Course Code : PMAT 42803
Title : Advanced Mathematical Methods
Pre-requisites : PMAT 22583
Learning Outcomes:
At the end of this course, the student should be able to demonstrate knowledge of solving problems involving partial differential equations.
Course Content:
Special Functions: Legendre Polynomials, Bessel Functions
Laplace Transforms: Laplace Transform. Linearity, Shifting Theorems, Transforms of Derivatives and Integrals, Unit Step Function (Heaviside Function), Differentiation and Integration of Transforms.
Fourier Series: Fourier Series, Even and Odd Functions, Half-Range Expansions, Fourier Integral, Fourier Cosine and Sine Transforms
Partial Differential Equations: Introduction to first order and second order partial differential equations. Parabolic, elliptic and hyperbolic partial differential equations
Integral Transforms: Laplace Transforms, Fourier Transforms, Hankel Transforms, Fourier method for partial differential equations.
Applications of Boundary Value Problems
Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.
Assessment: Based on tutorials, tests, presentations and end of course examination.
Recommended Reading:
- Kreyszig, E., (10th edition, 2011) Advanced Engineering Mathematics, Wiley.
- Pinsky, M.A., (2011) Partial Differential Equations and Boundary Value Problems with Application, American Mathematical Soc.
- Raisinghania, M.D., (1995). Advanced Differential Equations, S.Chands, India.