**Class meets:** MTWF 10:45am - 11:35am

**Where:** MWF: LCB 323, T: JWB 308

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

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

**Instructor:** Fernando Guevara Vasquez

**Office:** LCB 212

**Office hours:** MTW 2pm-3pm 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

- Please check your U-mail account for your grades for this class, the final and projects.
- Here are histograms for the grades for the class:

`histogram for final (mean = 115.2) histogram for class grades 150 : * 110 : 140 : * 100 : * 130 : ** 90 : ******* 120 : ***** 80 : *** 110 : ** 70 : *** 100 : 60 : 90 : ** 50 : ** 80 : * 70 : *`

grade scale:

A 91, A- 85,

B+ 79, B 73, B- 67,

C+ 61, C 55, C- 49,

D+ 43, D 37, D- 31,

E 0

- Your finals are available for pick up. You can come either tomorrow 9-2pm or some other time (provided you email me the day before so that I can expect you).

- Here are the practice final solutions: final_practice_sol.pdf.

- Here is a practice final: final_practice.pdf and a review sheet: final_rev.pdf.
- The class notes for eigenvalues are here math5620s12_11.pdf.

- The
**final**will be now a take home final. (Several of you asked me to change the exam date).- You must work individually and with a 3h limit of time.
- The final exam will be handed out on
*Tue 04/24*in class and is due on*Wed 04/25***in class**, it will not accepted late. - You may use your notes and/or the class text book. No computers or calculators are required.
- There will be a practice final done in class on the
*Mon 04/23*lecture.

- The
**projects**will be solely evaluated using your reports, there will be no presentations. The**project reports**are due on the last day of classes*Wed 04/25*, but may be accepted until*Mon 05/07*at the latest. - I have updated the projects.pdf to fix a typo regarding the 2D wave equation project.
- The notes for finite elements are here: math5620s12_10.pdf. We have covered 1D P1 finite elements, basic error estimates and 2D P1 finite elements.
- The 1D P1 finite element code is here: rg.m and the 2D P1 finite element code on triangles is here: fem2d.m.

- Here are the notes for this week: math5620s12_09.pdf. We finished covering hyperbolic problems and multidimensional problems.
**Homework 5**is due*Fri April 6*and is available here: hw05.pdf.

- Here are the class notes for the week: math5620s12_07.pdf and math5620s12_08.pdf. We finished covering elliptic problems (the Laplace equation), parabolic problems (the heat equation) and the Lax equivalence theorem. We just started with hyperbolic problems (the advection equation).

- Here is a description for the projects: projects.pdf. You have to
**decide**for a project (and email me your choice)**before***Mon April 02*(but the earlier the better).

**Homework 4**is due on*Mon March 19*and is available here: hw04.pdf.- Here is the sample code: prob1_sample.m, prob2_sample.m, rk4.m, rk4_example.m, linfd.m, linshoot.m, nonlinfd.m, nonlinshoot.m.

- Here are the notes for Boundary Value Problems (Chapter 11): math5620s12_06.pdf. We are skipping for now the Rayleigh-Ritz method of your book, as it will be covered when we cover Finite Elements.
- Here are the demos we showed in class for the linear and non-linear shoothing methods: shootingdemo.m and shootingdemo2.m. (clicking the mouse will change the initial condition of the IVP associated with the BVP, requires a vectorized version of
`rk4.m`

).

- Below are histograms of the midterm grades and a partial grade. The partial grade was computed by weighting by 55% the HW average and 45% the midterm grade (over 95).

`midterm 1 partial grades 1 110 : ** 100 : ** 100 : **** 90 : *** 90 : **** 80 : 80 : **** 70 : *** 70 : ** 60 : **** 60 : 50 : 50 : * 40 : * 40 : * 30 : 20 : *`

- Here are the solutions to
**HW1**(hw01_sol.pdf) and**HW2**(hw02_sol.pdf). I had forgotten to post these solutions, my apologies!

- The
**solutions to the practice midterm**are here: exam1_practice_sol.pdf. - The
**HW3**solutions are here: hw03_sol.pdf.

- Here is a
**practice midterm**: exam1_practice.pdf. It is harder and longer than the actual exam. We will solve this together on Wed. - Here is the
**review sheet**for the midterm: exam1_rev.pdf.

**Homework 3**is due*Fri Feb 17*and is available here: hw03.pdf.**No late homework please**. You may use the code stubs drvab.m, drvpc.m, ab2.m, ab3.m, ab4.m, ab5.m, a4pc.m. The first two files are drivers and include typical output (which can be double checked with the answers on the back of the book).**Note**: These functions use Runge-Kutta to prime the multistep methods.Please copy`rk4.m`

(from HW2) in the same directory.

- The due date for
**HW2**has been extended to*Mon 02/13*.**HW3**will be posted this Friday and due a week later. - The
**midterm**is scheduled for*Fri 02/24*. Here is a more detailed calendar of the next few lectures*F 02/10*– finish 5.10 theorem proof. LTE for multistep methods. HW3 posted (multistep methods)*M 02/13*– GTE for multistep methods, systems. HW2 due.*T 02/14*– 5.11 – absolute stability.*W 02/15*– linear shooting methods.*F 02/17*– non-linear shooting methods. HW3 due*M 02/20*– no class (President’s day). Practice Midterm Posted.*T 02/21*– finite difference methods for BVP*W 02/22*– Practice midterm solution*F 02/24*– Midterm 1, HW 4 posted

- The notes for multistep methods are here: math5620s12_04.pdf.
- The notes for stability, consistency, convergence are here here: math5620s12_05.pdf.

- Here are the class notes for today: math5620s12_03.pdf. We covered Runge-Kutta-Fehlberg adaptive methods for IVP.
- I mentioned in class that in order to test your Conjugate Gradient you need to use a symmetric positive definite matrix. Examples of this are available in the class textbook. Or you can generate one in Matlab with the following commands
`A = randn(n,n); A=A'*A;`

(which will give a spd matrix with essentially probability 1).

- The class notes for last week and today are here: math5620s12_02.pdf. We covered numerical methods for initial value problems (IVP), including Euler’s method, higher order Taylor methods and Runge-Kutta methods.

- The handwritten notes for iterative methods are here: math5620s12_01.pdf. These notes are from last year, so the numbering in red takes precedence. So far we have covered iterative methods (Jacobi, Gauss-Seidel, SOR, extrapolation and Chebyshev acceleration). We just started with the Conjugate Gradient methood.