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Course Contents

Introduction, Engineering Systems, Physical and Mathematical Modeling, Error Analysis Approximations and round off and Truncation errors, Roots of Equations single variable Method of Bisection, Method of Interpolation, Secant Method, One point Methods, Newton Raphson method, Secant Method, Multiple roots, Solution of Linear Simultaneous Equations Direct Methods Gauss Elimination, Gauss Jordan, LU decomposition; iterative Methods Gauss Seidel, Conjugate Gradient, Banded and Sparse systems Solution of Nonlinear Simultaneous Equations, Curve Fitting, Least Square regression, Interpolation including spleens, Fast Fourier Transforms, Regression Analysis for Multivariable, Eigen Values and Eigen Vectors Power method, Relaxation Method, Diagonalization method. Numerical Differentiation and Integration. High Accuracy Differentiation Formulas, Derivatives of Unequal Spaced Data. The trapezoidal Rule, Simpson’s rule, Integration with unequal segments, Open Integration Formulas, Ordinary Differential Equations Finite Difference method, Method of Weighted Residuals, Analytical versus Numerical Methods, Initial Value and Boundary Value Problems, Euler’s method, Improvement of Euler’s method, Runge Kutta Method, Multiple Steps Method, Partial Differential Equations. Elliptic and parabolic Equations, Explicit and Implicit Methods, Crank Nicholson Method, ADI method; Introduction to Finite Element Method, Applications.