Numerical Analysis and Approximation II

Math 702: Numerical Analaysis and Approximation II

Days & Times 	Room 	Instructor 	Meeting Dates
------------------------------------------------------------------------
MWF 10:00am     AB635   Eric Olson      08/27/2012 - 12/19/2012

Course Information

Instructor:
Eric Olson
email:
ejolson at unr edu
Office:
Monday, Wednesday and Thursday 1pm DMS 238 and by appointment.
Homepage:
http://fractal.math.unr.edu/~ejolson/702

Required Text:
J.W. Thomas, Numerical Partial Differential Equations: Finite Difference Methods, Springer Verlag, 2010.

Supplemental Texts:
David Kincaid, Ward Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd Edition, American Mathematical Society, 2002.

J Stoer, R Burlisch, Introduction to Numerical Analysis, 3rd Edition, Springer, 2002.

William Press, Saul Teukolsky, William Vetterling, Brian Flannery, Numerical Recipes, 3rd Edition, Cambridge University Press, 2007.

Roger Peyret, Spectral Methods for Incompressible Viscous Flow, Springer, 2002.

Evans, Blackledge and Yardley, Numerical Methods for Partial Differential Equations, Springer, 2000.

Evans, Blackledge and Yardley, Analytic Methods for Partial Differential Equations, Springer, 1999.

Announcements

[10-May-2013] Programming Project 2

Programming project 2 will be due May 10.

[06-May-2013] Crank-Nicolson Method

The code we wrote in class implementing the Crank-Nicolson method for solution the one way wave equation is available through the web.

[03-May-2013] Final Exam Review

The final exam will cover the following topics:

[26-Apr-2013] Nonlinear Schrodinger Equation

There was a handout given in class discussing 7 numerical schemes for approximating solutions to the nonlinear Schrodinger equation.

[10-Apr-2013] Upwind Methods

The code we wrote in class to compare stable upwind and unstable downwind schemes is available through the web.

[08-Apr-2013] Lax-Wendroff Scheme

Codes based on the code we wrote in class to compare the Lax-Wendroff scheme with the unstable central difference method is available through the web.

[06-Apr-2013] Seventh Computer Workshop

Our seventh computer workshop will be April 6 in DMS 106 from 1pm to 3pm. We learned how to use Octave and Matlab as a shell for calling C code and did some elementary image processing. Note that the class photo we used is available here. The program files are available through the web.

[10-Apr-2013] Programming Project 1

Programming project 1 will be due April 10. Note there was a typo in the numerical scheme of the original version of the project. Namely the definition of the ghost point at K+1 should read 
	unK+1 = - unK-1
in all the stated algorithms. This has been corrected in download available above.

[30-Mar-2013] Sixth Computer Workshop

Our sixth computer workshop will be March 30 in DMS 106 from 1pm to 3pm. We implemented the Douglas-Rachford alternating direction implicit scheme for solving the heat equation. The program files are available through the web.

[15-Mar-2013] Exam 1

Exam 1 will be Friday in class. It will cover the proof of convergence of Euler's explicit method for the heat equation as given in Example 2.2.1 on pages 42-43; definitions of consistency and stability; statement of Taylor's theorem with remainder term; and homework problems 2.3.1ade, 2.3.2a and 2.3.3ab from the book. Please note the following errata: 
The last line in the solution to HW2.3.1(a) should read

    taun = ... = O(Δt) + O(Δx2)

The last line in the solution to HW2.3.2(a) should read

    taun = ... = O(Δt) + O(Δx4)

[12-Mar-2013] Homework One

Homework 1 is due in class on March 12.

[09-Mar-2013] Fifth Computer Workshop

Our fifth computer workshop will be March 9 in DMS 106 from 1pm to 3pm. We used Maple to derive finite difference scheme and generate code to solve the Kuramoto-Sivashinsky equation. We also created animated plots. The program files are available through the web.

[02-Mar-2013] Fourth Computer Workshop

Our fourth computer workshop will be March 2 in MIKC 114 from 1pm to 3pm. We used the tridiagonal equation solved to implement an implicit scheme to solve the heat equation. The program files are available through the web.

[23-Feb-2013] Third Computer Workshop

Our third computer workshop was February 23 in DMS 106 from 1pm to 3pm. We created a tridiagonal equation solver. The program files are available through the web.

[16-Feb-2013] Computer Workshop

There will be no computer workshop Saturday February 16.

[09-Feb-2013] Computer Workshop

There will be no computer workshop Saturday February 9.

[08-Feb-2013] Friday Class

I will be out of town Friday February 8. I have found a video lecture on MIT Open Courseware that coveres the CFL condition and one-way wave equation. The lecture of interest is Lecture 3. This is an introductory lecture that covers some of the things we have been discussing in class. You may watch it in the classroom Friday or on your own outside of class.

[26-Jan-2013] Second Computer Workshop

Our second computer workshop will be February 2 in DMS 106 from 1pm to 3pm. The program files are available through the web.

[26-Jan-2013] First Computer Workshop

Our first computer workshop will be January 26 in DMS 106 from 1pm to 3pm.

[30-Jan-2013] Undergraduate PDEs

Here is a handout that reviews separation of variables for solving the heat equation.

[26-Jan-2013] First Computer Workshop

Our first computer workshop will be January 26 in DMS 106 from 1pm to 3pm.

[23-Jan-2013] Chapter 1

Since the book didn't arrive in the bookstore I have made handouts for you to read.

Additional Resources

The following books contain useful information about computer programming:
Brian Kernighan, Dennis Ritchie, C Programming Language, 2nd Edition, Prentice Hall, 1988.

Brian Kernighan, Rob Pike, The Unix Programming Environment, 1st Edition, 1984.

Robert Glassey, Numerical Computation Using C, Academic Press, 1993

Internet Resources

Grading

    2 Homework Assignments    20 points each
    2 Programming Projects    20 points each
    1 Midterm                 30 points
    1 Final Exam              50 points
   ------------------------------------------
                             160 points total

Homework and Exams

    Homework #1 due March 12 (solutions)
        Problems 1.2.1, 1.3.1, 1.3.2, 1.5.1, 1.5.2, 1.5.3, 1.5.7
    Exam 1 will be March 15
    Programming Project 1 is due April 10
    Homework #2 due May 10
        Problems 5.3.2, 5.6.3, 5.6.4, 5.7.1, 5.9.2
    Programming Project 2 is due May 10 (solutions)

Final Exam

The final exam will be held on Friday May 10 from 10:15-12:15 in AB635.

Equal Opportunity Statement

The Mathematics Department is committed to equal opportunity in education for all students, including those with documented physical disabilities or documented learning disabilities. University policy states that it is the responsibility of students with documented disabilities to contact instructors during the first week of each semester to discuss appropriate accommodations to ensure equity in grading, classroom experiences and outside assignments.

Academic Conduct

Bring your student identification to all exams. Work independently on all exams and quizzes. Behaviors inappropriate to test taking may disturb other students and will be considered cheating. Don't talk or pass notes with other students during an exam. Don't read notes or books while taking exams given in the classroom. You may work on the programming assignments in groups of two if desired. Homework may be discussed freely. If you are unclear as to what constitutes cheating, please consult with me.
Last updated: Tue Dec 18 13:23:13 PST 2012