COURSE SUMMARY
Course Title: 
Calculus of Variations & Numerical Methods
Course Code: 
15MAT211
Year Taught: 
2015
2016
2017
2018
Semester: 
4
Degree: 
Undergraduate (UG)
School: 
School of Engineering
Campus: 
Coimbatore

'Calculus of  Variations & Numerical Methods' is a course offered in the fourth semester of B. Tech. in Aerospace Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.

Unit 1

Calculus of Variations: Maxima and minima - The simplest case - Illustrative examples - Natural boundary conditions and transition conditions – Concept of functional with simple example – Variation of a functional (only necessary conditions) - Simple variational problem - Euler equation - The more general case of variational problems - Constraints and Lagrange multipliers - Variable end points.

Unit 2

Sturm-Liouville problems - Hamilton's principle - Lagrange's equations - Generalized dynamical entities - Constraints in dynamical systems - Applications in dynamics of particles, vibrating string, vibrating membranes, theory of elasticity - The variational problem of a vibrating elastic plate – Direct methods in calculus of variations - The Rayleigh-Ritz and finite difference methods. (Book-1)

Unit 3

Numerical Methods: Solution of Equations by iteration methods. Interpolations.
Numerical Integration and Differentiation. (Book-2: Sections: 19.1-19.5)

  • M. Gelfand and S. V. Fomin, Calculus of Variations, Dover Publications, 2000
  • Advanced Engineering Mathematics, E Kreyszig, John Wiley and Sons, Ninth Edition, 2012
  • A. S. Gupta, calculus of Variations with Applications, Prentice Hall of India, 1997
  • M. K. Venkatraman, Advanced Engineering Mathematics, 2010.
  • M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical methods for Scientific and Engineering Computation, New Age International Publishers, Fifth ed., 2007.
  • Steven Chapra and Raymond Canale, Numerical Methods for Engineers, McGraw Hill, 2007.