**Class meets:** MTWF 8:35am - 9:25am

**Where:** MWF: LCB 323, T: JTB 320

**Textbook:** Burden and Faires, Numerical Analysis, Thomson Brooks/Cole, eighth edition.

**Prerequisites:** Math 5610 or instructor's permission. Basic
Matlab programming.

**Instructor:** Fernando Guevara Vasquez

**Office:** LCB 212

**Office hours:** MTW 9:30am-10:30am or by appointment

**Phone number:** +1 801-581-7467

**Email:** fguevara(AT)math.utah.edu

(replace (AT) by @)

**Homeworks** 40%, **Project** 15%, **Midterm** 15%, **Final** 30%. Expect between 6 and 8 homeworks during the semester. Projects will be announced in class.

- Kincaid and Cheney, Numerical Analysis: Mathematics of Scientific Computing, Brooks/Cole 2001
- Stoer and Burlisch, Introduction to Numerical Analysis, Springer 1992
- Trefethen and Bau, Numerical Linear Algebra, SIAM 1997
- Golub and Van Loan, Matrix Computations, John Hopkins 1996
- Brenner and Scott, The Mathematical Theory of Finite Elements, Springer 2002
- Ciarlet, Finite Element Methods for Elliptic Problems,SIAM 2002
- LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations,SIAM 2007

- Guidelines for numerical experiments
- Submitting you homework electronically
- Printing to a PS or PDF file
- Installation instructions for Matlab and Octave
- How to access the computer lab

- The solutions to the practice final are here: final_practice_sol.pdf.
- The solutions to
**HW5**are here: hw05sol.pdf.

- Here is a practice final exam: final_practice.pdf. We will solve this together on the last day of classes
*Wed April 27*. It is maybe 10-20% longer than the actual final. - The schedule for the talks is as follows. The order of the talks is up to the speakers. To give all time possible to your classmates,
**please plan on coming on time on both Monday and Tuesday**.*Monday 04/25*: Tim (Burgers equations), Steven (truncated SVD), Zach (coupling heat equation and bar equation), James (eikonal equation, visibility and other applications)*Tuesday 04/26*: Christine and Javier (eikonal equation and applications), Quinton (truncated SVD), Katrina (advection diffusion using Lax-Wendroff in 2D), Xiaoshi (differentiation using wavelets)

- There is no need for having slides for your presentation. It is completely OK to bring your numerical experiments as a PDF and present your project on the board.
- I will bring my laptop. If you will be using my laptop for your presentation, I strongly recommend you bring your presentation or plots in PDF (on a USB key, online, etc…). If you decide to use your laptop, come a few minutes earlier to make sure all works well with the projector.

- The applications of SVD we saw were:
- Face recognition using eigenfaces by Christopher de Coro
- Ranking and web search, Bryan and Leise, “The $25,000,000,000 eigenvector: the linear algebra behind Google”, SIAM Review 48, pp569-581, also available from the authors webpage.

- The final exam review sheet is here: final_rev.pdf.
- The class notes for the Singular Value Decomposition are here: math5620s11_12.pdf.

**Homework 6**is optional,**extra credit**and is available here: hw06.pdf. It is due on the last day of class*Wed 04/27*.

- Here is the calendar for the last two weeks of classes:
- Tue 04/19 – SVD applications: eigenfaces
- Wed 04/20 – review for final 1/2
- Fri 04/22 – review for final 2/2
- Mon 04/25 – project presentations 1/2 (Tim, Steve)
- Tue 04/26 – project presentations 2/2
- Wed 04/27 – practice final solutions
- Fri 04/29 – final (8am-10am in LCB 323)

- Please email me your day of preference for the project presentations.
- If I do not hear from you by Friday, you will be assigned a presentation day. Please note that your project grade will be 20% for the presentation and 80% for the report. The project presentation should be no more than say 10 minutes and should be understandable for your classmates. Project reports are officially due on the last day of classes (04/29) but I can accept them up to Thu 05/12.
- Class notes for eigenvalues are here: math5620s11_09.pdf (some linear algebra basics, power method, inverse iteration, Rayleigh Quotient iteration), math5620s11_10.pdf (reduction to Hessenberg or tridiagonal form, Householder reflectors), math5620s11_11.pdf (simultaneous iteration, QR algorithm).

**HW4**solutions are here: hw04_sol.pdf.

- The class notes for the finite element method are here: math5620s11_08.pdf.
- Demo codes that were shown in class are here: rg.m (P1 1D elements) and fem2d.m (P1 2D triangular elements).
**HW5**is due next*Tuesday April 12*and is available here: hw05.pdf.

- The class notes for last week and the beginning of this week are here: math5620s11_07.pdf. We covered numerical methods for hyperbolic problems (Lax-Friedrichs, Euler, Lax-Wendroff, upwind and Leapfrog). We have also started doing finite elements, the notes will be posted later.
- The Matlab code I used to demonstrate different methods for solving the advection equation is here: hyper.m.

**HW4**is due*Fri 03/11*and is available here: hw04.pdf.- Some project suggestions are here: projects.pdf. You must tell which project you want to do by
*April 1st*.

- The solutions to the practice exam are here: exam1_practice_sol.pdf.

- Solutions to
**HW3**are here: hw03_sol.pdf.

- Here is a
**practice midterm**: exam1_practice.pdf. We will solve this together next Monday.

- The
**Midterm**will be on*Tuesday March 1st*in class.- This is a 50min exam. Please
**plan on arriving 5min early**. - A study sheet is available here: exam1_rev.pdf.
- No books or notes are allowed.
- A one-sided, letter-sized, handwritten cheat sheet is allowed.
- Calculators are not needed and are not allowed.

- This is a 50min exam. Please
- The class notes for last week and Tuesday are here: math5620s11_06.pdf. Please note the midterm covers everything up to p103 in the notes.
- Solutions to
**HW2**are available here: hw02_sol.pdf. - Here is a code for computing the absolute stability region of a linear multistep method: absstab.m
- The schedule for the lectures remaining before the midterm:
*Wed 02/23*:**Practice midterm**will be posted in this website.*Fri 02/25*:**HW3**will be graded and handed back. Specific questions on material will be answered.*Mon 02/28*:**Practice midterm**solutions.

- In
**HW3**you are requested to use Runge-Kutta 4 for systems (rk4.m) to compute the solution to the IVP involved in the shooting methods. Please see this example usage (with sample output inside): rk4_example.m - We do not have class next Monday as it is President’s day. You can turn in
**HW3**on*Tuesday 02/22*. **Midterm 1**is coming and will tentatively be on*Monday Feb 28*.

**HW3**is due*Fri February 18 2011*and is available here: hw03.pdf.- Please pay particular attention to the implementation tips as they should make your codes much easier to write than in your book.
- The Runge-Kutta 4 code for systems is here: rk4.m
- Reference output for the linear and non-linear shooting methods is here: drvlinshoot.m and drvnonlinshoot.m.

- The class notes for the week are here: math5620s11_05.pdf and incude the shooting and finite differences method for linear and non-linear BVP.
- Solutions for
**HW1**are here: hw01_sol.pdf

**Homework 2**is due*Friday Feb 11*and is available here: hw02.pdf.- The class notes up to Wednesday are here: math5620s11_04.pdf. We finished covering iterative methods for solving linear systems and we should start partial differential equations with finite differences on Friday.

- The notes for the week are here: math5620s11_03.pdf. We covered iterative methods (Richardson, Jacobi, Gauss-Seidel) and their convergence properties. We also started Chebyshev acceleration.
- If you want to know more about direct methods for sparse systems, look at this book and talk by Tim Davis from the University of Florida. The very brief introduction to these methods we saw last week was based on this talk.

- The class notes for last week and today are here: math5620s11_02.pdf. We finished with direct methods for solving linear systems, including a brief intro to sparse direct methods. We also started iterative methods for solving linear systems.
**HW1**is available here: hw01.pdf and is due*Mon January 31*. Here is sample code for testing your LU routine: test_mylu.m.

- The notes for the week are here: math5620s11_01.pdf. We covered the LU and Cholesky factorizations.
- Here is a short linear algebra refresher: linalg.pdf. Please make sure you are familiar with Chapters 6.3 and 6.4 in your book.

You should receive an email announcement on Tuesday, please make sure you got it and contact me if you did not. I am using your uxxxxxx@utah.edu email address by default. Please let me know if you want me to use another email address.