Math 5610/6860 Intro to Numerical Analysis (Fall 2009)

Class information

Class meets: MTWH 8:35am - 9:25am
Where: LCB 225
Textbook: Burden and Faires, Numerical Analysis, Thomson Brooks/Cole, eighth edition.
Prerequisites: Multivariate calculus (e.g. Math 2210 Calculus III), basic linear algebra (e.g. Math 2250 or Math 2270) and basic 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]

(Tue, Dec 8, 2009, 10:03 AM)

Final exam practice problems solutions.
  • The solutions to the final exam practice problems are here: fp2sol.pdf.
  • As a reminder the Final exam is Wednesday Dec 16 2009, 8am-10am in our usual classroom (LCB 225). Good luck in this and other finals you have.

(Mon, Dec 7, 2009, 10:45 PM)

Practice final problems and Q&A session.
  • More practice final problems are here: fp2.pdf. Solutions will be posted on 12/8.
  • The especial Q&A session will be held on Tue 12/8, 11am-12pm in Naval Science 202.

(Thu, Dec 3, 2009, 10:43 AM)

Final Exam, practice problems and study sheet.
  • As a reminder the Final exam is Wednesday Dec 16 2009, 8am-10am in our usual classroom (LCB 225). The conditions for this exam are the same as for the midterm: no notes, calculators or books are allowed. You may bring your own paper or use the paper that will be provided. You may also bring two one-sided (or one two-sided) letter-sized and handwritten cheat sheet.
  • Here is the final study sheet that we saw yesterday in class: final_study_sheet.pdf.
  • Today we did some practice final problems: fp1.pdf. The solutions are here: fp1sol.pdf.
  • I expect to give out 3-4 problems at every lecture until the end of the semester so that you have an idea of typical final exam problems.

(Mon, Nov 30, 2009, 03:19 PM)

Presentations, lecture notes and HW solutions.
  • Solutions for HW5 are here: hw05_sol.pdf.
  • Solutions for HW7 are here: hw07_sol.pdf.
  • Lecture notes for the week are here: math5610_012.pdf. We covered the Fast Fourier Transform with application to fast convolution. The reference code for this lecture is fftconv1d.m
  • We will have a Q&A session for the final on Tue 12/8 11am-12pm, room TBA.
  • You should have received an email today with the project presentation dates.

(Tue, Nov 24, 2009, 10:50 AM)

HW 6 Solution and Class notes.
  • Class notes for the week are here: math5610_011.pdf and include discrete least squares, least squares approximation, Chebyshev polynomials, and trigonometric interpolation.
  • The material that will be included in the final is up to Chapter 8, we should be able to finish this chapter with the Fast Fourier Transform tomorrow. I will prepare a set of problems that you do not need to turn in but that could help you with the exam. Solutions will be provided.
  • Solutions to HW6 are here: hw06_sol.pdf.

(Mon, Nov 16, 2009, 02:18 PM)

  • For the project presentations, please email me with your preference for either 12/3, 12/7 or 12/8.
  • Lecture notes for the past week are here: math5610_010.pdf and include iterative methods for solving linear systems (Jacobi, Gauss-Seidel, conjugate gradient). This finishes Chapters 6 and 7. We will move to Chapter 8 (Approximation theory) either tomorrow or on Wednesday.
  • HW6 due Mon Nov 23:
    • Problems B&F 7.3.6, 7.3.8, 7.3.14 (only parts b,d). For Gauss-Seidel and SOR: do not use backslash to solve the triangular system. Write your own forward substitution function. In addition to the results that are asked in the textbook, please do a table comparing the number of iterations required to converge for Jacobi, Gauss-Seidel and SOR for both systems b,d.

(Mon, Nov 9, 2009, 04:53 PM)

Lecture notes and last two lectures.
  • The lecture notes covering Romberg integration, adaptive integration methods, direct methods for linear systems, and iterative refinement are available here: math5610_009.pdf
  • There will be no lecture on Wed Dec 9 and Thu Dec 10. We will make up for this time by spending less time reviewing homeworks on Tuesdays. I you are curious, I will be in the SIAM PDE conference in Miami, Florida.

(Thu, Nov 5, 2009, 11:29 PM)

Homework 6.
  • HW6 is here: hw06.pdf and is due Thu Nov 12. The class notes for the week will be posted online soon.

(Fri, Oct 23, 2009, 05:25 PM)

HW5 Typo and Office hours.
  • There will be no office hours on Monday 10/26
  • There is a typo in HW5 Problem 2 b: the correct expression for h is: h = 10.^(0:-1:-20) (use .^ operator and the minus sign in front of 20 was missing)

(Thu, Oct 22, 2009, 07:30 PM)

Projects and HW5.
  • Lecture notes for the week are here: math5610_008.pdf. We covered numerical differentiation, Richardson extrapolation, numerical integration, composite integration rules and Gaussian quadrature rules.
  • Projects: I’ve included project suggestions, important deadlines and what I am expecting from you here: projects.pdf.
    • You should tell me before Nov 2 the project you would like to do.
    • You can also propose your own project, however you have to run it by me to make sure it is appropriate.
  • HW5 is due on Thu Oct 29 and is here: hw05.pdf.

(Mon, Oct 19, 2009, 08:23 AM)

Midterm exam.
  • The average for the midterm was 76
  • The solutions to the midterm are here: midterm_sol.pdf
  • You should receive an email today with a partial grade for the class
  • Here is a histogram for the midterm grades:

(Tue, Oct 6, 2009, 05:44 PM)

Practice Midterm Solutions.

(Fri, Oct 2, 2009, 05:44 PM)

Practice Midterm Exam.
  • A study sheet for the Thursday Oct 8 Midterm is here study_sheet.pdf.
  • The practice midterm we will do together next Wednesday is here: midterm_practice.pdf.
  • HW3 solutions are here: hw03_sol.pdf.
  • The conditions for the midterm are:
    • No calculators, books or notes are allowed. Of course I will make sure any calculations in the exam are simple. If the reasonment seems sound I will be lenient with any calculation errors.
    • Bring your own paper.
    • You may bring a letter-sized, single sided, hand-written cheat sheet.
    • You should justify all your work.
    • Please come on time. We will start the exam at 8:35am.

(Tue, Sep 29, 2009, 10:46 PM)

Homework 4, problem 6 hint.
  • In HW4 Problem 6 ( extra credit ) you are asked to prove Leibniz formula for divided differences. The proof is longer and more challenging than I thought so the main steps are here: hw04_hint.pdf.
  • Lecture notes for Monday are here: math5610_006.pdf.
  • Expect a practice midterm by the end of the week (we will do it together on Wed Oct 7).

(Thu, Sep 24, 2009, 12:02 PM)

Homework 4, Midterm Thu 10/08.
  • HW4 is here: hw04.pdf and is due Mon Oct 5. It includes divided differences that we will finish next Monday, but you sould be able to do half of this.
  • The Midterm Exam will be on Thu Oct 8 and will include sections 1.1-1.3, 2.1-2.6 and 3.1-3.2.
  • HW4 will be graded for Tue Oct 6 so that you can study from it for the exam. Homework will be due in class, no late homework will be accepted.
  • We will do a Practice Midterm exam together during the class before the exam (Wed Oct 7).
  • Lecture notes for the week are here: math5610_005.pdf
  • Solutions for HW2 are here: hw02_sol.pdf

(Mon, Sep 21, 2009, 08:14 AM)

HW 3 Typo.
  • On HW3, Problem 1:
    • You may choose to do any two of the four functions in B&F 2.4.2 and 2.4.4 (of course being consistent in order to compare the two methods). Since I omitted this when writing HW3, the other two functions will be counted as extra credit.
    • Unfortunately there is a typo in the function given in the textbook B&F 2.4.2 b. The correct one should be the polynomial x 6 + 6 x 5 + 9 x 4 – 2 x 3 – 6 x 2 + 1 (the incorrect version has as first term x 2). Thanks to SangWook for spotting this one.
  • We will have a Q&A session tomorrow in the usual classroom.

(Thu, Sep 17, 2009, 12:36 PM)

Homework 3.
  • HW3 is here hw03.pdf and is due on Thu September 24 in class.
  • Lecture notes for the week are available here: math5610_004.pdf.
  • The solutions for HW1 are available here: hw01_sol.pdf.
  • Next week we will finish Section 2.6 and cover sections 3.1-3.3 on polynomial interpolation.

(Thu, Sep 10, 2009, 04:34 PM)

Lecture Notes 3.

(Thu, Sep 10, 2009, 03:49 PM)

Homework 2.
  • HW2 is here hw02.pdf and is due on Thu September 17 in class.
  • Next week we shall finish Section 2.4 (adapting Newton’s method to multiple roots). We will continue with Sections 2.5, 2.6, 3.1.

(Thu, Sep 3, 2009, 11:20 AM)

Lecture Notes 2.
  • Lecture notes for the week are available here: math5610_002.pdf.
  • Next Tuesday will be a question and answer session, in the usual classroom.
  • So far we have done sections 1.1-1.3, 2.1 and 2.3. Next week we will do sections 2.2 and 2.4.

(Tue, Sep 1, 2009, 11:17 AM)

Computer Lab 2.
  • The handout for computer lab 2 is here: computerlab02.pdf. The solutions with considerably more comments than what we did together are here: cl02_p1.m, cl02_p2.m, cl02_p3.m. The convergence rate estimation is done without resorting to Matlab’s linear fitting routine by solving a linear least squares problem (cf linear algebra class).

(Mon, Aug 31, 2009, 11:36 PM)

Homework 1.
  • HW1 is due on Thu Sep 10 and is available here: hw01.pdf.
  • Homework policy
    • The preferred method to turn in your HW is in class. You can also send it by email (see below for guidelines), leave it under my office door or in my mailbox. Please email me every time you use any of this alternatives.
    • Typed solutions are not required.
    • You may work in pairs, in that case turn in only one writeup.

(Fri, Aug 28, 2009, 04:51 PM)

Lecture Notes 1.
  • Lecture notes for the week are available here: math5610_001.pdf.
  • Your first homework will be posted on the website on Monday.
  • I sent an email on 8/25 to your u?????? email account. By default this is the email I will use to make important announcements (HW, exams etc…). If you did not receive this email, please contact me ASAP. Please let me know if you prefer to receive announcements to another email account.

(Tue, Aug 25, 2009, 11:04 AM)

Computer Lab 1.

The objectives of this computer lab were:

  • Log in the Math department system. If you haven’t tried to login please see access for information about your login/password. If this does not work, contact me ASAP.
  • Familiarize with Matlab and its environment. The Matlab installation instructions has some tutorials so you can be quickly up and running with Matlab or Octave in your system. I recommend the following (in order of increasing difficulty):
  • Approximate log with Taylor’s theorem. This is to make yourself familiar with Matlab. For the flyer see: computerlab01.pdf. The code we wrote together is here: computerlab1.m (the main script), logtaylor1.m (the straighforward for-loop based implementation) and logtaylor2.m (the niftier array based implementation). Some of you asked for the command history of the session. It is here: computer_lab_hist.txt. The actual Taylor approximation will be covered in class tomorrow.

(Sun, Aug 23, 2009, 10:40 PM)

Next computer labs.

On Tue Aug 25 and Tue Sep 1st class will meet in the computer lab LCB 115 at the usual time.