**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

- This is a friendly reminder that the final for this class on:

Thursday May 6 8am-10am in our regular classroom LCB 323.

- Please come 5-10min earlier. We will start at 8am sharp.
- Bring your own paper. You may also bring two letter-sized handwritten cheat sheets (or one double sized letter sized cheat sheet).
- Please do let me know ASAP (no later than Tuesday May 4 evening) if you cannot come to the Final at the prescribed time. It is possible to arrange for another testing time on the same day (starting 5pm-6pm), however I need to know ahead of time to make arrangements with the testing center.
- Project reports will be accepted until Wednesday May 12.

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

- For the
**final review**we will meet on*Fri May 30*(8:35am-9:25am) in room**JTB 320**(the same room we had on Tuesdays). We will review together the solutions to the practice final.

- Here is the final review sheet: final_rev.pdf and a practice final: final_practice.pdf.
- The schedule for the project presentations is as follows:
*Mon*: Patrick (ADI method)*Tue*: Andy (2D advection diffusion), Seong Jun (3D anisotropic diffusion equation), SangWook (singular value decomposition), Michael (domain decomposition)*Wed*: Jan (Navier-Stokes), Savas (why RKF fails)

- As a friendly reminder: the final for this class is Thu May 6 8am-10am in LCB 323.
- The solutions for
**HW4**are here: hw4_sol.pdf - The solutions for
**HW5**are here: hw5_sol.pdf

- Here are the class notes for finite elements: na012.pdf, na013.pdf, na014.pdf, na015.pdf, na016.pdf. We covered 1D and 2D finite elements and some error estimates. It is probably easier to read the recap first (na016.pdf).
- The implementation of 2D P1 triangular elements is based on Remarks around 50 lines of Matlab: short finite element implementation by Alberty, Carstensen and Funken. (There are other very instructive implementations of finite elements in the software section of Carsten Carstensen’s webpage).
- Here is an
**optional**assignment**HW6**: hw6.pdf on finite elements, that is due*Wed April 21*in class, as we will do it together during the 04/21 lecture. If you choose to do this assignment, your lowest HW grade will be dropped from the HW average. - The schedule for the rest of the semester is as follows:
*Th 04/15*: finish up FEM + 1D implementation*F 04/16, M 04/19, T 04/20*: Optimization*W 04/21*: HW6 done in class*F 04/23*: Review for the final + practice final*M 04/26, T 04/27, W 04/28*: project presentations and practice final solution

**HW5**is here: hw5.pdf and is due*Fri April 2nd 2010*.- The latest class notes for eigenvalues are here: na009.pdf (some linear algebra basics, power method, inverse iteration, Rayleigh Quotient iteration), na010.pdf (reduction to Hessenberg or tridiagonal form, Householder reflectors), na011.pdf (simultaneous iteration, QR algorithm).
- The references we used for eigenvalues algorithms are:
- Threfethen and Bau, Numerical Linear Algebra, SIAM 1997
- Golub and Van Loan, Matrix Computations, 3rd edition, John Hopkins, 1996

- Here are the project guidelines, calendar and some suggested projects for the class: projects.pdf. On Friday’s lecture we will spend about 15min talking about these projects.

**HW4**is here: hw4.pdf and is due*Fri March 19 2010*.**Reminder**: unless otherwise posted we now have class every**Thursday**at the usual time in LCB 215. Thank you for your flexibility.**Projects**will be announced this Friday. I expect you choose a project by the first lecture after the Spring break.

- Lecture notes are here: na006.pdf, na007.pdf and covers the finite differences method (in 1D and multidimensional) for elliptic and parabolic problems (corresponds to 12.1-12.2 in your book, however this material comes from Leveque’s book).
- Solutions to
**HW2**are here: hw2_sol.pdf and to**HW3**here: hw3_sol.pdf. - Solutions to the
**practice exam**are here: exam1_practice_sol.pdf

- The
**Midterm exam**will be next*Friday February 26*in class. The material covered is: initial value problems (5.1-5.12) and boundary value problems (11.1-11.4).- A review sheet for the exam is 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.
- The lecture on
*Thu Feb 25*will be a review for the midterm. We will solve this practice midterm: exam1_practice.pdf in class.

**Cancelled lectures**:*Mon March 1st*and*Tue March 2nd*.**Make up lecture next week**:*Thu Feb 25*in LCB 215 at the usual time.- The deadline for
**HW3**has been extended to next*Mon Feb 23*. You should get it back graded by*Thu Feb 25*(no late homework will be accepted after this date). **HW2**will be given back graded next Monday.

**HW3**is due*Friday Feb 19*and is available here hw3.pdf.- Please do read the
**implementation tips**as they should make it easier for you to write the codes. You will end up with codes that are easier to write, read and debug than the ones in your book.**Please ask**if there is something not clear about these instructions. - The numerical solution for Problems 2 and 3 will be slightly different (because the methods are different). Here are some numbers for comparison: drva.m, res_drva.txt (for 11.1.3 a,b) and res_drvb.txt (for 11.2.3 a,b,c). These solutions have the same number of accurate digits as the book’s solutions.

- Please do read the
**Class notes**for the week are here: stiff differential equations, A-stability, region of absolute stability (na004.pdf) and boundary value problems 11.1-11.4 (na005.pdf).**Absolute stability region**: Here is a code for plotting the absolute stability region of a linear multistep method: absstab.m.**Solutions to HW1**are available here: hw1_sol.pdf.**Reminder:**There is an extra lecture tomorrow*Thu Feb 11*at the usual time in LCB 215.**Cancelled lectures:**There will be no lecture on*Tue Feb 16*and*Wed Feb 17*, as I am gone for an interview. Two additional lectures will be scheduled on Thursdays 02/25 and 03/04 at the usual class time (room TBA). Thank you for your understanding!

**Homework 2**is available here: hw2.pdf and is due*Wed Feb 10 2010*.- Class notes for the past weeks are available here: na002.pdf (Multistep methods, RKF and extrapolation), na003.pdf (stability, difference equations fundamentals, local truncation error and global truncation error theorems, systems and higher order ODEs).
**Reminder**: No lecture this*Friday Feb 5 2010*.

**Homework 1**is due on*Mon Feb 1st*and is available here: hw1.pdf.**Reminder**: extra Thursday lecture tomorrow in LCB 215 8:35am-9:25am.

- We will have additional lectures on
**Thu 01/21**,**Thu 02/11**and**Thu 02/18**to substitute for the lectures that I cancelled. I will remind you about these in class and by email. The room is*LCB 215*and we meet at the regular class time*(8:35am-9:25am)*. Thank you for your patience and understanding. - The lecture notes for the week are here: na001.pdf.

You should have received an email announcement today, 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.

- There will be no lecture on W 01/27, F 01/29 and F 02/05 (I will be gone interviewing). We will catchup these lost lectures on Tuesdays and Thursdays on dates to be announced.