AMAT 41433: Boundary Value Problems

Course Code      : AMAT 41433

Title                 : Boundary Value Problems

Pre-requisites   : PMAT 42373, PMAT 32322

Learning Outcomes:  

After the completion of this course unit, the student will be able to:

1. classify partial differential equations

2. transform boundary value problems to other coordinate systems

3. solve two dimensional and three-dimensional boundary value problems in real life

4. apply Green’s theorem in boundary value problems

5. identify proper boundary conditions

6. apply method of images in boundary value problems.

Course Contents:

Partial Differential Equations in two variables: 

• Linear second order equations in two independent variables, Normal forms, Hyperbolic, parabolic and elliptic equations, Boundary value problems in rectangular and cylindrical coordinates, Applications to heat flow, Vibrations and waves, Laplace and Poisson equations in two dimensions.

Boundary Value Problems in Three Dimensions: 

• Green’s theorem in three dimensions, Uniqueness of solutions with Dirichlet and Neumann boundary conditions , Formal solutions of Boundary value problems in electrostatics, Method of images, Laplace equation in spherical polar coordinates, Boundary value problems with spherical symmetry, heat and wave equations , Three dimensional boundary value problems with azimuthal symmetry , Legendre functions and applications to gravitation and electrostatics, Potentials of circular rings and discs.

Method of Teaching and Learning : A combination of lectures and tutorial discussions.

Assessment : Based on tutorials, tests and end of course examination.

Recommended Reading :

1. Hebernsann, R. (1987). Elementary Applied Partial Differential Equations, Prentice-Hall.

2. Raisinghania, M.D. (1991). Ordinary and Partial Differential Equations, S. Chands, India.

3. Zill, D.G. & Cullen, M.R. (2018). Differential Equations with Boundary Value Problems, Cengage.