Computation and Simulation Techniques TS1C300017

1. Introduction, course topics, literature, assessment rules. Role of a computer in a design process. Mathematical modelling of physical phenomena. (2 h)
2. Models and macromodels, small-signal models and large-signal models. Problems of interpolation, approximation, and extrapolation. Polynomials – advantages and disadvantages. Polynomial interpolation and approximation of single-variable functions. (2 h)
3. Mean-square approximation of single-variable functions. Correlation coefficient. Discrete and Fast Fourier Transform (DFT and FFT). (2 h)
4. Analysis of branched linear circuits. Indeterminate matrix of nodal admittances. Example of calculations for a small-signal model of a low-frequency amplifier. (2 h)
5. Numerical methods for solution of systems of linear algebraic equations. Gauss elimination, Gauss-Jordan method, [L][U] decomposition. Gauss-Seidel iteration method. (2 h)
6. Numerical methods for solution of non-linear equations and of non-linear equation systems. Bisection, golden section, Newton-Raphson method. (2 h)
7. Method of state variables. Methods for numerical integration of first-order ordinary differential equation systems: Euler method, Heun method, Runge-Kutta methods. Adams-Bashforth and other algorithms. (2 h)
8. Final test. (1 h)