Math 329 -- Numerical Analysis

Math 329 -- Numerical Analysis webpage

Class syllabus (in pdf format).

Assignments

Unit 1: Rootfinding Due end of day Friday September 12, 2014
Unit 2: Linear Systems of Equations Due end of day Friday September 26, 2014
Unit 3: Interpolation Due end of day Wednesday October 8, 2014
Unit 4: Integrals and Derivatives Due end of day Wednesday October 22, 2014
Unit 5: Initial Value Problems Due November 12, 2014
Unit 6: Boundary Value Problems and PDEs Due November 21, 2014

Final Projects: Requirements and timeline

Lab handouts:

Introduction to Matlab.
odelab.pdf The ODE lab. (Python example code for odes: exampleode.py)
bvplab.pdf The BVP lab.

Example programs and data:

newton.m for rootfinding. (newton.py -- Python version)
lusolve.m An incomplete version for a linear systems solver with P'LU already known. (lusolve.py -- Python version)
bvpfd.m Example finite difference solver for boundary value problems. (bvpfd.py -- Python version)
bvpshoot.m Example shooting solver for boundary value problems. (bvpshoot.py -- Python version)
nonlinearbvpfd.m Nonlinear BVP finite difference solver for boundary value problems. (nonlinearbvpfd.py -- Python version)
Reaction Diffusion
stepRD.m One step of a PDE solver for unit 6 project.
RD.m Script to run the PDE solver and animate. (RD.py -- Python version includes stepRD)
Brusselator Reaction Diffusion
stepbruss.m One step of a PDE solver for the Brusselator.
bruss.m Script to run the Brusselator simulations.
bruss_cont.m Continue the simulation where you left off.
2-D Reaction Diffusion
fastspirals.m One step of a 2D PDE solver.
fastrunspirals.m Script to run the 2D PDE simulations.
fastrunspirals_cont.m Continue the simulation where you left off.

Readings
These textbooks are good complements to the lectures. There are many other sources of information about Numerical Analysis, and actually, Wikipedia is pretty good if you know what you are looking for. I chose Moler because it is very well integrated with Matlab. I chose Numerical Recipes because it has good descriptions of the methods and also good "practical" advice on what tends to work (or not). You can ignore the actual code in Numerical Recipes if you want.

Numerical Computing with Matlab, by Cleve Moler (available by chapter)
Numerical Recipes in C or in Fortran by William Press et al. (they have the same text). Unfortunately nrbook.com uses a copy-protected pdf format that requires a special plugin for Adobe Reader to use. If that is too cumbersome to install on your device, the book is also on 2 hour reserve in the Cooley Science Library.

Unit	Topic	Moler	Num Rec
1	Rootfinding	4.1-4.4	9.0-9.2, 9.4, 9.6
2	Linear Systems	2.1-2.6,2.8-2.10	2.0-2.3
3	Interpolation	3.1-3.6	3.0-3.1,3.3
3b	Least Squares	5.0-5.1	15.0-15.1
		(all of 15 in Num Rec is good for those of you destined for econometrics)
		Note: we won't be doing justice to least squares in this class. Take Econ Stats.
4	Derivatives and integrals	6.1,6.2,6.4,6.5	4.0-4.3; 5.7
5	Initial Value Problems (ODE-IVPs)	7.1-7.5,7.7-7.15	16.0-16.2, 16.6
6	Boundary Value Problems (ODE-BVPs)	11.1-11.4	17.0,17.1, 17.3
	Partial Differential Equations (PDEs)		19.0-19.3

Useful webpages for this class:

An basic tutorial for matlab (put out by University of Michigan and Carnegie-Mellon University)
Fairly complete guide to writing functions using matlab (By Gerald Recktenwald).
A fairly reasonable description of why Gaussian Elimination is O(n^3) upon first inspection. It also hints that there are methods which are faster than this.
An attempt to describe how to connect to the lab and run matlab remotely. If this works for you, you can edit and run scripts without actually being in the lab.

Matlab website resources:

Matlab Examples in their documentation section.
Matlab Tutorials (some video, some text).