Courses Catalogue

Mathematical Physics Iii

COURSE CODE: PHY2209
COURSE CREDIT UNIT: 3
ACADEMIC PROGRAMME: Physics BSc
COLLEGE/SCHOOL/FACULTY: School of Natural and Applied Sciences
STATUS: Core
PROGRAMME TYPE: Undergraduate

Course Description

COURSE DESCRIPTION

 

To provide course topics of the complex number system, Cauchy-Riemann conditions, analytic functions, integration and line integrals, Cauchy's theorem, Cauchy representation, conformal mapping, Taylor and Laurent Series expansions; the calculus of residues and various applications. Further study of ordinary differential equations; second order homogeneous and non-homogeneous equations with constant coefficients; Power series solutions; Applications.

 

COURSE JUSTIFICATION/RATIONALE

 

This module aims to provide the students with some of the essential mathematical tools to model and understand the world around us. Vector calculus is essential to describe real and virtual objects that move in space and time. Complex variables are often the natural setting for many seemingly unrelated problems, from numerical methods to integral transforms and the study of the response of dynamical systems

 

LEARNING OBJECTIVES

 

By the end of this course, the student should be able to:

§  Discuss the theory of Complex Variables which are most useful in applications in Physics.

§  Explain methods of ordinary differential equations, concepts of vector spaces, application of vectors, coordinate geometry of lines and planes in space

§  Apply techniques in dealing with differential equations, integration to problems of mathematical Physics.

§  Discuss the techniques of Fourier series and integral transform (Fourier and Laplace) and find their basic role in different physical applications.

§  Utilize special functions like Gamma, Beta, Bessel, Legendre, Laguerre and Hermite in solving physical problems.

 

LEARNING OUTCOMES

 

A student completing the course is expected to:

  • Compute the Fourier series expansion of a given function
  • Solve a range of first and second order ordinary differential equations, including both initial and boundary value problems, using exactness, integrating factors and methods of reduction of order and variation of parameters
  • Solve a range of first and second order partial differential equations using methods of characteristic curves and separation of variables
  • Solve some of the fundamental equations of mathematical physics using methods of separation of variables and Fourier series.

§  Evaluate line, surface and volume integrals in simple coordinate systems;

§  Use Gauss’s and Stokes’ theorems to simplify calculations of integrals and prove simple results;

§  Parametrize a path and evaluate some complex integrals directly;

§  Evaluate real and complex integrals using the Cauchy integral formula and the residue theorem.