Core course for B.Sc. (Research) Mathematics.
Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)
Prerequisites: MAT 102 Calculus II or MAT 103 Mathematical Methods I. MAT 230 Ordinary Differential Equations or MAT 104 Mathematical Methods II.
Overview: Many physics principles like conservation of mass, momentum, energy, when applied to real life scenarios, take the form of PDEs. In this course we will learn how basic physics concepts together with simple calculus translate into mathematical models of many engineering problems in the form of PDEs. We will learn some well-known techniques to solve these problems in simple settings. We will also learn approximation techniques which will be needed in cases where it is impossible to get analytical solutions.
Essentially Chapters 1, 2, 4, 5, 6, and 8 of the book by Strauss. This material will be supplemented with exercises from other prescribed texts and Matlab exercises. The list of topics covered is:
- Definition of PDEs, well-posedness, initial value and boundary value problems
- Examples of PDEs, classification of PDEs
- Wave equation, diffusion equation
- Source terms
- Boundary conditions and their impact on solution
- Fourier Series and their use in solving PDEs
- Harmonic equations and their solution
- Numerical methods
- Partial Differential Equations, an Introduction, Second Edition, by Walter A. Strauss
- Applied Partial Differential Equations by Paul DuChateau, David Zachmann
- Partial Differential Equations for Scientists and Engineers, by Stanley J. Farlow
Past Instructors: Ajit Kumar, Samit Bhattacharyya, Srinivas VVK