Educational guide 2015_16 Escola de Enxeñaría Industrial

Contents

Topic	Sub-topic
Numerical methods for solving nonlinear equations and systems	Bisection and successive approximation methods. The Newton-Raphson method. Variants of Newton method for solving equations and systems of nonlinear equations. Algorithms for simultaneous approximation of all zeros of a given polynomial.
Numerical methods for solving equations and systems of differential equations	Numerical solution of initial value problems: one-step and multistep methods. Numerical solution of boundary value problems: finite difference method and shooting method.
Complex variable	Functions of one complex variable. Complex integration. Power series and Laurent series. Singularities, zeros and residues. Applications
Transforms for continuous and discrete systems.	Laplace transform. Z transform. Fourier transform. Discrete Fourier transform: FFT algorithm. Applications.
Graphs and discrete optimization	Graphs, digraphs and interconnecting nets. Trees. Spanning tree of minimal cost. Flows and connectivity. Applications.