|
Many people think that learning mathematics is difficult, and that
they're just not made for it. Both may be true, but it shouldn't stop
you from becoming a productive mathematician, or at least someone who
feels comfortable with mathematics. By way of a metaphor, my wife,
several friends and I have done RAGBRAI a couple of
times, a 500-mile, 7-day bike ride across Iowa. We are all decent bike
riders, and 70-miles per day is a long day in the saddle but quite
feasible. But there are people whose body shapes would suggest that
they can't walk a mile without fainting — yet they, too, seem to
have practiced enough to ride those 70 miles every day, even if they
won't come in first at the end of the day. The message is
that by trying and practicing, I believe everyone can learn enough
mathematics to do things most of us can't.
A colleague of mine, Jean
Marie Linhart, has put together a little page
on how to have success in mathematics. Go check it out if you have
a minute. One tool that I find the most productive in learning
anything is to do it in groups. Jean Marie also has a few
suggestions on group work worth reading.
A segment on finite element software in MATH-610
The slides for my lectures are here.
KAUST AMCS 312: High performance computing II
The slides for my lectures are here.
For homework 4 and to follow the discussion of the tutorial programs,
you will want to
- download the deal.II library from http://www.dealii.org
- follow the installation instructions on the ReadMe page
- If you're not familiar with C++, you may also be interested in a
primer on C++ templates as they are used in deal.II.
Finally, here is your class
assignment #4.
Spring 2011: MATH 676 — Finite element methods in scientific computing
Course outline
First day
handout
Following are notes for some of the classes:
2011-01-18
|
First day stuff;
getting a
copy of deal.II and installing it
|
2011-01-20
|
Installation,
basics of finite element methods
|
2011-01-25 to 27
|
Basics of finite element methods, initial
project presentations
|
2011-02-01
|
step-1
|
2011-02-03
|
A
lesson on C++ templates
|
2011-02-08
|
step-2
|
2011-02-10
|
step-3
|
2011-02-15
|
step-4
|
2011-02-17
|
Homework: Read through the
step-5 and
step-6
tutorial programs. Classwork: Discuss the concept of hanging
nodes. Practice.
|
2011-02-22
|
Homework: Read through section 4 of the
deal.II wiki. Classwork:
Vector-valued
problems
|
2011-02-24
|
Finish-up of Vector-valued
problems: how to describe vector components in
output formats. Also: A failsafe way of solving linear
system using the
SparseDirectUMFPACK
class. Project work.
|
2011-03-01
|
Kainan Wang: Dealing with input parameter files using the
ParameterHandler
class. Project work.
|
2011-03-03
|
Andrea Bonito: Solving partial differential equations on surfaces. Project work.
|
2011-03-08
|
Assertions, exceptions |
2011-03-10
|
Project work |
2011-03-22
|
Project work |
2011-03-24
|
Project work |
2011-03-29
|
Guido Kanschat: the MeshWorker framework |
2011-03-31
|
Project work; last day before midterm
presentations are due |
2011-04-05
|
A taxonomy of time dependent problems:
parabolic, second order hyperbolic, first order
hyperbolic, parabolic with "few" constraints (the DAE
case, Stokes), time dependent equations with
quasistationary parts (two-phase flow) |
2011-04-07
|
An overview of time stepping for parabolic problems |
2011-04-12
|
An overview of time stepping for second order hyperbolic problems |
2011-04-14
|
An overview of time stepping for first order hyperbolic problems |
2011-04-19
|
An overview of time stepping for
differential-algebraic equations like the two-phase flow
equations, and the IMPES scheme |
Fall 2010: MATH 442 — Mathematical Modeling
Resources:
- Click here
for the first day handout, including a list of topics that
I intend to cover.
- Two of my colleagues, Peter Howard and Tom Vogel, have
taught this class several times and have an extensive list
of excellent documents on various aspects of this class. Take a look
here
and here.
Class notes, homework and project descriptions:
2010-08-31
|
Maple
worksheet (use the right mouse button on the link
to save the file on your machine in some directory using the
"Save as" menu item; then open it again from this directory
using Maple)
|
2010-09-02
|
Homework 1,
due 9/9/2010
|
2010-09-09
|
Homework 2,
due 9/16/2010
|
2010-09-09
|
The LyX file we
worked on
|
2010-09-14
|
Maple
worksheet on parameter estimation using the least-squares method
|
2010-09-16
|
Homework 3,
due 9/23/2010
|
2010-09-23
|
Partial answers to
Problem 1
and
Problem 2
as Maple worksheets. Save them on your machine and
then open in Maple.
|
2010-09-23
|
Homework 4,
due 9/30/2010
|
2010-09-30
|
Partial answers to Problem 1
as a Maple
worksheet
and
as a pdf
file.
Partial answers to Problem 2
as a Maple
worksheet
and
as a pdf
file.
|
2010-09-30
|
Homework 5,
due 10/7/2010
|
2010-10-07
|
Group project,
due 10/28/2010
Group 1: Cmajdalka, Thompson, Truong
Group 2: Larimore, Lee, Slawson
Group 3: Cortez, Hagel, Su
Group 4: Ball, Jones, Woelfel
Group 5: Carter, Chen, Weiss
Group 6: Cantu, Wesson, Yunkun
Group 7: Bauer, Molitor, Tietze
Group 8: Bartholomew, Gallegos
|
2010-10-15
|
Since we didn't get to it yesterday in class, I've put
together a few comments on how to efficiently write
scripts in Maple if we want to solve differential
equations for multiple bodies each of which have multiple
vector components. Take a look at these notes
as a Maple
worksheet
or
as a pdf
file.
|
2010-10-24
|
Solutions
to the midterm exam.
|
2010-10-28
|
Homework 6,
due 11/4/2010
|
2010-11-1
|
Partial answers to homework 6
as a Maple
worksheet.
|
2010-11-15
|
Individual project,
due 12/09/2010
|
2010-11-18
|
This is the worksheet on using Maple for graph-based models,
specifically the decay chain problem:
as a Maple
worksheet
or
as a pdf
file.
|
2010-11-30
|
This is the worksheet we had in class today on probabilities
as a Maple
worksheet
or
as a pdf
file.
|
Spring 2010: MATH 652 — Optimization II
Traditionally, this course has put a lot of emphasis on theoretical
aspects of optimization, such as for example the conditions under
which an optimum exists, or under what conditions it is unique if it
exists. I intend to put more emphasis on practical aspects, in
particular how optima can actually be found for practical problems
using computer algorithms.
Click
here
for the first day handout, including a list of topics that
I intend to cover.
Following are notes for some of the classes:
2010-01-21
|
Homework
1, due 1/28/2010
|
2010-01-28
|
Partial answers to
homework 1
|
2010-01-28
|
Homework
2, due 2/4/2010
|
2010-02-04
|
Answers to
homework 2
|
2010-02-04
|
Homework
3, due 2/11/2010
|
2010-02-11
|
Homework
4, due 2/18/2010
|
2010-02-18
|
Homework
5, due 3/2/2010
|
2010-03-04
|
Homework
6, due 3/11/2010
|
2010-03-11
|
Homework
7, due 4/1/2010
|
2010-04-01
|
Homework
8, due 4/8/2010
|
2010-04-08
|
Homework
9, due 4/15/2010
|
2010-04-20
|
Answers to
homework 9
|
2010-04-15
|
Homework
10, due 4/22/2010
|
|
|
2010-04-29
|
All slides
|
Fall 2009: MATH 651 — Optimization I
Traditionally, this course has put a lot of emphasis on theoretical
aspects of optimization, such as for example the conditions under
which an optimum exists, or under what conditions it is unique if it
exists. I intend to put more emphasis on practical aspects, in
particular how optima can actually be found for practical problems
using computer algorithms.
The first day handout, including a list of topics that I intend to
cover,
can be found
here.
Following are notes for some of the classes:
2009-09-08
|
Homework
1, due 9/15/2009
|
2009-09-15
|
Homework
2, due 9/22/2009
|
2009-09-24
|
Homework
3, due 10/1/2009
|
2009-10-01
|
Homework
4, due 10/8/2009
|
2009-10-08
|
Homework
5, due 10/15/2009
|
2009-10-15
|
Homework
6, due 10/22/2009
|
2009-10-22
|
Homework
7, due 11/05/2009
|
2009-11-05
|
Homework
8, due 11/12/2009
|
2009-11-12
|
Homework
9, due 11/19/2009
|
2009-11-19
|
Homework
10, due 12/03/2009
|
|
|
2009-12-03
|
All slides so far
|
Fall 2008: MATH 676 — Finite element methods in scientific computing
Course outline
First day
handout
Following are notes for some of the classes:
2008-08-26
|
Getting a
copy of deal.II and installing it
|
2008-08-28
|
Installation,
basics of finite element methods
|
2008-09-02
|
Templates,
step-1, step-2
|
2008-09-04
|
step-3; project presentations |
2008-09-09
|
step-4; project presentations
|
2008-09-11
|
step-4; project presentations |
2008-09-16
|
step-5 |
2008-09-18
|
step-6 |
2008-09-23
|
Wrap-up step-6: assertions, exceptions; step-7 |
2008-09-25
|
Visualization, basics of vector-valued
problems |
2008-09-30
|
Vector-valued problems: setting up block matrices
and vectors, partitioning degrees of freedom |
2008-10-02
|
Vector-valued problems: deriving block solvers by
considering matrices only as linear operators; using templates to
describe concepts instead of actions. |
2008-10-07
|
Vector-valued problems: the block solver
of step-22 |
2008-10-09
|
Time-dependent problems: classification
and examples. |
2008-10-14
|
Time-dependent problems: the heat equation;
explicit and implicit schemes. |
2008-10-16
|
Time-dependent problems: the wave equation;
explicit and implicit schemes. |
2008-10-21
|
The ParameterHandler class to deal with
run-time parameters. |
2008-10-23
|
Multithreading. |
2008-10-28
|
Project work in anticipation to the
mid-semester presentations. |
2008-10-30
|
Mid-semester presentations. |
2008-11-04
|
Mid-semester presentations. |
2008-11-06
|
Differential-algebraic equations, IMPES
schemes. |
2008-11-11
|
Time step choice in transport
equations. |
2008-11-13
|
Project work. |
Fall 2007: MATH 151 — Engineering Mathematics
I
A lot of material for this course is available online on departmental
web pages. Click here for catalog
description, weekly schedule, sample homework problems, past exams,
and other information. Amy Austin will give a
Live
Week in Review Session that you may be interested in. She also has
a collection of streaming video
sessions on Math 151 and excellent
class notes that you may find helpful.
Here are some other links:
Click
here
for the first day handout.
Please go to
this site for
your online homework. Online homework is always posted on Monday
morning and is due on Sunday at 11pm. No late homework will be
accepted.
Locations and times for the common exams are posted
here.
Fall 2007: MATH 412-503 — Theory of Partial
Differential Equations
Click on the following links to get a pdf file:
First day
handout
Homework assignment 1
(due 9/6/2007) |
Questions |
Homework assignment 2
(due 9/13/2007) |
Questions |
Homework assignment 3
(due 9/20/2007) |
Questions |
Homework assignment 4
(due 9/27/2007) |
Questions |
Homework assignment 5
(due 10/4/2007) |
Questions |
Homework assignment 6
(due 10/11/2007) |
Questions |
Homework assignment 7
(due 10/18/2007) |
Questions |
|
|
Spring 2007: MATH 417 — Numerical Analysis
I
Click on the following links to get a pdf file:
First day
handout
Homework assignment 1
(due 2/1/2007) |
Questions |
Homework assignment 2
(due 2/8/2007) |
Questions |
Homework assignment 3
(due 2/15/2007) |
Questions |
Homework assignment 4
(due 2/27/2007) |
Questions |
Homework assignment 5
(due 3/8/2007) |
Questions |
Homework assignment 6
(due 3/22/2007) |
Questions |
Homework assignment 7
(due 3/29/2007) |
Questions |
|
Homework assignment 8
(due 4/5/2007) |
Questions |
Homework assignment 9
(due 4/19/2007) |
Questions |
Homework assignment 10
(due 4/26/2007) |
Questions |
|
Fall 2006: MATH 412-503 — Theory of Partial
Differential Equations
Click on the following links to get a pdf file:
First day
handout
Homework assignment 1
(due 9/7/2006) |
Questions |
Homework assignment 2
(due 9/14/2006) |
Questions |
Homework assignment 3
(due 9/21/2006) |
Questions |
Homework assignment 4
(due 9/28/2006) |
Questions |
Homework assignment 5
(due 10/5/2006) |
Questions |
Homework assignment 6
(due 10/12/2006) |
Questions |
Homework assignment 7
(due 10/26/2006) |
Questions |
|
Homework assignment 8
(due 11/2/2006) |
Questions |
Homework assignment 9
(due 11/9/2006) |
Questions |
Homework assignment 10
(due 11/16/2006) |
Questions |
Homework assignment 11
(due 11/30/2006) |
Questions |
|
Fall 2006: MATH 417-501 — Numerical Analysis
I
Click on the following links to get a pdf file:
First day
handout
Homework assignment 1
(due 9/7/2006) |
Questions |
Homework assignment 2
(due 9/14/2006) |
Questions |
Homework assignment 3
(due 9/21/2006) |
Questions |
Homework assignment 4
(due 9/28/2006) |
Questions |
Homework assignment 5
(due 10/05/2006) |
Questions |
Homework assignment 6
(due 10/12/2006) |
Questions |
Homework assignment 7
(due 10/26/2006) |
Questions |
|
|
Spring 2006: MATH 664-600 Computational
Software for Large-Scale PDE Solvers
Click on the following links to get a pdf file:
Course outline
First day
handout
Following are notes for some of the classes:
2006-01-18
|
Getting a
copy of deal.II and installing it
|
2006-01-19
|
Installation.
C++ templates
|
2006-01-24
|
Next week's
projects; collaboration between class groups; grids; finite
elements
|
2006-01-25
|
DoFHandlers;
step-2.
|
2006-01-26
|
step-3.
|
2006-01-31
|
Student
project discussion.
|
2006-02-02
|
Student
project discussion. Step-4 and step-5. Assertions.
|
2006-02-07
|
More
assertions. Optimized and debug mode. Hanging nodes.
|
2006-02-09
|
Other linear
solvers and preconditioners. Boundary integrals
(step-7). Vector-valued finite elements (step-8).
|
2006-02-14
|
Vector-valued finite elements
(step-20, step-8).
|
2006-02-16
|
Block systems
and solvers
(step-20).
|
2006-02-21
|
Complex-valued
equations, project work.
|
2006-02-23
|
Heat equation.
|
2006-03-01
|
More heat equation, project work.
|
2006-03-02
|
Wave equation, project work.
|
2006-03-07
|
More wave equation, project work.
|
2006-03-09
|
More wave equation, project work.
|
2006-03-21
|
Boundary values for the wave
equation. Energy conservation.
|
2006-03-23
|
Writing documentation inside the program.
|
2006-03-28
|
Writing
documentation for introduction and results sections. The
notes for this class contain links to doxygen sections
that may be of interest to you, links to visualization
programs, and a link to the Subversion book.
|
2006-03-30
|
Visualization with gnuplot |
2006-04-04
|
Visualization with gmv |
2006-04-05
|
No topic, only project work since short
class. Moved from 2006-04-06 due to travel. |
2006-04-11
|
Evaluating discrete functions (e.g. finite
element solutions) at arbitrary points, and why this is
expensive |
2006-04-13
|
Integrating functions defined on one mesh
against shape functions defined on a different mesh. |
2006-04-18
|
Some approaches to parallelization of
programs |
2006-04-20
|
Project work |
2006-04-25
|
Nonlinear equations |
2006-04-27
|
|
Here are the notes from Fabien's lab:
Fall 2005: MATH 609-602 — Numerical Methods
for Engineers
Click on the following links to get a pdf file:
First day
handout
Homework assignment 1
(8/30/2005) |
Questions |
(Answers no longer available) |
Homework assignment 2
(9/6/2005; due 9/13/2005) |
Questions |
(Answers no longer available) |
Lab 2
(9/7/2005) |
Question +
solution |
|
Homework assignment 3
(9/13/2005; due 9/20/2005) |
Questions |
(Answers no longer available) |
Homework assignment 4
(9/20/2005; due 9/27/2005) |
Questions |
(Answers no longer available) |
Test 1
(9/27/2005; due 10/04/2005) |
Questions
(latex file)
|
(Answers no longer available) |
Homework assignment 5
(10/04/2005; due 10/11/2005) |
Questions
(latex file) |
(Answers no longer available) |
Homework assignment 6
(10/11/2005; due 10/18/2005) |
Questions
(latex file) |
(Answers no longer available) |
Homework assignment 7
(10/18/2005; due 10/25/2005) |
Questions
(latex file) |
(Answers no longer available) |
Homework assignment 8
(10/25/2005; due 11/1/2005) |
Questions
(latex file) |
(Answers no longer available) |
Homework assignment 9
(11/1/2005; due 11/8/2005) |
Questions
(latex file) |
(Answers no longer available) |
Test 2
(11/08/2005; due 11/15/2005) |
Questions
(latex file)
|
(Answers no longer available) |
Homework assignment 10
(11/15/2005; due 11/22/2005) |
Questions
(latex file) |
(Answers no longer available) |
Homework assignment 11
(11/22/2005; due 11/29/2005) |
Questions
(latex file) |
(Answers no longer available) |
Finals, part 1
(12/01/2005; due 12/09/2005) |
Questions
(latex file)
|
(Answers no longer available) |
Finals, part 2
(in-class work, 12/09/2005) |
Questions
(latex file)
|
(Answers no longer available) |
|
