Math 5620/6865 (Spring 2011)

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]

(Wed, Apr 27, 2011, 04:30 PM)

Practice Final Solution.

(Fri, Apr 22, 2011, 02:49 PM)

Practice Final and project presentations.
  • 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.

(Thu, Apr 21, 2011, 10:46 PM)

Applications of SVD.

(Wed, Apr 20, 2011, 08:24 AM)

Final Exam Review.

(Mon, Apr 18, 2011, 10:40 AM)

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

(Mon, Apr 18, 2011, 09:59 AM)

Project Presentations.
  • 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).

(Tue, Apr 12, 2011, 01:29 PM)

HW 4 Solution.

(Tue, Apr 5, 2011, 03:02 AM)

Homework 5.
  • 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.

(Fri, Mar 18, 2011, 01:23 PM)

Hyperbolic Problems.
  • 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.

(Fri, Mar 4, 2011, 03:55 PM)

Homework 4.
  • 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.

(Mon, Feb 28, 2011, 01:21 PM)

Practice Exam Solutions.

(Fri, Feb 25, 2011, 11:54 AM)

HW3 Solutions.

(Wed, Feb 23, 2011, 09:10 PM)

Practice Midterm.
  • Here is a practice midterm: exam1_practice.pdf. We will solve this together next Monday.

(Tue, Feb 22, 2011, 11:42 PM)

  • 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.
  • 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.

(Wed, Feb 16, 2011, 04:54 PM)

Runge-Kutta 4.
  • 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.

(Fri, Feb 11, 2011, 09:40 PM)

Homework 3.
  • 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

(Thu, Feb 3, 2011, 11:39 PM)

Homework 2.
  • 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.

(Fri, Jan 28, 2011, 10:23 AM)

Iterative methods for solving linear systems.
  • 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.

(Mon, Jan 24, 2011, 06:18 PM)

Homework 1.
  • 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.

(Fri, Jan 14, 2011, 11:26 AM)

LU and Cholesky factorization.
  • 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.

(Mon, Jan 10, 2011, 11:42 PM)


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