Notes for MA780:

These notes cover mainly those classical numerical techniques for nonlinear problems. The lectures are organized as follows. Additional materials, including those graphical demonstrations and some newly developed techniques, will be added in class.

Chapter 6. System of Nonlinear Equations (postscript)(pdf)

· Theory of Newton-Raphson Method

· The Broyden Method

· Sturm Sequence

· Methods for Polynomials

Chapter 7. Approximation Theory (postscript)(pdf)

· Lagrangian Interpolation Formula

· Newton's Interpolation Formula

· Osculatory Interpolation

· Spline Interpolation

· Trigonometric Interpolation

· Fast Fourier Transform

Chapter 8. Differentiation and Integration (postscript)(pdf)

· Numerical Differentiation

· Richardson Extrapolation

· Newton-Cotes Quadrature

· Gaussian Quadrature

· Weight Functions and Special Integrals

· Adaptive Integration

Chapter 9. Numerical Ordinary Differential Equations - Initial Value Problems (postscript)(pdf)

· Linear Multi-step Methods

· Stability Theory of Multi-step Methods

· Predictor and Corrector Methods

· Runge-Kutta Methods

Chapter 10. Numerical Ordinary Differential Equations - Boundary Value Problems (postscript)(pdf)

· Ordinary Shooting Method --- An Example

· Multiple Shooting Methods --- The Set-up

· Solving Nonlinear Equations --- Homotopy Method

· Finite Difference Method

· Finite Element Methods