Almost every system in this universe is governed by a specific equation which, in most cases, is non-linear. The course gives a brief overview of the methods which could be employed to solve the governing equations of a few specific non-linear systems and thus, predict their behaviour in future.
The course has 3 lecture hours per week – two 1.5 hours slot. There are 6 quizzes, 1 mid-sem, 1 end-sem and several ungraded tutorials. Apart from these, there is also a weightage given to attendance. The course starts off with minimization of functionals and then moves on to Lagrangian Mechanics. Post mid-sem, the course focuses solely on solving partial differential equations for various cases.
- Minimization of Functionals – one/many dependent/independent variables
- Euler-Lagrange Equation
- Brachistocrone Problem
- Lagrangian Mechanics – one/many dependent/independent variables
- Partial Differential Equations and their solutions – Heat Equation, Wave Equation
- Solution of General Partial Differential Equations using Separation of Variables
- Fourier Series, Fourier Transform, Reverse Fourier transform
- General nature of Boundary Value Problems, Interior & Exterior Dirichlet, Neumann & Robin Problems
Class notes and the tutorial problems are more than enough for understanding concepts and solving problems in examinations. Apart from that, specific chapters from the following books are also prescribed –
- Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow
- The Calculus of Variations by Bruce van Brunt
(Written by Amit Sarkar; Course taken in Spring 2013-2014 under Prof. Dnyanesh Pawaskar)