Laplace Transform: General theories, Transform of special functions, the Heaviside Expansion Theorem, Transform of periodic functions, Convolution and the Duhamel formulas, The Complex Inversion Integral, Stability Criteria Z-transform. Partial Differential Equations: Derivation of equations, d'Alembert solution of the wave equations, Characteristic and the classification of partial differential equations, Separation of variables, Orthogonal Functions and the general expansion problem, Bessel functions, Laplace transform methods, Numerical solutions of partial differential equations. Numerical Analysis: The differences of a function, Interpolation formula, Difference Equations, Spline functions. Numerical Methods in Linear Algebra: Gauss elimination, LU-factorization, Iteration methods, Norms and conditions, Eigenvalue problems.

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