Lecture Notes
## 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 19 Boundary value problems: Boundary conditions, nonlinear, nonuniform

#### 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 (Python)

#### 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

#### Class 42 Final Review

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**NOTE: nbviewer.org is not rendering plots in julia. You will need to download the notebook and open it locally to see the plots.**

- Notes
- Some good links
- Cook: What’s so hard about finding a hypotenuse?
- Cook: Math library functions that seem unnecessary
- Cook: Anatomy of a floating point number
- What every computer scientist should know about floating point arithmetic
- Base 3 is best
- Brian Hayes, “Third Base,” American Scientist 89(6):490-494(2001).

- Notes
- Corresponding jupyter notebook file (right click, save as)

- 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.