Many people think that learning mathematics is difficult, and that they're just not made for it. Both may be true (though I don't believe that there are people who can't learn math), 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.
Spring 2020: Math 317 — Advanced Calculus of One Variable
The worksheets we discuss in class are posted on the Canvas page for this course.
Fall 2019: DSCI 320 — Optimization Methods in Data Science
First day handout, including syllabus
Slides: Part 1, part 3, part 4, part 6, part 7.5, part 7.9, part 15, part 16, parts 17+18, parts 34, parts 22
| Homework assignment 1 (due 9/20/2019) | Questions |
| Homework assignment 2 (due 10/04/2019) | Questions |
| Homework assignment 3 (due 10/19/2019) | Questions |
| Homework assignment 4 (due 11/01/2019) | Questions |
| Homework assignment 5 (due 11/15/2019) | Questions |
Fall 2019: MATH 651 — Numerical Analysis II
First day handout, including syllabus
| Homework assignment 1 (due 9/13/2019) | Questions |
| Homework assignment 2 (due 9/27/2019) | Questions |
| Homework assignment 3 (due 10/11/2019) | Questions |
| Homework assignment 4 (due 10/25/2019) | Questions |
| Homework assignment 5 (due 11/15/2019) | Questions |
Spring 2019: MATH 546 — Partial Differential Equations II
First day handout, including syllabus
| Homework assignment 1 (due 3/1/2019) | Questions |
| Homework assignment 2 (due 3/15/2019) | Questions |
| Homework assignment 3 (due 4/5/2019) | Questions |
| Homework assignment 4 (due 4/26/2019) | Questions |
Fall 2018: MATH 545 — Partial Differential Equations I
First day handout, including syllabus
| Homework assignment 1 (due 9/17/2018) | Questions |
| Homework assignment 2 (due 9/28/2018) | Questions |
| Homework assignment 3 (due 10/12/2018) | Questions |
| Homework assignment 4 (due 10/26/2018) | Questions |
| Homework assignment 5 (due 11/9/2018) | Questions |
| Homework assignment 6 (due 11/30/2018) | Questions |
Fall 2018: MATH 620 — Variational Methods and Optimization I
First day handout, including syllabus
| Homework assignment 1 (due 9/17/2018) | Questions |
| Homework assignment 2 (due 9/28/2018) | Questions |
| Homework assignment 3 (due 10/12/2018) | Questions |
| Homework assignment 4 (due 10/26/2018) | Questions |
| Homework assignment 5 (due 11/9/2018) | Questions |
| Homework assignment 6 (due 11/30/2018) | Questions |
Spring 2018: MATH 451 — Introduction to Numerical Analysis II
First day handout, including syllabus
| Homework assignment 1 (due 2/9/2018) | Questions |
| Homework assignment 2 (due 2/23/2018) | Questions |
| Homework assignment 3 (due 3/21/2018) | Questions |
| Homework assignment 4 (due 4/6/2018) | Questions |
Spring 2018: MATH 676 — Finite element methods in scientific computing
First day
handout, including syllabus
Slides
with commands and ideas that we use when working through
tutorials in class
The video lectures that accompany this course can be found here. Here's the schedule for watching them during the first few weeks:
- Week 1 (January 15-19):
Lectures 1,
2,
4
(If you want to install deal.II by yourself, you may also want to watch lecture 3.) - Week 2 (January 22-26):
Lectures 5,
6,
9,
10.
Please also watch lectures 32.75 and 32.8 on the use of git and github. If you have never used a version control system, you may also want to take a look at lecture 32.5, which gives an introduction using a simpler system, subversion. - Week 3 (January 29-February 2): Lectures 13, 7, 8, 11, 12
- Week 4 (February 5-9): Lectures 14, 15, 16, 17, 18
- Week 5 (February 12-16): Lectures 21.5, 24, 25, 42, 43
These lectures form the basis of what you will need to know for this class (I will assign a few more lectures to each student depending on their relevance for individual projects). My goal with assigning so many lectures right at the beginning of the semester is to get you up to speed with it all so that you can focus on your project during the second half of the semester.
Please note in your journals which lectures you have watched and what questions you have -- we will use these questions for short discussions at the beginning of each class. Please also take the time after each lecture to briefly reflect on what you have learned and how that relates to what you already know, need to know, etc.
Fall 2017: MATH 651 — Numerical Analysis II
First day handout, including syllabus
| Homework assignment 1 (due 9/12/2017) | Questions |
| Homework assignment 2 (due 9/26/2017) | Questions |
| Homework assignment 3 (due 10/24/2017) | Questions |
| Homework assignment 4 (due 11/06/2017) | Questions |
| Homework assignment 5 (due 11/27/2017) | Questions |
Spring 2017: MATH 561 — Numerical Analysis I
First day handout, including syllabus
My slides on optimization (including much more material than we will cover).
| Homework assignment 1 (due 1/31/2017) | Questions |
| Homework assignment 2 (due 2/14/2017) | Questions |
| Homework assignment 3 (due 2/28/2017) | Questions |
| Homework assignment 4 (due 3/21/2017) | Questions |
| Homework assignment 5 (due 4/11/2017) | Questions |
| Homework assignment 6 (due 4/25/2017) |
Spring 2016: MATH 442 — Mathematical Modeling
First day
handout, including syllabus
Assignment 1 (draft due 1/28/2016, final version due 2/1/2016)
Assignment 2 (draft due 3/1/2016, final version due 3/4/2016)
Assignment 3 (draft due 3/22/2016, final version due 3/25/2016)
Assignment 4 (draft due 4/21/2016, final version due 4/27/2016)
Examples of using Maple (open with Maple)
Maple worksheet showing an example of solving ODEs
Maple worksheet showing how to numerically solve ODEs that don't have a closed form solution
Maple worksheet on moose and wolves
Maple worksheet on moose and wolves, modified by a carrying capacity
Maple worksheet on least squares regression for the growth of tuition
Maple worksheet on least squares regression for the tiger population in India
Maple worksheet on the movement of a marble on a string
Maple worksheet on the movement of a marble in a 2d environment
A Maple worksheet with a few tools for project 4 (also available as a pdf file).
Fall 2015: MATH 442 — Mathematical Modeling
First day
handout, including syllabus
Assignment 1
Examples of using Maple
(open with Maple)
Maple worksheet
showing an example of solving ODEs
Maple
worksheet showing how to numerically solve ODEs that don't
have a closed form solution
Maple worksheet
on moose and wolves
Assignment 2
Maple worksheet
on least squares regression for the growth of tuition
Assignment 3
Maple worksheet
on the movement of a marble on a string
Maple worksheet
on the movement of a marble in a 2d environment
Assignment 4
A Maple
worksheet with a few tools for project 4
(also available
as a pdf
file).
Spring 2015: MATH 676 — Finite element methods in scientific computing
Course outline
First day
handout
Slides
with commands and ideas that we use when working through
tutorials in class
The video lectures that accompany this course can be found here. Here's the schedule for watching them during the first few weeks:
- Week 1 (January 19-23):
Lectures 1, 2, 4
(If you want to install deal.II on another system, you may also want to watch lecture 3.) - Week 2 (January 26-30): Lectures 32.5, 5, 6, 9, 10
- Week 3 (February 2-6): Lectures 13, 7, 8, 11, 12
- Week 4 (February 9-13): Lectures 14, 15, 16, 17, 18
- Week 5 (February 16-20): Lectures 21.5, 24, 25, 42, 43
These lectures form the basis of what you will need to know for this class (I will assign a few more lectures to each student depending on their relevance for individual projects). My goal with assigning so many lectures right at the beginning of the semester is to get you up to speed with it all so that you can focus on your project during the second half of the semester.
Please note in your journals which lectures you have watched and what questions you have -- we will use these questions for short discussions at the beginning of each class. Please also take the time after each lecture to briefly reflect on what you have learned and how that relates to what you already know, need to know, etc.
Fall 2014: MATH 442 — Mathematical Modeling
First day
handout, including syllabus
Assignment 1
Assignment 2
Assignment 3
Assignment 4
Spring 2014: MATH 689 — Special Topics in Numerical Optimization
First day
handout, including syllabus
Slides part 1,
Slides part 2
| Homework assignment 1 (1/21/2014) | Questions |
| Homework assignment 2 (2/4/2014) | Questions |
| Homework assignment 3 (2/11/2014) | Questions |
| Homework assignment 4 (2/18/2014) | Questions |
| Homework assignment 5 (2/25/2014) | Questions |
| Homework assignment 6 (3/4/2014) | Questions |
| Homework assignment 7 (3/18/2014) | Questions |
| Homework assignment 8 (3/25/2014) | Questions |
| Homework assignment 9 (4/1/2014) | Questions |
| Homework assignment 10 (4/8/2014) | Questions |
| Homework assignment 11 (4/15/2014) | Questions |
Fall 2013: MATH 437 — Principles of Numerical Analysis
| Homework assignment 1 (9/05/2013) |
Questions |
| Homework assignment 2 (9/12/2013) |
Questions |
| Homework assignment 3 (9/19/2013) |
Questions |
| Homework assignment 4 (9/26/2013) |
Questions |
| Homework assignment 5 (10/03/2013) |
Questions |
| Homework assignment 6 (10/10/2013) |
Questions |
| Homework assignment 7 (10/24/2013) |
Questions |
| Homework assignment 8 (10/31/2013) |
Questions |
| Homework assignment 9 (11/7/2013) |
Questions |
| Test 1 | |
| Homework assignment 10 (11/14/2013) |
Questions |
| Homework assignment 11 (11/21/2013) |
Questions |
| Bonus homework (12/03/2013) |
Questions |
Spring 2013: MATH 676 — Finite element methods in scientific computing
Course outline
First day
handout
The video lectures that accompany this course can be found here.
Fall 2012: MATH 601 — Methods of Applied Mathematics I
Following are notes for some of the classes:
| 2012-09-05 |
Quiz 1, with answers |
| 2012-09-10 |
Quiz 2, with answers |
| 2012-09-19 |
Quiz 3, with answers |
| 2012-09-26 |
Quiz 4, with answers |
| 2012-10-03 |
Quiz 5, with answers |
| 2012-10-08 |
Quiz 6, with answers |
| 2012-10-17 |
Quiz 7, with answers |
| 2012-10-31 |
Quiz 8, with answers |
| 2012-11-07 |
Quiz 9, with answers |
| 2012-11-14 |
Quiz 10, with answers |
| 2012-11-28 |
Quiz 11, with answers |
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. |
|
2010-10-28 |
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
|
|
Spring 2007: MATH 417 — Numerical Analysis I
Click on the following links to get a pdf file:
First day
handout
|
|
Fall 2006: MATH 412-503 — Theory of Partial Differential Equations
Click on the following links to get a pdf file:
First day
handout
|
|
Fall 2006: MATH 417-501 — Numerical Analysis I
Click on the following links to get a pdf file:
First day
handout
|
|
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:
| Containers |
| Algorithms |
| Streams |
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) |
| 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) |
| 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) |