Numerical methods and programming

Course Description

COURSE CONTENT

The task of numerical mathematics. Elements of error theory. Calculation of the value of some elementary functions by using the Taylor's polynomial. Calculation the value of some elementary functions by using Taylor's polynomial with the help of the Maxima software package.

Algorithms, flow diagrams and pseudoprograms. Relational and logical operators. Conditional statements. Loop.

Iteration methods for solving system of linear equations (Jacobin method and Gauss-Seidel method). Matrix operations, direct methods and iteration methods for solving linear equation systems using the Maxima program package.

Discrete case. Continuous case. Trigonometric polynomial; Fourier polynomial. Computer implementation with the help of the Maxima software package.

Newton's method (method of tangent). Method of secant. Iteration method. Systems of nonlinear equations. Computer implementation with the help of the Maxima software package.

Lagrange's form of interpolation polynomial. Aitken interpolation scheme. The general Newton's form of interpolation polynomial. Hermite interpolation polynomial. Interpolation by parts with polynomials. Numerical differentiation and integration. Calculate the interpolation polynomial with the Maxima software package.

Talor's method. The method of unspecified coefficients. Picard's method. Linear differential equations and Laplace transformation. Euler's method. Runge-Kutta’s methods. A finite difference scheme for partial differential equations. Computer implementation with the help of the Maxima software package.

The method of golden ratio. Computer implementation with the help of the Maxima software package.

LEARNING OUTCOMES

• define and describe a wide range of numerical methods, their properties and the conditions under which they can be applied
• analyze problems and choose the appropriate numerical method for solving them
• analyze the importance and accuracy of the results obtained by calculating
• comparing alternative methods for numerical solutions of a given problem
• use computer tools to help in mathematical processes and to acquire the new information
• implement numerical methods by using a computer

To enrol in this course, the following courses must be completed:

• Matemathics 1
• Matemathics 2
• Basic Informatics