Teaching

Office Hours Fall 2007

Monday	Tuesday	Wednesday	Thursday	Friday
	9:30--11:00	9:30--10:30	9:30--11:00
by appointment

Classes Fall 2007

• Math 2650 Linear Differential Equations

• Syllabus.
• Class information September 19.

Maple Worksheets and Class Notes

• Introduction - pendulum animation; pdf version.
• Examples of things to come what is a d.e., i.v.p., and a solution; pdf version.
• Separation of variables; pdf version.
• Qualatative analysis direction fields; pdf version.
• More qualatative analysis isoclines, trapping regions, and comparison; pdf version.
• Linear equations; pdf version.
• Exact differential equaions; pdf version.
• Euler's method; pdf version.
• More on Euler's method; pdf version.
• Second order equations; pdf version.
• Summary, second order equations and undetermined coefficients; pdf version.
• Oscillatory motion; pdf version.
• Forced oscillations; pdf version.
• Laplace transforms; pdf version.

Maple Stuff

• Some simple examples of Maple, you can also download the Maple Worksheet that was used to generate these.
• View an html version of Introduction to Maple or download the Maple Worksheet Introduction to Maple
• View an html version of More on Maple or download the Maple Worksheet More on Maple
• View an html version of Even more on Maple (for differential equations) or download the Maple Worksheet Even more on Maple (for differential equations)

• Math 5620/6620 Mathematical Computation and Scientific Visualization

• Syllabus.
• MPI test programs: Fortran Baton Pass and C Test MPI.
• MPI script for batch jobs.
• Alabama Supercomputer Documentation.

Classes Summer 2007

• Math 5630/6630 Introduction to Numerical Analysis I

• Syllabus.

Course Outline

• Overview
• Review of calculus
• Principles of numerical mathematics and floating point arithmetic, stability and condition.
• Root finding for nonlinear equations.
• Polynomial interpolation and approximation.
• Numerical differentiation, and numerical integration.
• Numerical approximation of solution of ordinary differential equations (initial-value problems).
• If time permits, numerical approximation of solution of ordinary differential equations (two point boundary-value problems).

Homework

• Homework 1.
• Homework 2.
• Homework 3.
• Homework 4.
• Homework 5.
• Homework 6.
• Homework 7.
• Homework 8.
• Homework 9.
• Homework 10.

"Quizes" and such

• Quiz 1.
• Quiz 2.
• Quiz 3.

M-files and such

• m-file directory look here for m-files mentioned in class.

Classes Spring 2007

• Math 5640/6640 Introduction to Numerical Analysis II

• Syllabus.

Course Outline

• Overview
• Review of linear algebra
• Numerical mathematics: computer arithmetic, stability and condition.
• Source of problems (as time permits).
• Linear systems of algebraic equations (direct and iterative solvers).
• Eigensolvers.

Classes Fall 2006

• Math 6620 Mathematical Computation and Scientific Visualization

• Syllabus

Resources

• A nice tutorial for Unix commands with most everything you will ever need (see also the links on this page).
• Pacheco's MPI book, in particular see the link to "A User's Guide to MPI".
• The Alabama Supercomputing Authority and the Users Manual
• Some very good tutorials from Lawrence Livermore National Laboratory
• Parallel computing tutorial.
• MPI tutorial.
• OpenMP tutorial.
• For those who want a Unix-like environment on their Windows machine, consider Cygwin or Cygwin/X which includs an X-server and several X-clients.
• Temporarily, the directory which contains some programming examples.




• Math 7000 Applied Mathematics

• Syllabus

Classes Fall 2005

• Math 5630/6630 Introduction to Numerical Analysis I

• Syllabus




• Math 7620 Introduction to Optimization

• Syllabus

Classes Spring 2005

• Math 2650 Linear Differential Equations

Homework Assignments

• Review Calculus.
• Section 1.2 problems 1-15 odd, and 17-24.
• Last problem in worksheet due Fri. Jan 28.
• Section 1.3 problems 1-10 odd, and 21-29.
• Project 1 (see end of qualatative analysis worksheet, below) due Mon. Feb. 7.
• Section 1.4 problems 1, 2, and 7-24.
• Section 1.5 problems 1, 2, and 3.
• Section 1.6 problems 1-4, 11, 19, and 26.
• Section 2.1 problems 1-10 odd, 29-35, 37, and 38.
• Section 2.3 problems 4-10, 13-16, and 17-24.
• Section 3.1 problems 1-6, 7, 9, and 11.
• Section 4.1 problems 6-8 and 33-35.
• Section 4.2 problems 6-12, 13, 15, 17, 19-25, and 26.
• Section 4.3 problems 7, and 8.
• Section 4.4 problems 1-8, and 11-14.
• Section 4.5 problems 5-20.
• Section 4.7 problems 1 and 2.
• Section 6.1 problems 1, 6, and 7.
• Section 6.3 problems 5-10.
• Section 6.4 problems 1-13.

Maple Worksheets and Class Notes

• Introduction - pendulum animation; pdf version.
• Examples of things to come what is a d.e., i.v.p., and a solution; pdf version.
• Separation of variables; pdf version.
• Qualatative analysis direction fields; pdf version.
• More qualatative analysis isoclines, trapping regions, and comparison.
• Euler's method.
• Linear equations.
• Modeling.
• Exact equations.
• Existence and uniqueness.
• Second order equations.
• Linear, constant coefficient, second order equations.
• Free oscillations.
• Forced oscillations (undamped and damped).
• Laplace transforms.

Maple Stuff

• Some simple examples of Maple, you can also download the Maple Worksheet that was used to generate these.
• View an html version of Introduction to Maple or download the Maple Worksheet Introduction to Maple
• View an html version of More on Maple or download the Maple Worksheet More on Maple
• View an html version of Even more on Maple (for differential equations) or download the Maple Worksheet Even more on Maple (for differential equations)

Classes Fall 2004

• Math 2650 Linear Differential Equations

Homework Assignments

• Review Calculus.
• Section 1.2 problems 1-15 odd, and 17-24.
• Section 1.3 problems 1-10 odd, and 21-29.
• Section 1.4 problems 1, 2, and 7-24.
• Section 2.1 problems 1-10 odd, 29-35, 37, and 38.
• Section 2.3 problems 4-10, 13-16, and 17-24.
• Homework 1 - 1.2 problem 18, 1.3 problem 27, 2.1 problem 35, and 2.3 problem 6. Due Wed. Sep. 8.
• Project 1 - due Wednesday September 15. Direction fields Maple worksheet and project1 assignment.
• Section 1.5 problems 1, 2, and 3.
• Section 1.6 problems 1-4, 11, 19, and 26.
• Isoclines Maple worksheet.
• Euler's method Maple worksheet.
• ModelingMaple worksheet.
• Section 3.1 problems 1-6, 7, 9, and 11.
• Section 4.1 problems 6-8 and 33-35.
• Section 4.2 problems 6-12, 13, 15, 17, 19-25, and 26.
• second order equations.
• linear, constant coefficient, second order equations.
• free oscillations.
• forced oscillations (undamped and damped).
• Section 4.3 problems 7, and 8.
• Section 4.4 problems 1-8, and 11-14.
• Section 4.5 problems 5-20.
• Section 4.7 problems 1 and 2.
• pendulum demo.
• Section 6.1 problems 1, 6, and 7.
• Section 6.3 problems 5-10.
• Section 6.4 problems 1-13.
• Laplace transforms.
• Section 7.1 problems 1-4, 9, and 11.
• Section 7.2 problems 1-4, 11, 12, 17, 18, 21, and 22.

• Math 7600 Advanced Numerical Matrix Analysis

Classes Spring 2004

• Math 7610 Numerical Solution of Partial Differential Equations

Matlab Programs

• heat1d.m a program to construct approximate solutions of the heat eq. using the finite difference method.
• laxf.m Lax-Freidrichs scheme for the one-way wave equation.
• laxw.m Lax-Wendroff scheme the one-way wave equation.
• leapfrog.m Leapfrog scheme the one-way wave equation.
• FEM directory Matlab M-files comprising a 2-d finite element code.

Classes Fall 2003

• Math 6970/7970 Mathematical Computation and Scientific Visualization

Matlab Programs

• cache.m
• heat1d.m
• wave1d.m
• heat2d.m
• lap2dd.m
• lap2dn.m
• lap2ddx.m
• lap2dnx.m

Classes Spring 2003

• Math 7680 Introduction to Multigrid Methods

Matlab Programs

• plotsine.m - a program to plot some Fourier modes on a grid with n=12 on the interval [0,1] (illustrates how smooth and oscillatory modes are represented and aliasing).
• jacobi.m - a program that performs a Jacobi and weighted Jacobi iteration (starting with an eigenvector of the iteration matrix, illustrates smoothing property for the various modes).
• The files you need for the multigrid mu cycle MGmu.m, mg.m, or mg_nr.m, relax.m, restrict.m, and intadd.m.
• A fortran version of the multigrid mu cycle mg_mu.f.
• The relaxation demonstration program and three types of relaxations using matrices a point by point scheme (using a for loop) and a vectorized point by point (avoiding a for loop).
• The additional, or replacement files you need in order to implement the full approximation scheme FMV.m the driver routine, fmg.m full approximation scheme multigrid, put.m, and subtract.m.

Classes Fall 2002

• Math 1120 Pre-Calculus Algebra

• Syllabus
• Teaching assistants and important dates
• Tutoring and help sessions
• Math Help Center - Monday--Thursday from 4:00pm to 8:00pm, Parker Hall 360, 362, and 364.
• Supplemental Instruction (offered by the university for PreCalc students) - Monday, Wednesday, and Thursday 4:00pm to 5:00pm, Parker Hall 249.
• Study Partners (a free tutoring service offered by the university) - RBD Library 0176. For more information see the detailed schedule.
• See also the Academic Support web page.

Teaching Assitants

Li Fan 204 Mell Hall, 844-3737
fanli01@auburn.edu

Kang Jin 210 Mell Hall, 844-3621
jinkang@auburn.edu

Kelly Sweetingham 206-A Mell Hall, 844-3742
sweetka@auburn.edu



TAs' Office Hours

TA	Monday	Tuesday	Wednesday	Thursday	Friday
L.F.		1:00-2:30		1:00-2:30	1:00-2:00
K.J.	1:00-2:30	1:00-2:30		2:00-3:00
K.S.	1:00-2:30		1:00-2:30		9:00-10:00




Homework

• Review: Read Sections 1.1--2.2.
• Homework 1: Section 2.3 (page 90) Problems: 1, 2, 7, 9, 15--17, 19, 21, 22, 25, 27--29, 31--43 odd problems, 53, 55, 57, and 61.
• Homework 2: Section 2.4 (page 101) Problems: 1, 3, 9, 15,19--25 odd problems, 29, 35, 36, and 39--47 odd problems.
• Homework 3: Section 2.5 (page 107) Problems: 1--11 odd problems, 15, 17, 21, 27, 35, 37, 45, 47, 51, 53, 55, 59, 61, and 63.
• Homework 4: Section 2.6 (page 117) Problems: 3, 5, 7, 9, 13, 15, 17, 27--37 odd problems, 41, 43, 53--63 odd problems, 71, 75, and 83.
• Homework 5: Section 2.7 (page 125) Problems: 1--27 odd problems, 37, 39, 43, 45, and 47.
• Solution of quiz 1
• Homework 6: Section 3.1 (page 139) Problems: 3, 7, 9, 13, 15, 19--27 odd problems, and 31.
• Homework 7: Section 3.2 (page 154) Problems: 3--6, 15, 17--19, 21, 27--33 odd problems, 35, 39--45 odd problems, 51, 53, 59, and 61.
• Homework 8: Section 3.3 (page 170) Problems: 7, 15--23 odd problems, 33, 35, 39, 47, 51, 55, 57, and 61.
• Homework 9: Section 3.4 (page 189) Problems: 3, 9, 17--21, 33--39, 45--49 odd problems, 53, 57--59, 61, and 65.
• Homework 10: Section 3.5 (page 204) Problems: 1--5 odd problems, 11, 12, 15, 17, 25--37 odd problems, 41--47 odd problems, and 53--57 odd problems.
• Homework 11: Section 3.6 (page 219) Problems: 1, 3, 7, 9, 13--21 odd problems, 27--31 odd problems, 33, 34, 38, 39, 41, and 43.
• Homework 12: Section 3.7 (page 232) Problems: 3, 5, 7, 11--17 odd problems, 21--27 odd problems, 33, 35, 37, 45, and 47.
• Homework 13: Section 3.8 (page 243) Problems: 1--11 odd problems, 15--35 odd problems, 39, and 41.
• Homework 14: Section 4.1 (page 269) Problems: 1, 3, 5--23 odd problems.
• Homework 15: Section 4.2 (page 279) Problems: 1--3, 5--15 odd problems, 17--20, 39, and 41.
• Homework 16: Section 4.3 (page 291) Problems: 1--9 odd problems, 15--19 odd problems, 23, 25, and 47.
• Homework 17: Section 4.4 (page 301) Problems: 1--17 odd problems.
• Homework 18: Section 4.5 (page 318) Problems: 3--23 odd problems, 29, 31, 33, 37, 39, 41, 43--45, 47, 52, and 53.
• Homework 19: Section 5.1 (page 335) Problems: 1, 3--5, 7, 9--12, 17--23 odd problems, 25, 27, 31, 33, 42, 43, 47, and 48.
• Homework 20: Section 5.2 (page 345) Problems: 3--8, 11-15 odd problems, 19, 21, 25, 27, and 28.
• Homework 21: Section 5.3 (page 359) Problems: 1--13 odd problems, 17--33 odd problems, 51, 55, 57, 59, 62, and 70.
• Homework 22: Section 5.4 (page 370) Problems: 1, 5, 7, 11--31 odd problems, 41, 43, 45, 53, 54, 56, and 59.
• Homework 23: Section 5.5 (page 381) Problems: 1--7 odd problems, 11--33 odd problems, 49, 50, 54, and 57.
• Homework 24: Section 9.1 (page 632) Problems: 1--30 odd problems, 33, 34, and 35.
• Homework 25: Section 9.2 (page 641) Problems: 7--15 odd problems, 19, 21, 29, and 31.
• Homework 26: Section 9.5 (page 675) Problems: 1--13 odd problems, 19, 21, 24, and 31.
• Homework 27: Section 9.3 (page 650) Problems: 3--9 odd problems, 11--25 odd problems, 27, 28, 29, and 31.
• Homework 28: Section 9.4 (page 659) Problems: 1--7 odd problems in these problems find both min. and max., 9, 13, and 17.
• Homework 29: Section 10.4 (page 760) Problems: 1--13 odd problems, 19, 23, 27, and 31.
• Homework 30 (the last one): Section 10.5 (page 769) Problems: 1--11 odd problems, 13--15, 17--21, 27--35 odd problems, and 39--43 odd problems.
• That's it!





Important Dates

Tentative test dates are: Friday September 6, Friday September 27, Friday October 18, Friday November 8, and Wednesday December 4. The final exam will be administered on Monday December 9, 11:00- 1:30 (see Fall schedule for details).



Online Tutorial

You can try the Brooks Cole online tutorial for our textbook. Go to the Brooks Cole web site select Register, select our school (Auburn University), and for the pin use 0534377599. From the products choose tutorials, click on the book cover and start working problems. Note, I have already found problems that don't behave exactly right, and in my opinion the interface is a little quirky... Also you must have a supported web browser (a recent version of Internet Explorer or Netscape. Enjoy, and let me know what you think of it.



Test 4 will cover sections 2.3--5.4

Be sure to bring your Student ID on test days.




• Math 6000 Mathematical Modeling: Continuous

Some Maple Demos

• Simulator of a mass spring system.
• A linear pendulum simulation.
• My solution to Problem 9.6.
• Nonlinear Pendulum
• Spring Pendulum or a draft for the elastic pendulum and also a draft for the numerical procedure for approximating solutions. A link to Mathscinet.
• Maple worksheets for systems of o.d.e.s: Graphical Analysis, Phase Portraits, and Linear Algebra.

Classes Spring 2002

• Math 7610 Numerical Solution of Partial Differential Equations

The numerical solution of partial differential equations using the finite difference and the finite element methods.

• Course description

Notes and bibliography

• Syllabus
• Course outline
• Bibliography
• Notes




Homework

• Homework 1 (due Wednesday January 23).
• Programming example and the actual Maple worksheet.
• Homework 3 do problems 5, or 7 and 6 (due Monday February 25).




Additional resources

• Here you can find the old fortran finite element code mentioned in class and the M-files that make up it revised Matlab counterpart.

Classes Fall 2001

• Math 7000 Applied Mathematics

• Syllabus

• Math 7680 Advanced Topics in Numerical Analysis: Introduction to Computational Fluid Dynamics

• Syllabus

Overheads of lectures

• Lecture 1 (August 20)
• Lecture 2 (August 22)
• Lecture 3 (August 24)
• Lecture 4 (August 27)
• Lecture 5 (August 29)
• Timeline
• Lecture 6 (August 31)
• Existence and uniqueness results
• Lecture 7 (September 5)
• Lecture 8 (September 7)
• Lecture 9 (September 10)
• Lecture 10 (September 12)
• Lecture 11 (September 14)
• Lecture 12 (September 17)
• Lecture 13 (September 19)
• An example of the finite difference method for a simple steady one-dimensional convection diffusion equation download the Maple worksheet.
• Lecture 14 (September 21)
• Lecture 15 (September 24)
• Lecture 16 (September 26)
• Lecture 17 (September 28)
• Lecture 18 (October 1)
• Lecture 19 (October 3)
• Lecture 20 (October 5)
• Lecture 21 (October 8)
• Lecture 22 (October 10)
• An example of the Euler and Backward Euler methods and the difference in stability for an unsteady one-dimensional convection diffusion equation, download the Maple worksheet.
• Lecture 23 (October 12)
• Lecture 24 (October 15)
• Lecture 25 (October 17)
• Lecture 26 (October 19)
• Lecture 27 (October 22)
• Lecture 28 (October 24)
• Lecture 29 (October 26)
• Lecture 30 (October 29)
• Lecture 31 (October 31)
• Lecture 32 (November 2) guest lecture by Jay Khodadady, visualization examples.
• Lecture 33 (November 5)
• Lecture 34 (November 7)
• Lecture 35 (November 9)
• Lecture 36 (November 12)
• Lecture 37 (November 14)
• Lecture 38 (November 16)
• Lecture 39 (November 26) guest lecture by Xundan Shi, flow in a driven cavity with a moving membrane and flow in a driven cavity with with a fin.
• Lecture 40 (November 28) student presentations.



• Overheads for forthcoming lectures
• Lecture ??? (last updated September 21)
• Lecture ??? (last updated September 24)
• Lecture ??? (last updated September 26)
• Lecture ??? (last updated October 10)
• Lecture ??? (last updated November 5)
• Lecture ??? (last updated November 7)
• Lecture ??? (last updated November 28)
• Lecture ??? (last updated November 30)
• Lecture ??? (last updated December 5)

Bibliography

• Bibliography
• Additional bibliography
• Additional bibliography stability of time discretizations
• Additional bibliography spatial discretizations, boundary conditions, and benchmarks

Homework and other handouts

• Homework 1 (August 24)
• Flow Equations (August 27)
• Homework 2 (August 29)
• Homework 3 (September 14)
• Homework 4 (September 24)

Software

• MOUSE an object oriented framework for finite volume computations on unstructured grids.
• NaSt2D a rather simple finite volume code for the Navier-Stokes equations.
• CFD codes by Milovan Peric (various Fortran codes). You can also get my modified code and see the example run in class. If you do not have a Fortran compiler, or would rather run C code, you can automatically convert the code to C. Download and build f2c. Run f2c on the fortran code to convert to C and then compile the C code and link with the library libf2c that you will also need to build and which can be found at the same place.
• Demo code by Suhas V. Patankar.
• CFDnet Computational Fluid Dynamics on the Internet (Java-based). CFDnet provides users with interactive Internet-based access to powerful server-side meshing, solving, and solution visualization routines for solving practical engineering problems in fluid flow.

Links of iterest

• FEAST currently available software by the FEAST group, in particular, featflow.
• Netlib Netlib Repository at UTK and ORNL (Netlib is a collection of mathematical software, papers, and databases), in particular, see this site for blas, clapack, lapack, lapack++, lapack90, and scalapack.
• OpenDX A powerful visualization tool.



• See also links on my ``Useful Links'' page
• Software
• Research Areas
• Mathematics Related Sites

Classes Fall 2000

• Math 6630 Intrtoduction to Numerical Analysis I

• Syllabus.

Homework Assignments

Homework 1: Problems 2a. and b., 6, and 9 on page 13, and 1a.-d., 4, and 17 on page 26.

Some links of interest

• Some additional numerical analysis references.
• Some additional programming references.
• Floating point arithmetic What Every Scientist Should Know About Floating-Point Arithmetic (from Sun Microsystems).
• More floating point information is available in the Fortran Programming Guide (from Sun Microsystems).
• Some disasters attributable to bad numerical computing.
• Information about Scientific Computing in Object-Oriented Languages.
• An example: using make files.
• Some links
• Software
• Research Areas
• Mathematics Related Sites

Maple Stuff

Basics

• Some simple examples of Maple, you can also download the Maple Worksheet that was used to generate these.


• View an html version of Introduction to Maple or download the Maple Worksheet Introduction to Maple


• View an html version of More on Maple or download the Maple Worksheet More on Maple


• View an html version of Even more on Maple (for differential equations) or download the Maple Worksheet Even more on Maple (for differential equations)



• How to configure Netscape Navigator to use Maple as helper applications.


Home Current Activities Magnetohydrodynamics (MHD)


ajm@math.auburn.edu
Last modified January 25, 2005
Copyright © A. J. Meir 1996-2004, 2005 all rights reserved.