Mathematical Methods in Engineering II

3 Credits

Theory of complex functions; Cauchy-Riemann relations. Integration in the complex plane, Cauchy’s integral formula. Laurent series; singular points; contour integrals; Fourier and Laplace transforms. Evaluation of real integrals; Cauchy principal values. Laplace’s equation; conformal mappings; Poisson formulae. Singular integral equations. Classification of partial differential equations. Hyperbolic systems of partial differential equations; uniqueness, shock formation. Nonlinear parabolic equations; Burger’s equation.