NUMERICAL ANALYSIS

1st module

Dott. Paola Zanolli

A.A. 1998/99

PROGRAMME

1.  Algebraic and Transcendental Systems: Matrices and Linear Systems, Gauss Elimination, Tridiagonal Systems, The Generalized Newton's Method, Remarks on the Generalized Newton's Method, Eigenvalues and Eigenvectors.

2.  Approximation: Discrete Functions, Piecewise Linear Interpolation, Piecewise Parabolic Interpolation, Cubic Spline Interpolation, Lagrange Interpolation, Least Squares.

3.  Approximate Integration and Differentiation: The Trapezoidal Rule, Simpson's Rule, Romberg Integration, Numerical Differentiation.

4.  Initial Value Problems for Ordinary Differential Equations: Euler's Method, Convergence of Euler's Method, A Runge-Kutta Method, Higher Order Runge-Kutta Formulas, Kutta's Fourth-Order Method for a System of Two First-Order Equations, Kutta's Fourth-Order Formulas for Second-Order Differential Equations, The Method of Taylor Expansions, Instability, Approximation of Periodic Solutions of Differential Equations.