PMAT 42803: Advanced Mathematical Methods

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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:

 

  1. Kreyszig, E., (10th edition, 2011) Advanced Engineering Mathematics, Wiley.
  2. Pinsky, M.A., (2011) Partial Differential Equations and Boundary Value Problems with Application, American Mathematical Soc.
  3. Raisinghania, M.D., (1995). Advanced Differential Equations, S.Chands, India.
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