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Unit-I (Numerical solution of transcendental equations, Interpolation)
Roots of polynomial and transcendental equations – bisection method, Regula-falsi method and Newton-Raphson method, Finite differences, Newton's forward and backward interpolation formulae, Lagrange interpolation, divided differences
Unit-II(Numerical integration and numerical solution of IVP)
Trapezoidal rule, Simpson's 1/3rd rule and 3/8th rule for numerical integration, Solution of IVP by Euler and Runga-Kutta method.
Unit-III(Linear Algebra)
Vector Spaces, Linear Combinations of Vectors, Linear dependence and Independence, System of Linear Equations, Rank of a Matrix, Inverse of a matrix, Eigen values and Eigen Vectors. Properties for various types of matrices (i.e symmetric, skew-symmetric, Hermitian, Skew - Hermitian, Orthogonal, Unitary matrices and Idempotent matrix)
Unit-IV (Vector Calculus )
Scalar and vector fields, level surfaces, directional derivative, Gradient, Curl, Divergence, Laplacian, line and surface integrals,Green, Gauss and Stokes theorems (without proof) and problems
Unit-V (Complex variables and Complex integration )
Regions in the complex plane, Limit, Continuity, Elementary functions, Differentiability and Analyticity of functions, Cauchy-Riemann equations, Line integrals in complex plane, Cauchy’s integral theorem, Independence of paths, Existence of indefinite integral, Cauchy’s integral formula, Derivatives of analytic functions
Unit-VI (Residue and applications )
Taylor’s series, Laurent’s series, Zeros and singularities, Applications of Residue theorem, Evaluation of real integrals.
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