Lecture Notes on Numerical Methods

Taught by Tiejun Li


Chapter 1 Solving linear system

Lect1 Introduction

Lect2 Direct methods for solving linear system

Lect3 Iterative methods for solving linear system

Lect4 Eigenvalue problem for linear system

Lect5 Singular value decomposition and applications (PCA)

Chapter 2 Numerical optimization

Lect6 Linear programming

Lect7 Nonlinear programming

Lect8 Integer programming and other topics

Chapter 3 Solving nonlinear system

Lect9 Solving nonlinear system

Chapter 4 Approximation of functions

Lect10 Polynomial interpolation

Lect11 Fast Fourier Transform (FFT)

Lect12 Wavelets and applications

Chapter 5 Numerical integration

Lect13 Numerical integration: basics

Lect14 Numerical integration: adaptive and Gaussian quadrature

Chapter 6 Monte Carlo methods

Lect15 Generation of RVs

Lect16 Monte Carlo integration

Lect17 Metropolis algorithm and SSA

Lect18 Simulated annealing and Genetic algorithm

Chapter 7 Numerical ODEs

Lect19 One-step method for numerical ODEs

Lect20 Multi-step method and stability condition

Lect21 Stability regions and stiff ODEs

Lect22 Symplectic algorithm