Graduate study programme

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Numerical Mathematics DKa1-04

ECTS 5 | P 30 | A 30 | L 0 | K 0 | ISVU 149782 | Academic year: 2019./2020.

Course groups

Prikaži sve grupe na predmetu

Course lecturers

HARTMANN-TOLIĆ IVANA, Associate
KATIĆ ANITA, Lecturer

Goals

Explain to students the meaning and application of numerical algorithms and methods in electrical engineering. Present them the work of numerical algorithms on concrete examples on the computer.

Conditions for enrollment

Requirements met for enrolling in the study programme

Course description

Errors. Types of errors. Significant digits of an approximate number. Function error. Inverse problem. Interpolation. Interpolation problem. Lagrange, Newton and spline interpolation. Solving set of linear equations. Vector and matrix norm. Conditionality. Solving triangular systems. Direct methods (Gauss elimination methods without pivoting, partial pivoting and complete pivoting), LU decomposition, Cholesky decomposition, QR decomposition and iterative methods (Jacobi, Gauss-Siedel). Solving nonlinear equations (bisection method, simple iteration, Newton method and Newton modification). Solving a set of nonlinear equations (Newton method, quasi-Newton methods). Approximation of functions. The least squares problem. Numerical integration (Trapezoidal rule, Newton-Cotes rule, Simpson’s rule). Solving ordinary differential equations – initial value problems and boundary value problems (Euler’s methods, Runge-Kutta methods, the finite difference method, finite element method and shooting method).

Student requirements

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Monitoring of students

Defined by the Student evaluation criteria of the Faculty of Electrical Engineering, Computer Science and Information Technology Osijek and paragraph 1.9

Obligatory literature

1. 1 Scitovski, R. Numerička matematika Osijek: Sveučilište J.J.Strossmayera u Osijeku, Odjel za matematiku, 2015.

2. 2 Chapra, S.C; Canale, R.P. Numerical methods for engineers New York: McGraw-Hill Education, 2015.


Pretraži literaturu na:

Recommended additional literature

1. 1 G.Dalquist, A.Björck Numerische Methoden R. Oldenbourg Verlag, München, 1972.

2. 2 D.Kincaid, W.Cheney Numerical Analysis Brooks/Cole Publishing Company, New York, 1996.

3. 3 J.Stoer, R.Bulirsch Introduction to NumericalAnalysis, 2ndEd. SpringerVerlag, New York, 1993.

4. 4 W.H.Press, B.P.Flannery, S.A.Teukolsky, W.T.Vetterling Numerical Recipes Cambridge University Press, Cambridge, 1989.

Course assessment

Conducting university questionnaires on teachers (student-teacher relationship, transparency of assessment criteria, motivation for teaching, teaching clarity, etc.). Conducting Faculty surveys on courses (upon passing the exam, student self-assessment of the adopted learning outcomes and student workload in relation to the number of ECTS credits allocated to activities and courses as a whole).

Overview of course assesment

Learning outcomes
Upon successful completion of the course, students will be able to:

1. define and calculate errors in numerical problems and conclude the reasons for error occurrence

2. based on a data analysis, create a function using approximation and interpolation

3. describe and solve a nonlinear equation and sets of linear and nonlinear equations with numerical methods

4. create a numerical integration problem model using practical examples

5. create a model for practical numerical problems

6. build a model for the finite difference method and finite elements method



Aktivnosti studenta: Vidi tablicu aktivnosti