Didactic units and topics
Integrals Transforms and Differential Equations
ET1.1] Laplace Transform. Piecewise continuous functions. The Laplace Transform. Properties
of Laplace Transform. Inverse Laplace Transform. Application of Laplace Transform. Transfer
functions.
[ET1.2] Stability of Differential Equations: Stability. Stability criteria for linear systems. Stationary
points. Hyperbolic points. Local stability for non linear systems.
[ET1.3] Series and Fourier Transform. Fourier series and its convergence. Fourier series for
even and odd functions. Periodic extensions. The Fourier Transform. Properties of the Fourier
transform. Inverse Fourier Transform.
[ET1.4] Partial Differential Equation. Basic definitions. Second order linear equations. Separation
of variables. Wave, heat and Laplace equations. Solving EDP with integral transform.
Optimization.
[ET2.1] Non linear optimization. Basic definitions. Nonlinear programming program. Karush
Kuhn-Tucker theorem. Lagrange theorem. Sufficient conditions.
[ET2.2] Variational calculus and optimal control. Variational method: The Euler-Lagrange
equation. Optimal control for Continous Systems: state and co-state equations. Pontryagin
Minimum Principle. Bang-Bang and Bang-Off-Bang control.
