ECE220 Numerical Analysis

1.Theory:

• Floating-point arithmetic.
• Methods of function and data approximation with polynomials, partially polynomial functions(splines) and Fourier series.
• Numerical methods for solving linear and nonlinear systems of equations (direct and iterative methods) .
• Numerical approximation of matrices’eigenvalues ​​and eigenvectors.
• Numerical integration and differentiation.
• Methods for solving ordinary and partial differential equations .

2. Lab sessions:

• MATLAB Programming: data structures (vectors, arrays and complex numbers ), control structures, definition and function calls .
• MATLAB programming of numerical methods (taught in theory). Introduction and use of MATLAB toolboxes.
• Creation of two (2) and three (3) dimensions graphs.
• Creation of Graphical User Interfaces (GUIs).
• Interaction of MATLAB with FORTRAN and C.
• Introduction to object-oriented programming.

The course aims to give students the necessary knowledge and tools to solve known mathematical problems arising directly problems from hardware and telecommunications (including solution of systems of linear and nonlinear equations, solution of differential equations, data approximation, etc.). MATLAB software, which is well known and used by engineers and computer scientists, makes it possible to implement and study the methods presented in theory.

Upon successful completion of this course the student will :

• Have a great understanding on how to solve linear systems by direct and iterative methods and will be able to choose the proper method per problem.
• Have knowledge of basic methods of solving systems of nonlinear equations.
• Have knowledge of data approximation and interpolation methods using polynomials/splines and/or trigonometric functions (Fourier).
• Have knowledge in basic numerical methods of finite differences differentiation and integration, which will be extremely useful for the numerical solution of differential equations.
• Be able to understand the effect of finite arithmetic errors and errorsof methods in numerical results.
• Have basic knowledge of MATLAB software and its toolboxes.