At the end of this course, the students will be able to 1. Use the concepts and methods of standard ODE analysis including linearity, linear independence, homogeneity, constant coefficient and equidimensional equations, system of equations, operator notation and variation of parameters. 2. Develop series solutions for linear second order ODE’s, using regular and singular point expansions. 3. Identify and solve Legendre and Bessel equations using Legendre polynomials and Bessel functions, respectively. 4. Develop Fourier series and Fourier integral representations of given suitable functions. 5. Develop operational skills to use Fourier, Fourier sine and Fourier cosine transforms. 6. Identify and solve Sturm-Liouville problems. 7. Identify and solve parabolic PDE’s, e.g. the heat equation, using separation of variables, Fourier and Laplace transforms. 8. Identify and solve hyperbolic PDE’s, e.g. the wave equation, using separation of variables, D’Alembert’s method and Fourier and Laplace transforms. 9. Identify and solve elliptic PDE’s, e.g. the Laplace equation, using separation of variables and Fourier transform.