FIZ 321E - Mathematical Mthds in Physc I

Course Objectives

1.To introduce Complex numbers and functions ; to define singularities , to study the Cauchy theorem and Taylor-Laurent series;
2.Compute definite integrals using residue method.
3.To solve second order homogenous linear ordinary differential equations with variable coefficients using the Forbenius method;
4.To find solutions of special functions like Bessel and Legendre functions.

Course Description

Complex numbers. Basic operations with complex functions, analytic functions. Cauchy theorem.
Singularities. Taylor and Laurent series. Residue theorem and applications. Complex functions.Second
order differential equations: introduction. Singularities and series solutions. Frobenius method. Special
.
functions: cylindrical and spherical coordinates.. Sturm-Liouville problem. Bessel, Neumann, Modified
Bessel functions. Legendre polynomials. associated Legendre functions. spherical harmonics. Fourier-
Legendre series. Asymptotic behaviors of certain special functions.