Office Hours Fall 2007
Monday  Tuesday 
Wednesday  Thursday 
Friday 

9:3011:00 
9:3010:30 
9:3011:00 

by appointment 
Classes Fall 2007
Classes Summer 2007
Math 5630/6630 Introduction to Numerical Analysis I
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 (initialvalue problems).
 If time permits, numerical approximation of solution of ordinary
differential equations (two point boundaryvalue problems).
Homework
"Quizes" and such
Mfiles and such
Classes Spring 2007
Math 5640/6640 Introduction to Numerical Analysis II
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
Classes Fall 2005
Math 5630/6630 Introduction to Numerical Analysis I
Math 7620 Introduction to Optimization
Classes Spring 2005
Math 2650 Linear Differential Equations
Homework Assignments
 Review Calculus.
 Section 1.2 problems 115 odd, and 1724.
 Last problem in worksheet
due Fri. Jan 28.
 Section 1.3 problems 110 odd, and 2129.
 Project 1 (see end of
qualatative analysis worksheet,
below) due Mon. Feb. 7.
 Section 1.4 problems 1, 2, and 724.
 Section 1.5 problems 1, 2, and 3.
 Section 1.6 problems 14, 11, 19, and 26.
 Section 2.1 problems 110 odd, 2935, 37, and 38.
 Section 2.3 problems 410, 1316, and 1724.
 Section 3.1 problems 16, 7, 9, and 11.
 Section 4.1 problems 68 and 3335.
 Section 4.2 problems 612, 13, 15, 17, 1925, and 26.
 Section 4.3 problems 7, and 8.
 Section 4.4 problems 18, and 1114.
 Section 4.5 problems 520.
 Section 4.7 problems 1 and 2.
 Section 6.1 problems 1, 6, and 7.
 Section 6.3 problems 510.
 Section 6.4 problems 113.
Maple Worksheets and Class Notes
Maple Stuff
Classes Fall 2004
Math 2650 Linear Differential Equations
Homework Assignments
 Review Calculus.
 Section 1.2 problems 115 odd, and 1724.
 Section 1.3 problems 110 odd, and 2129.
 Section 1.4 problems 1, 2, and 724.
 Section 2.1 problems 110 odd, 2935, 37, and 38.
 Section 2.3 problems 410, 1316, and 1724.
 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 14, 11, 19, and 26.
 Isoclines Maple worksheet.
 Euler's method Maple worksheet.
 ModelingMaple worksheet.
 Section 3.1 problems 16, 7, 9, and 11.
 Section 4.1 problems 68 and 3335.
 Section 4.2 problems 612, 13, 15, 17, 1925, 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 18, and 1114.
 Section 4.5 problems 520.
 Section 4.7 problems 1 and 2.
 pendulum demo.
 Section 6.1 problems 1, 6, and 7.
 Section 6.3 problems 510.
 Section 6.4 problems 113.
 Laplace transforms.
 Section 7.1 problems 14, 9, and 11.
 Section 7.2 problems 14, 11, 12, 17, 18, 21, and 22.
Math 7600 Advanced Numerical Matrix Analysis
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 LaxFreidrichs
scheme for the oneway wave equation.
 laxw.m LaxWendroff
scheme the oneway wave equation.
 leapfrog.m Leapfrog
scheme the oneway wave equation.
 FEM directory Matlab Mfiles
comprising a 2d finite element code.
Math 6970/7970 Mathematical Computation and Scientific Visualization
Matlab Programs
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.
Math 1120 PreCalculus Algebra

Syllabus

Teaching assistants and important dates
 Tutoring and help sessions
 Math Help Center  MondayThursday 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, 8443737fanli01@auburn.edu
Kang Jin 210 Mell Hall, 8443621jinkang@auburn.edu
Kelly Sweetingham 206A Mell Hall, 8443742sweetka@auburn.edu
TAs' Office Hours
TA  Monday  Tuesday 
Wednesday  Thursday 
Friday 
L.F.  
1:002:30 

1:002:30 
1:002:00 
K.J.  1:002:30 
1:002:30 

2:003:00 

K.S.  1:002:30 

1:002:30 

9:0010:00 
Homework
 Review: Read Sections 1.12.2.
 Homework 1: Section 2.3 (page 90) Problems: 1, 2, 7, 9, 1517, 19,
21, 22, 25, 2729, 3143 odd problems, 53, 55, 57, and 61.
 Homework 2: Section 2.4 (page 101) Problems: 1, 3, 9, 15,1925 odd
problems, 29, 35, 36, and 3947 odd problems.
 Homework 3: Section 2.5 (page 107) Problems: 111 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,
2737 odd problems, 41, 43, 5363 odd problems, 71, 75, and 83.
 Homework 5: Section 2.7 (page 125) Problems: 127 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,
1927 odd problems, and 31.
 Homework 7: Section 3.2 (page 154) Problems: 36, 15, 1719, 21,
2733 odd problems, 35, 3945 odd problems, 51, 53, 59, and 61.
 Homework 8: Section 3.3 (page 170) Problems: 7, 1523 odd problems,
33, 35, 39, 47, 51, 55, 57, and 61.
 Homework 9: Section 3.4 (page 189) Problems: 3, 9, 1721, 3339,
4549 odd problems, 53, 5759, 61, and 65.
 Homework 10: Section 3.5 (page 204) Problems: 15 odd problems, 11,
12, 15, 17, 2537 odd problems, 4147 odd problems,
and 5357 odd problems.
 Homework 11: Section 3.6 (page 219) Problems: 1, 3, 7, 9,
1321 odd problems, 2731 odd problems, 33, 34, 38, 39, 41, and 43.
 Homework 12: Section 3.7 (page 232) Problems: 3, 5, 7, 1117
odd problems, 2127 odd problems, 33, 35, 37, 45, and 47.
 Homework 13: Section 3.8 (page 243) Problems: 111 odd problems,
1535 odd problems, 39, and 41.
 Homework 14: Section 4.1 (page 269) Problems: 1, 3, 523 odd problems.
 Homework 15: Section 4.2 (page 279) Problems: 13, 515 odd problems,
1720, 39, and 41.
 Homework 16: Section 4.3 (page 291) Problems: 19 odd problems,
1519 odd problems, 23, 25, and 47.
 Homework 17: Section 4.4 (page 301) Problems: 117 odd problems.
 Homework 18: Section 4.5 (page 318) Problems: 323 odd problems,
29, 31, 33, 37, 39, 41, 4345, 47, 52, and 53.
 Homework 19: Section 5.1 (page 335) Problems: 1, 35, 7, 912,
1723 odd problems, 25, 27, 31, 33, 42, 43, 47, and 48.
 Homework 20: Section 5.2 (page 345) Problems: 38, 1115 odd problems,
19, 21, 25, 27, and 28.
 Homework 21: Section 5.3 (page 359) Problems: 113 odd problems,
1733 odd problems, 51, 55, 57, 59, 62, and 70.
 Homework 22: Section 5.4 (page 370) Problems: 1, 5, 7,
1131 odd problems, 41, 43, 45, 53, 54, 56, and 59.
 Homework 23: Section 5.5 (page 381) Problems: 17 odd problems,
1133 odd problems, 49, 50, 54, and 57.
 Homework 24: Section 9.1 (page 632) Problems: 130 odd problems,
33, 34, and 35.
 Homework 25: Section 9.2 (page 641) Problems: 715 odd problems,
19, 21, 29, and 31.
 Homework 26: Section 9.5 (page 675) Problems: 113 odd problems,
19, 21, 24, and 31.
 Homework 27: Section 9.3 (page 650) Problems: 39 odd problems,
1125 odd problems, 27, 28, 29, and 31.
 Homework 28: Section 9.4 (page 659) Problems: 17 odd problems
in these problems find both min. and max., 9, 13, and 17.
 Homework 29: Section 10.4 (page 760) Problems: 113 odd problems,
19, 23, 27, and 31.
 Homework 30 (the last one): Section 10.5 (page 769) Problems:
111 odd problems, 1315, 1721, 2735 odd problems, and 3943
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 2.35.4
Be sure to bring your Student ID on test days.
Math 6000 Mathematical Modeling: Continuous
Some Maple Demos
Math 7610 Numerical Solution of Partial Differential Equations
The numerical solution of partial differential equations using the finite
difference and the finite element methods.
Notes and bibliography
Homework
 Homework 1
(due Wednesday January 23).
 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 Mfiles that
make up it revised Matlab counterpart.
Classes Fall 2001
Math 7000 Applied Mathematics
Math 7680 Advanced Topics in Numerical Analysis: Introduction to Computational Fluid Dynamics
Overheads of lectures
Bibliography
Homework and other handouts
Software
 MOUSE an
object oriented framework for finite volume computations on unstructured
grids.

NaSt2D a rather simple finite volume code for the
NavierStokes 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 (Javabased). CFDnet provides users with
interactive Internetbased access to powerful serverside 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
Classes Fall 2000
Math 6630 Intrtoduction to Numerical Analysis I
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
Maple Stuff
Basics
Home
Current
Activities
Magnetohydrodynamics (MHD)
ajm@math.auburn.edu
Last modified January 25, 2005
Copyright © A. J. Meir 19962004, 2005 all rights reserved.