Math 5620/6865 (Spring 2010)

Class information

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.

Contact information

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)
(replace (AT) by @)


The syllabus is available here: syllabus.pdf


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

Reference books

Other useful information

Announcements [RSS]

(Mon, May 3, 2010, 03:30 PM)

Final exam reminder.
  • 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.

(Thu, Apr 29, 2010, 02:46 PM)

Final practice solutions.

(Wed, Apr 28, 2010, 03:46 PM)

Final review.
  • 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.

(Fri, Apr 23, 2010, 05:05 PM)

Practice final and project presentations.
  • 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)

(Wed, Apr 21, 2010, 02:03 PM)

Finite Element Method codes.

Here are some finite element codes that we saw in class. For 1D: rg.m and for 2D fem2d.m

(Tue, Apr 20, 2010, 10:23 PM)

Final Exam reminder, HW 4 and HW 5 solutions.
  • 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

(Wed, Apr 14, 2010, 10:33 AM)

Finite Element Method.
  • 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

(Thu, Mar 18, 2010, 11:16 PM)

Homework 5.
  • 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

(Thu, Mar 11, 2010, 04:14 PM)

  • 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.

(Thu, Mar 11, 2010, 12:17 AM)

Homework 4.
  • 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.

(Fri, Mar 5, 2010, 11:10 PM)

Hyperbolic problems.
  • Class notes for the week are here: na008.pdf. We covered hyperbolic problems.
  • The demo for different methods for the advection equation is here: hyper.m
  • Cancelled lectures: Mon March 8 and Tue March 9. Additional lecture: Thu March 11.

(Wed, Feb 24, 2010, 11:22 PM)

HW3 and practice exam solutions.
  • 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

(Fri, Feb 19, 2010, 03:17 PM)

  • 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.

(Wed, Feb 10, 2010, 11:02 AM)

Homework 3, class notes and makeup lectures.
  • 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.
  • 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!

(Wed, Feb 3, 2010, 02:08 PM)

Homework 2 and class notes.
  • 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.

(Wed, Jan 20, 2010, 11:58 AM)

Homework 1.
  • 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.

(Tue, Jan 19, 2010, 11:20 AM)

Make up Thursday lectures.
  • 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.

(Wed, Jan 13, 2010, 11:38 AM)

Email Announcements.

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 email address by default. Please let me know if you want me to use another email address.

(Mon, Jan 11, 2010, 10:45 PM)

Cancelled lectures.
  • 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.