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 –

  1. Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow
  2. 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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