Lecture Notes

(Refresh browser to see latest content)

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

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 14-15 Stability, consistency, stiffness

Class 16 BVPs: shooting methods

Class 17 BVPs: relaxation methods

Class 18 BVPs: Boundary conditions, nonlinear, nonuniform

Class 19 PDEs: introduction

Class 20 PDEs: parabolic

Class 21 PDEs: stability

Class 22 PDEs: multidimensional

Class 23 PDEs: ADI method

Class 24 PDEs: Finite volume method

Class 25 PDEs: Finite volume method 2

Class 26 PDEs: Advection and diffusion (Python)

Class 27 PDEs: Advection and diffusion II exponential scheme

Class 28 Hyperbolic equations

Class 29 projects

Class 30 projects

Class 31 Hyperbolic equations, flux limiters, Euler equations

Class 32 Integration I, Trapezoid, Simpson’s

Class 33 Integration II, adaptive, Monte Carlo

Class 34 Sample from PDF