The goal of this subject is to introduce the students with the theory and applications of basic numerical methods and their implementations in MATLAB.

After finishing the coursework, the student knows how to: - solve the system of linear equations with prescribed accuracy; - solve the nonlinear equation or the system of nonlinear equations with prescribed accuracy; - determine interpolation polynomial of a given function and compute an approximate value of the function at a given point; - compute an approximate value of the derivative of a function of a given order at a given point using interpolation polynomial; - compute an approximate value of the integral of a given function; - determine an approximate solution of Cauchy problem for first order ordinary differential equations. Those tasks student is capable to solve in general and using MATLAB. The student knows how to determine the accuracy of the computation and to evaluate the reliability of the obtained results by estimating the error.

Introductory concepts in numerical mathematics. Elements from the theory of errors: - concept and types of errors; - approximate numbers; - errors of approximate values ​​of functions; - inverse error problem. Systems of linear equations: - direct methods (Gaussian elimination, LU factorization); - iterative methods (Jacobi method, Gauss-Seidel method). Nonlinear equations: - interval halving method; - regula-falsi method; - secant method; - Newton's method; - simple iteration method. Systems of nonlinear equations: - Newton's method; - simple iteration method. Polynomial interpolation: - Lagrange interpolation; - Newton's divided difference interpolation; - Newton's finite difference interpolation; - Hermite interpolation; Least squares method. Numerical differentiation. Numerical integration: - Newton-Cotes quadrature rules; - Gaussian quadrature rules. First order ordinary differential equations (Cauchy problem): - linear multistep methods (Euler's method); - Runge-Kutta methods.

Introductory concepts in numerical mathematics. Elements from the theory of errors: - concept and types of errors; - approximate numbers; - errors of approximate values ​​of functions; - inverse error problem. Systems of linear equations: - direct methods (Gaussian elimination, LU factorization); - iterative methods (Jacobi method, Gauss-Seidel method). Nonlinear equations: - interval halving method; - regula-falsi method; - secant method; - Newton's method; - simple iteration method. Systems of nonlinear equations: - Newton's method; - simple iteration method. Polynomial interpolation: - Lagrange interpolation; - Newton's divided difference interpolation; - Newton's finite difference interpolation; - Hermite interpolation; Least squares method. Numerical differentiation. Numerical integration: - Newton-Cotes quadrature rules; - Gaussian quadrature rules. First order ordinary differential equations (Cauchy problem): - linear multistep methods (Euler's method); - Runge-Kutta methods.

The course attendance condition is determined by the curriculum of the study program.

Literature: A. Cvetković, M. Spalević, Numerical methods, 2013, University of Belgrade - Faculty of Mechanical Engineering, ISBN: 987-86-7083-786-7 (in Serbian). Software: MATLAB.

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 5

Auditory exercises: 25
Laboratory exercises: 10
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 5
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 5
Test: 0
Final exam: 5

Activity during lectures: 0
Test/test: 20
Laboratory practice: 20
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 60
Requirement for taking the exam (required number of points): 10

A. Cvetković, M. Spalević, Numerical methods, 2013, University of Belgrade - Faculty of Mechanical Engineering, ISBN: 987-86-7083-786-7 (in Serbian).; M. Spalević, M. Pranić, Numerical methods, 2007, University of Kragujevac Faculty of Science, ISBN: 978-86-81829-84-4 (in Serbian).; E. Suli, D. Mayers, An Introduction to Numerical Analysis, 2003, Cambridge University Press, ISBN: 0-521-00794-1.