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.


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.


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!


Time: (12 hour) MWF 12:30 - 1:35
Room: Haldeman Center 028
X-hour: Tu 1:00-1:50  (used as needed)


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


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?


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.