Lecture Notes

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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