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Methods for Solving Algebraic and Transcendental Equations :
1.1 Ramanujan
1.2 Bisection
1.3 Regula Falsi
1.4 Secant
1.5 Newton-Raphson
Unit-II
Interpolation and Numerical Integration :
2.1 Lagrange interpolation
2.2 Finite difference operators
2.3 Interpolation formula using Differences
2.3.1 Gregory-Newton Forward Difference Interpolation
2.3.2 Gregory-Newton Backward Difference Interpolation
2.4 Numerical Integration
2.4.1 Newton-Cote’s formulae
2.4.2 Trapezoidal rule
2.3.2 Simpson’s 1/3 Rule
2.4.4 Simpson’s 3/8 Rule
2.4.5 Gauss Integration
Unit-III
Methods to Solve System of Linear Equations :
3.1 Direct method for solving system of linear equations
3.1.1 Gauss elimination
3.1.2 LU decomposition
3.1.3 Cholesky decomposition
3.2 Iterative method
3.2.1 Jacobi
3.2.2 Gauss-Seidel
Unit-IV
Numerical Solution of Ordinary Differential Equations :
4.1 Single step methods
4.1.1 Picard
4.1.2 Taylor’s series
4.1.3 Euler
4.1.4 Runge-Kutta
4.2 Multistep methods
4.2.1 Predictor-corrector
4.2.2 Modified Euler
4.2.3 Milne-Simpson
