Topic 1

Introduction to working with the Matlab program system: Entering variables, vectors and matrices, managing variable in Matlab, grafiphic output, creating scripts.

Topic 2

Fundamentals of algorithmization: Properties of algorithms, elementary algorithms.

Topic 3

Calculation of function values: Calculation of the value of a polynomial, tabulated functions, drawing the graph of a targeted function, determining the maximum of a discretized function.

Topic 4

Solving nonlinear algebraic equations: Iteration, iterative methods of solving nonlinear algebraic equations.

Topic 5

Sorting algorithms: Bubble sort, Select sort, Insert sort, Quick sort, Shell sort.

Topic 6

Systems of linear equations: Direct methods of solving systems of linear equations - solving a triangular system, Gaussian and Gauss-Jordan elimination method, LU and Cholesky decomposition.
Iterative methods of solving systems of linear equations - Jacobi iteration, Gauss-Seidel iteration method, sparse and band matrix, Conjugate gradient method.

Topic 7

Topic 8

Numerical integration of a definite integral: Rectangle, trapezoid, Simpson's and Romberg's methods of numerical integration, Adaptive integration, Gaussian method.

Topic 9

Numerical derivation: Finite difference method, numerical differentiation with a variable difference, partial derivatives.

Topic 10

Solving differential equations: Ordinary differential equations of the first order, Euler's method, Runge-Kutta method, Leapfrog method.

Topic 11

Interpolation and approximation: Linear interpolation, Lagrange interpolation, Newton's interpolation, aproximation bz the method of least squares - linear and by m-th degree polynomial.

Learning materials - printable version: