATURE:
   Z. Drmač, M. Marušić, M. Rogina, S. Singer, Sanja Singer: Numerička analiza, script on web, 2003, https://web.math.pmf.unizg.hr/~rogina/2001096/num_anal.pdf
   Trefethen, L. N.: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Cornell University, 1996.
   Isaacson, E., H. B. Keller: Analysis of Numerical Methods, John Wiley and Sons, London 1966.
   Buchanan, J. L., P. R. Turner: Numerical Methods and Analysis, McGraw-Hill, Inc., 1992.
2. Trefethen, L. N.: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, Cornell University, 1996.
3. Buchanan, J. L., P. R. Turner: Numerical Methods and Analzsis, McGraw-Hill, Inc., 1992.
4. E. Isaacson, H. B. Keller: Analysis of Numerical Methods, John Wiley and Sons, London 1966.

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