128C Numerical Solution of Differential Equations

Class Time/Place: 11:00 AM - 11:50 AM MWF Chemistry 166

Instructor: Jesus A. De Loera

TA: (Jessie) Xiaotie Chen

Course Description: This course is an introduction to the numerical solution of differential equations. The focus is more on applied and computational aspects of many of the subjects you saw in 22B. Differential equations are important as they appear everywhere in engineering and science, but we rarely can solve them analytically. This course deals with the more realistic way to study equations, through computation and approximation. We will spend most of the time in ODEs (ordinary differential equations), but discuss the basics of PDEs (partial differential equations).

Textbook: Numerical Analysis (10th Edition) by Burden, Faires and Burden. Published by Brooks Cole (Cengage Learning).

Note that this textbook has many editions, preferably buy 10th edtion, but it is possible to read earlier editions and understand the theory.

Another useful references to support programming skills is C. Moler: Numerical Computing with MATLAB by Cleve Moler, SIAM 2004 (available freely online)

Here are the key topics:

Applications and Motivation: Kepler's problem of motion, Chemical Kinetics problems, Lotka-Volterra population models.
Existence and uniqueness of solutions, Euler's method
Higher order Taylor Methods
Runge-Kutta Methods
Multistep Methods, Extrapolation Methods
Higher-order equations and systems of Differential Eqs.
Stability and Stiff Differential Equations.
Boundary-Value Problems (BVPs) for ODEs
BVPs shooting methods
BVPs direct methods
Basics of numerical Partial Differential Equations
A quick introduction of Finite-Element methods

Prerequisite and Expectations

MAT 22A,22B (i.e., practical understanding of elementary linear algebra).
Solid knowledge of programming is required. Some experience in MATLAB is preferable, but MATLAB is very easy to learn. If you do not know how to use MATLAB, then you need to self-study using the MATLAB Primer and other material listed below.
Formal attendance will not be taken. However, whether you are able to attend class or not, you are responsible for all the material presented in class.
This is a 4 unit course! You are expected to work 3 hours at home for each hour of lecture. In other words, expect to have 10 hours of homework each week.

Grading:
The grades will be calculated using the average and standard deviation of the class. 100 points are possible which will be divided as follows:

4 Homeworks, 15 points each (with the lowest score dropped),
1 midterm exam, 20 points (in class, April 23rd).
Final Project + Exam 35 points

Some important rules will be followed:

The homework has to be submitted online Through CANVAS web site. LATE HOMEWORK WILL NOT BE ACCEPTED.
Your work is not being graded solely from the final answer, I expect you to write neatly, justify your reasoning and show all missing details.
I will assign programming project that require you to use MATLAB.
All exams are closed book. No calculators or cell phones allowed.
There will be NO MAKE-UP EXAMS.
All projects should be done in a team of 2 or 3 students. The project will include writing MATLAB code to investigate one of the application topics presented in class.

SOFTWARE and other RESOURCES:

Create an account at the Math Department. Visit http://www.math.ucdavis.edu/comp/class-accts and follow the instructions.
It is important to create your account before you come to the Lab for the first time. You can then work either at the Undergraduate Computer Lab (2118 Math. Sci. Bldg.) or from any other lab in the campus or even from your home PC by remotely connecting to one of the departmental servers, such as [point,cosine,sine,tangent].math.ucdavis.edu. The lab is open 9am-5pm on weekdays.
Use your own account at your own department if your department has the MATLAB license. This is the case for most of the engineering departments.
Install Octave system on your own PC, which is free software and emulates MATLAB. Caution: Most likely you can do all the lab exercises, but I have not tested all the exercises yet. Visit the official web site of Octave at http://www.octave.org for downloading and installing information.

For those who have never used MATLAB before or need to brush up their MATLAB knowledge, please take a look at the following highly useful MATLAB primers and tutorials.

The official MATLAB online "getting started guide" is available from MATLAB (it is free, but registration of an account is required).
MATLAB offers a very nice online video tutorial
A Practical Introduction to MATLAB by Mark S. Gockenbach.
MATLAB Primer by Kermit Sigmon. This publicly available version was written for older version of MATLAB 3.5, but still useful. (Our current version of MATLAB is 7.x.)
MATLAB Tutorial at MIT. This is the shortest one, tailored to the linear algebra context.
Numerical Computing with MATLAB by Cleve Moler. This is a book by the creator of MATLAB. I highly recommend to read Chapter 1: Introduction to MATLAB as well as Chapter 7: Ordinary Differential Equations and Chapter 11: Partial Differential Equations.

HOMEWORKS & HANDOUTS

Guidelines for ALL projects

Homework 1, due April 18th:

Homework 2, due May 4th:

Homework 3, due May 23th:

Homework 4, due June 6st:

Final exam project, due June 8st: