Laplace Transform. Transforms of Derivatives and Integrals. s-Shifting, t-Shifting, Unit Step Function, Diracís Delta Function, Differentiation and Integration of Transforms, Convolution, The Heaviside Expansion Theorem, Periodic Functions. Fourier Series, Half-Range Expansion, Complex Fourier Series. Fourier Integrals. Fourier Transform. Series Solution of Differential Equations, Legendre Polynomial, Bessel Functions. Sturm-Liouville Problem, Eigenfunction Expansions. Partial Differential Equations. Separation Variables, Use of Fourier-Bessel Series, Use of Fourier-Legendre Series. Solution by Laplace Transforms, solution by Fourier Transforms.