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.