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The concept of ordinary differential equations (ODEs), the Laplace transform, the inverse Laplace transform, homogeneous linear ordinary differential equations, nonhomogeneous linear ordinary differential equations, linearization of a dynamic system using numerical techniques. 15 episodes.
Introduction to partial differential equations, derivation of the 1D wave equation, heat equation, derivation of Laplace's equation, derivation of the 2D wave equation, numerically solving partial differential equations. 11 episodes.
Optimization, 4 different ways to use/call Matlab’s ‘fminsearch’ function to perform unconstrained optimization, how to convert a constrained optimization problem into an approximately equivalent unconstrained optimization problem using the penalty method, how to solve a system of equations using numerical optimization instead of analytically solving, how to find a trim point of a dynamic system using numerical optimization techniques, and discussion of the Taylor Series (and the closely related Maclaurin Series) . 5 episodes.
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Numerical Recipes is the generic title of a series of books on algorithms and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986..