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