MA2030 Linear Algebra and Numerical Analysis


Course Details

Vector spaces, sub-spaces, basis, dimension, Linear transformations and their respresentation by matrices, rank and nullity.

Inner product spaces - Orthonormal sets, Gram Schmidt process and its application to the method of least squares, QR factorization, best approximations and best approximate solutions.

Contraction mapping theorem and its application to numerical solutions of linear and non linear equations, Vector norms, matrix norms, condition number of a matrix, Iterative methods of solving systems of linear equations, Gauss-Jacobi and Gauss-Seidel methods.

Linear functional, interpolation of functions, Numerical Differentiation and integration.


Course References:

Text:
1. Gilbert Strang, Linear Algebra and its Applications, Brooks/Cole, 2006.
2. S D Conte and C De Boor, Elementary Numerical Analysis: An Algorithmic Approach, McGraw Hill 1980.

REFERENCES:
1. J B Fraleigh and R A Beauregard, Linear Algebra, Addison-Wesley, 1995.
2. D Kincaid and W Chenny, Numerical Analysis: Mathematics of Scientific Computing, Brooks/Cole, 2009.