PMAT 32322: Mathematical Methods

Course Code            : PMAT 32322

Title                      : Mathematical Methods

Pre-requisites          : PMAT 22293

 Learning Outcomes:

At the end of this course, the student should be able to

• classify partial differential equations using various techniques learned

• solve hyperbolic, parabolic and elliptic equations using fundamental principles

• apply range of techniques to find solutions of standard PDEs

• demonstrate accurate and efficient use of Fourier analysis techniques and their applications in the theory of PDE’s

• solve real world problems by identifying them appropriately from the perspective of partial derivative equations.

 Course Contents:

Partial Differential Equations (PDEs): 

• Classification of PDE, First order partial differential equations: Lagrange’s method and Charpit’s method.

Second order partial differential equations: 

• Linear Partial Differential Equations with Constant Coefficients, Partial Differential Equations of Order two with Variables Coefficients, Classification of Partial Differential Equations Reduction to Canonical or Normal Form: Parabolic, elliptic and hyperbolic partial differential equations.

Fourier Series: 

• Fourier Series, Even and Odd Functions, Half-Range Expansions, Fourier Integral, Fourier Cosine and Sine Transforms.

Solutions of PDEs: 

• Separations of variables, Fourier Transforms, Laplace Transforms, D’Alembert’s Solution of the Wave Equation.

 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. Kreyszig, E. (10th Ed., 2011). Advanced Engineering Mathematics, Wiley.

2. 2. Zill, D.G. (7th Ed., 2020). Advanced Engineering Mathematics, Jones & Bartlett Learning.

3. 3. Raisinghania, M.D. (19th Ed., 2018). Advanced Differential Equations, S.Chands, India.