COURSE SUMMARY
Course Title: 
Linear Algebra, Legendre Equations and Numerical Methods
Course Code: 
18MA618
Year Taught: 
2019
Semester: 
1
Degree: 
Postgraduate (PG)
School: 
School of Engineering

'Linear Algebra, Legendre Equations and Numerical Methods' is a course offered in the first semester of M. Tech. program in Structural & Construction Engineering at the School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore campus.

Linear algebra: Review of matrices and linear systems of equations. Vector spaces and subspaces, linear independence, basis and dimensions, linear transformations, orthogonality, Orthogonal basis, Gram Schmidt Process, least-square applications.

Differential equation with series solutions: Legendre’s equation, Legendre’s polynomial Pn(x), Legendre’s function of the second kind [Qn(x)], General solution of Legendre’s equation, Rodrigue’s formula, Legendre polynomials, A generating function of Legendre’s polynomial, Orthogonality of Legendre polynomials, Recurrence formulae for Pn(x) Green's function – Green’s Identities – Generalized functions.

Numerical methods: Solution of systems of equations – iterative methods, method of determining Eigen values and Eigen vectors by Power method. Numerical solution of partial differential equations – Elliptic, parabolic and hyperbolic equations.

  • Elementary Linear Algebra, Howard Anton and Chris Rorrs, Ninth Edition, John Wiley and Sons, 2000.
  • Linear Algebra and Its Applications, Gilbert Strang, Fourth Edition, Cengage, 2006.
  • Orthogonal Functions, G. Sansone, Dover Phoenix Edition, 2004.
  • Special Functions, J .N .Sharma and R. K. Gupta, Krishna Prakashan, 2006.
  • Applied Numerical Analysis, Curtis. F. Gerald and Patrick O Wheatley, Fifth Edition, Addison Wesley, 2002.