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MTH-108.4 Applied and Computational Methods

Round off Errors and Computer Arithmetic.

Interpolation: Lagrange Interpolation, divided differences, Hermite interpolation, splines.

Numerical differentiation, Richardson extrapolation.

Numerical integration: Trapezoidal, Simpson’s, Newton-Cotes, Gauss quadrature, Romberg integration, multiple integrals.

Solutions of Linear Algebraic equations: Direct Methods, Gauss elimination, Pivoting, matrix factorizations.

Iterative Methods: Matrix norms, Jacobi and Gauss-Seidel methods, relaxation Methods.

Computation of Eigenvalues and Eigenvectors: Power Method, Householder's method, QR algorithm.

Numerical solutions of nonlinear algebraic equations: bisection, secant and Newton's method.

Zeros of polynomials, Horner and Muller methods, equations in higher dimensions.

Ordinary differential equations, initial value problems: Euler method, higher order methods of the Runge-Kutta type. Multi-step methods, Adams-Bashforth, Adams- Moulton methods, Systems of ODEs.

Ordinary differential equations, boundary value problems, shooting methods, finite differences, Rayleigh-Ritz methods.

Fast Fourier transforms.