## Welcome to Math 126

This is

**Math 126**:

** Topics in Applied
Mathematics**

Partial differential equations (PDEs) are essential for the
modelling of
physical phenomena appearing in a variety of fields from geophysics and
fluid dynamics to
geometry. In this course, we will study three major topics one should
understand when modelling with PDEs. The topics are:

(i) the theory (e.g. existence and uniqueness of solutions)>

(ii) when and how can solutions be found analytically>

(iii) classic numerical techniques (e.g. finite difference and finite
element methods) and how
to determine if the method is stable and convergent.

In addition, we will discuss the limitations of existing solution
techniques in the context of open research questions.

### Instructor

Adrianna
Gillman

Office: 210 Kemeny Hall

Office hours: Th 2:30-3:30 and by appointment

Phone: 646-2293 or email
(preferred)
Note that you do not need an appointment to attend
regularly-scheduled
office hours. If you have a conflict you may make an appointment to
meet outside those times.

### General Information

**Textbooks:** There is no required text for this course.
There are however several text from which the material will be taken
from. These are suggested text and are reserved in the library
for your refererence.

Suggested Textbooks:
Partial
Differential Equations by L. Evans

Numerical
Solution of Partial Differential Equations by K. Morton and D.
Mayers

Finite Difference
Equations for Differential Equations by R. LeVeque. Available

here.
### Dissabilities

I encourage any students with
disabilities, including "invisible" disabilities such as chronic
diseases and learning disabilities, to discuss appropriate
accommodations with me, which might help you with this class, either
after class or during office hours. Dartmouth College has an active
program to help students with disabilities, and I am happy to do
whatever I can to help out, as appropriate.

The Student Disabilities Center is
located at 318 Wilson Hall, ext. 6-9900,
http://math.dartmouth.edu/~accessability, if you have any
questions. Any student with a documented disability requiring academic
adjustments or accommodations is requested to speak with me by the end
of the second week of the term. All discussions will remain
confidential, although the Academic Skills Center may be consulted to
verify the documentation of the disability and advise on an appropriate
response to the need. It is important, however, that you talk to me
soon, so that I can make whatever arrangements might be needed in a
timely fashion.

### The Honor Principle

Students are encouraged to work
together to do homework problems. What is important is a student's
eventual understanding of homework problems, and not how that is
achieved. The honor principle applies to homework in the following way.
What a student
turns in as a written homework solution is to be his or her own
understanding of how to do the problem. Students must state what
sources they have consulted, with whom they have collaborated, and from
whom they have received help. Students are discouraged from
using solutions to problems that may be posted on the web, and as just
stated, must reference them if they use them. The solutions you submit
must be written by you alone. Any copying (electronic or otherwise) of
another person's solutions, in whole or in part, is a violation of the
Honor Code.

If you have any questions as to whether
some action would be acceptable under the Academic Honor Code, please
speak to me, and I will be glad to help clarify things. It is always
easier to ask beforehand than to have trouble later!

### Lectures

Time: (12 hour) MWF 12:30 -
1:35

Room: Haldeman Center 028

X-hour: Tu 1:00-1:50
(used as needed)

### Grading

Your grade will be based on homework, class participation, a project
and a paper reading.

### Homeworks

Assignments will be posted and due on Fridays.

### Paper Reading

You will present three major aspects of a paper of your choice.
(Note:
the paper must be related to class.) The three aspects you are to
discuss are:

1- What problem is the paper solving?

2- What are the difficulties associated with the problem?

3- How does the author(s) address these issues? Does it work?

### Project

The project will be due at the end of the term. You are free to
chose to create a computer program or write short paper. The computer
program should be accompanied by documentation. Independent of what you
choose the text should be written in Latex. Your choice of
project will be determined by an individual discussion with the
instructor during the third week of the term.

Last modified 3 Jan 2013
by AG.