petermchale / math105a

Numerical analysis course in Python

Math 105A Numerical Analysis

Instructor: Peter McHale

Course webpage: https://eee.uci.edu/17f/44635

Getting set up for the Lab section (the software below is FREE!)

In what follows, you will need to access the 'command line'. On a Mac, this is done by opening the Terminal app. On the lab (Windows) machines, this is done via Start -> Anaconda Prompt (type this into the search field to locate the program). Your TA will help you with this.

If on your own machine, install Python and Jupyter by installing Anaconda (Python 3.x version). Anaconda conveniently installs Python, the Jupyter Notebook, and other commonly used packages for scientific computing. Please type

conda create -n math105A python=2 ipython-notebook --yes

at the Terminal (Mac) or Anaconda (Windows) prompt to create a conda environment using Python 2. Then activate the environment. Your TA will help you with this.

If you are working at a lab computer, which already has Python and Jupyter installed, then type python --version at the command prompt to check the version of Python that is installed. It will hopefully say Python 2.x, which is what we will use in this course.

Open a Jupyter notebook by navigating to the directory in which it is located (the cd command is useful here, as is the ls command in Terminal or equivalently, the dir command in Windows) and typing jupyter notebook at the command prompt. A tab will open in your browser revealing the contents of the current directory. Seek out the TA for help.

Once you’re finished editing/running your notebook, press ctrl-c twice at the command prompt.

If Jupyter complains that a specific package is missing when you run your notebook, then return to the command line, execute conda install <name of package>, and re-run the offending notebook cell.

PLEASE BRING USB DRIVE TO LAB TO SAVE YOUR WORK.

Schedule

In the table below, Sections refers to sections of Numerical Analysis, R.L. Burden and J.D. Faires, 9th Edition. If you're new to programming, then you might like to consult the following book, though it is by no means compulsory: Scientific Computation: Python Hacking for Math Junkies, by B. Shapiro.

Click on the links to see nbviewer-rendered versions of the lecture.

Wk	Date	Lec	Sections	Topics
0	9/29	1	1.1	Review of calculus
1	10/2	2	1.2	Round-off errors and computer arithmetic
	10/4	3	2.1	Bisection Method
	10/6	4	2.2	Fixed-point iteration
2	10/9	5	2.3	Newton’s method
	10/11	6	2.4	Error analysis/Convergence
	10/13	7	2.6	Zeros of polynomials
3	10/16	8	6.1	Gaussian elimination
	10/18	9	6.1	Algorithm complexity
	10/20	10	6.1, .2	Algorithmic deficiencies of Gaussian elimination
4	10/23	11	6.2	Pivoting strategies
	10/25	12	6.3-6.4	Matrix inversion and Determinants
	10/27	13	6.5	LU factorization
5	10/30	14	6.5	PLU factorization
	11/1			Review of previous exams
	11/3		1, 2, 6	Midterm Exam
6	11/6	15	7.1	Norms of vectors and matrices
	11/8	16	7.2, 9.1	Eigenvalues, Spectral radius
	11/10		No class	Veterans’ Day
7	11/13	17	7.3	Iterative Methods: Jacobi Method
	11/15	18	7.3	Gauss-Seidel Method; convergence
	11/17	19	7.4	Accelerating convergence
8	11/20	20		Applications of Linear Systems
	11/22	21	9.1	Orthogonality (Gram Schmidt)
	11/24		No class	Thanksgiving
9	11/27	22	9.3	Power method
	11/29	23	9.5	QR factorization
	12/1	24	9.5	QR factorization (cont); QR eigenvalue algorithm
10	12/4	25	9.6	SVD theory
	12/6	26	9.6	SVD examples
	12/8	27		Review of previous exams
11	12/11		1, 2, 6, 7, 9	Final Exam 1.30pm – 3.30pm

Acknowledgements

The first half of this course is adapted from Tom Trogdon's course.