Learning Outcomes
After successfully completing the course, the student should be able to:
1. use complex analysis in solving physical problems;
2. solve ordinary and partial differential equation of second order that are common in the
physical science;
3. use the orthogonal polynomials and other special functions;
4. use fourier series and integral transformation; and
5. use the calculus of variations.
Course Contents
Linear Algebra and Functional Analysis. Transformations in linear vector spaces and matrix theory.
Hilbert space and complete sets of orthogonal functions. Special functions of Mathematical
Physics: the gamma function, hypergeometric functions, Legendre functions, Bessel functions,
Hermite and Laguerre function. The Dirac Delta function. Integral Transforms. Fourier Series:
Fourier series and Fourier transforms. Laplace transform. Applications of transform methods to
the solution of elementary differential equations of interest in physics and engineering. Partial
differential equations. Solution of boundary value problems of partial differential equations by
various methods which include: separation of variables, the method of integral transforms, SturmLiouville theory. Uniqueness of solutions. Calculus of residues and applications to evaluation of
integrals and summation of series. Applications to various physical situations, which may include
electromagnetic theory, quantum theory and diffusion phenomena.
