# ME 340: Analytical Methods in Engineering Applications

**Motivation** :

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.

**Overview** :

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.

**Contents** :

- 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

**References** :

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)

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