Mathematics 4347     Introduction to Partial Differential Equations      Course Description

Fall, 2011 (MWF 2:00 in Skiles Room 154)

Instructor: Evans Harrell, Office Skiles 218D, 894 3300, harrell at math.gatech.edu
Instructor's office periods: MW, 3:00-4:30 pm, in Skiles 218D.

Course Description

It is a profound and mysterious fact that most of the fundamental laws of physics have the form of partial differential equations. The Schrödinger equation of quantum physics, Clerk Maxwell's synopsis of electromagnetism, and the essential equations of both fluid and solid mechanics are all in the form of PDEs, and a vast number of other PDEs arise when these and other physical laws are used to generate practical models in engineering.

The underlying reason for this is that we use derivatives to describe change, and when, for example, change in time is related to variation in space, or temperature, or pressure, or any other continuous variable, that must be described by an equation containing different partial derivatives. Voilà - a PDE. We expect different physical laws to be connected to different types of PDEs. It will also turn out that if we can classify PDEs intelligently, we will understand what to expect of their solutions by analogy with prototypes we know from basic physical laws. Therefore the course will begin with a discussion of important model PDEs and their classification.

After classification and modeling we will turn to the enormous subject of methods of solution, and some related matters of theory, concentrating on:

The lectures will relate to the textbook Introduction to Partial Differential Equations, by Zachmanoglou and Thoe, and to web resources, especially parts of the on-line text by Evans Harrell and James Herod.

Prerequisites

Students should be familiar with calculus through vector analysis, linear algebra at the level of Tech's Math 2406 and ordinary differential equations at the level of Tech's Math 2403. Helpful, but not required, background would include some parts of science or engineering where partial differential equations arise as laws of nature or models..

Class web page

The class will be coordinated through T-Square, but you can also consult the Class web page directly. It is your responsibility to look at the web page regularly for information about the class, such as homework assignments. (It will be mirrored at T-Square, if you prefer.)

Grading and requirements

There will be exams on
  1. Monday, 19 September,
  2. Wednesday, 19 October, and
  3. Monday, 14 November,
as well as a final exam, and there may be short pop quizzes on other days. You will be able to review your class standing after each test from the Web page. Homework problems will be posed in the lectures or on the Web, and will be collected on Mondays, or Wednesdays when Monday is a holiday.

Missed tests, special accommodation, etc

There will never be an opportunity to retake a missed exam after the event. Any special accommodations must be requested by electronic mail at least two weeks in advance of any scheduled event. It is the student's responsibility to take the initiative for all such accommodations.

Tests may vary as to what materials are permitted, and whether part of the test can be prepared at home. In all cases work on the test is to be done by the student without collaboration and without consultation of materials other than those explicitly permitted.

Learning Disabilities

It is the right of any student with a certified learning disability to request necessary accommodation. Such requests must be made well in advance of the time that the accommodation is required and a letter of documentation from the ADAPTS office must be presented at the time of any request.

Academic Integrity

Students are expected to abide by the Georgia Tech Academic Honor Code. You are encouraged to discuss the homework and solutions with classmates, but you must later write up the work independently, without consultation or copying. No collaboration is permitted on quizzes or exams. 

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