Lecture Notes

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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 31 Hyperbolic equations