This course is designed to equip students with the basic techniques for the efficient numerical solution of problems in science and engineering. Topics will include: Curve fitting and function approximation.  Approximation formulae for kth derivatives.  Composite rules and Romberg integration, Gauss quadrature, numerical method for multiple integrals. Numerical methods for ordinary differential equations.  Numerical methods for Eigenvalues, the power method for finding dominant eigennvalues, the inverse power method for finding smallest eigenvalues, the shifted inverse power method, for finding an eigenvalues closest to a given approximate eigenvalue. Piece-wise polynomial interpolation, cubic splines.