MATHEMATICS-LINEAR ALGEBRA AND NUMERICAL ANALYSIS-IN HINDI: MATHEMATICS
About this ebook
Unit-2 Linear transformations and their representation as matrices, Algebra of linear transformations, Rank-Nullity theorem, Change of basis, dual space, Bi-dual space and natural isomorphism, Adjoint of a linear transformation. Eigen values and Eigen vectors of a linear transformation, Diagonalisation, Bilinear, Quadratic and Hermitian forms.
Unit-3 Inner Product Space : Cauchy-Schwar'z inequality, Orthogonal vectors, Orthogonal complements, Orthonormal sets and bases, Bessel's inequality for finite dimensional spaces. Gram-Schmidt orthogonalization process.
Unit-4 Solution of Equations : Bisection, Secant, Regula-Falsi, Newton's methods. Roots of second degree polynomials.
Interpolation : Lagrange interpolation, Divided differences, Interpolation formula using differences, Numerical quadrature, Newton-Cote's formulae, Gauss quadrature formulae.
Unit-5 Linear Equations : Direct methods for solving systems of linear equations (Gauss elimination, LU decomposition, Cholesky decomposition), Iterative methods (Jacobi, Gauss-Seidel reduction methods).
Ordinary Differential Equations : Euler method, Single-step method, Runge-Kutta's method, Multi-step methods. Milne-Simpson method, Methods based on Numerical integration, Methods based on Numerical differentiation.
