FCE562 - Numerical Analysis

Interpolation

 

Finite difference, interpolation formulae based on finite differences, lagrange interpolation including iterated interpolation.  Applications.

 

Curve-fitting

 

Least squares method.  Applications.

 

Numerical Differentiation and Integration: Optional

 

Derivatives from interpolating polynomials.  Trapezoidal rule.  Simpson's rule.  Newton-Cotes formulae.  Romberg integration.  The trapezoidal and Simpson's rules with end corrections.  Applications.

 

Numerical Solution of Ordinary Differential Equations: Optional

 

Taylor's series method.  Euler's methods.  Runge-kutta method.  Predictor-Corrector methods.  Extrapolation methods.  Simple boundary-value problems.  Applications.

 

Matrices and Simultaneous Linear Equations: Optional

 

Gaussiaan elimination and the LU decomposition methods for solving simultaneous linear equations.  Iterative methods-Jacobi, Gausseidel and introductory SOR methods.

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