Lecture Notes
(Refresh browser to see latest content)
Supplemental
Lectures
Class 1 Introduction
Class 2 Errors, accuracy, and roundoff
Class 3 Linear algebra review
Class 4 Linear systems-direct methods
Class 5-6 Linear systems-iterative methods
Class 7 Nonlinear equations I
Class 8 Nonlinear equations II
Class 9 Nonlinear equations III
Class 10 Numerical derivatives
Class 11 ODEs I
Class 12 ODEs II
Class 13 ODEs III
Class 14 Stability, consistency, stiffness
Class 15 Review
Class 16 Exam 1
Class 17 Boundary value problems: shooting methods
Class 18 Boundary value problems: Relaxation methods
Class 20 PDEs: introduction
Class 21 PDEs: parabolic
Class 22 PDEs: stability
Class 23 PDEs: multidimensional
Class 24 PDEs: ADI method
Class 25 PDEs: Finite volume method
Class 26 PDEs: Finite volume method 2
Class 27 PDEs: Advection and diffusion
Class 28 PDEs: Advection and diffusion II
Class 29 Exam 2 review
Class 30 Exam 2
Class 31 Hyperbolic equations
Class 32 Hyperbolic equations
Class 33 Integration I
Class 34 Numerical integration II
Class 35 Sample from PDF
Class 36 Gauss Quadrature
Class 37 Interpolation
Class 38 Curve fitting
Class 39 Spectral Methods
Class 40 Project
Class 41 Homotopy continuation
- Homotopy continuation
- Paper: Wayburn, Seader, 1987
Homotopy continuation methods for computer-aided process design.
- Paper: Kuno, Seader, 1988
Computing all real solutions to systems of nonlinear equations with a global fixed-point homotopy.
- Paper: Khaleghi, Jalali, 2007
Multiple solutions in stability analysis using homotopy continuation in complex space.
- Paper: Rahimian, Jalali, Seader, White, 2011
A new homotopy for seeking all real roots of a nonlinear equation.
- Paper: Jimenez-Islas, Martinez-Gonzalez, Navarrete-Bolanos, Botello-Alvarez Oliveros-Munos, 2013
Nonlinear Homotopic continuation methods: a chemical engineering perspective review.
Class 42 Final Review