Vector sub-spaces, dimension, Linear transformations and their representation by matrices, rank of a matrix, system of liner equations, eigen values and eigen vectors, diagonalization.
Inner product spaces - Orthonormal sets, Gram Schmidt process and its application to the method of least squares, QR algorithm, contraction mapping theorem and its application to numerical solutions of nonlinear equations
Approximation of linear transformation and functionals, numerical integration and differentiation.
Introduces the techniques for solving partial differential equations
Real Sequences – boundedness, convergence.Differential Calculus – Limit, continuity and differentiability of functions, properties of differentiable functions – Rolle’s theorem, Mean value theorem, Taylor’s formula, maxima, minima, points of inflection, asymptotes and curvature.Integral Calculus – Definite integral as a limit of a sum, properties of definite integrals, applications of definite integrals.Numerical Series – Test of convergence, alternating series, absolute convergence.Sequence