In this course we will discuss the following topics: scalars and vectors, triple product, gradient, divergence, curl, Stokes' theorem, Green's theorem, Divergence theorem, Poisson's and Laplace's equations, general curvilinear coordinate, Cartesian coordinates, cylindrical coordinates, spherical coordinates, separation of variables in curvilinear coordinates, first order differential equations, second order linear differential equations, method of variation of parameters, Euler differential equation, general form of Fourier series, Fourier expansion of odd and even functions, Parseval's theorem, integration and differentiation of Fourier series.