## Math 602

Methods and Applications of Partial Differential Equations (Graduate Level)

Math 602: Methods and Applications of Partial Differential Equations, section 601
Texas A&M University, Spring 2014
• Syllabus
• Office Hours: Tuesday, Thursday, 1:00-2:30 pm, or by appointment
• Contacting me: The best way to contact me is via email. Please note that you should not expect an immediate response 24 hours a day, but that I will try to answer your email in a reasonable amount of time (usually I am pretty fast). When emailing, be sure to include your full name, and put [Math 602] in the title.

• A YouTube video about the history of George Green and Green's function. Thanks to Kevin Laux for the link.

Test Keys:
Quiz 01 key.pdf Correction on #1: "cos" should be "-sin".
Quiz 02 key.pdf
Quiz 03 key.pdf Correction on #2: "0=h(0)" should be "0=h'(0)", so c4=0 and "sinh" is replaced with "cosh".
Quiz 04 key.pdf
Quiz 05 key.pdf
Quiz 06 key.pdf
Quiz 7: Canceledi
Quiz 08 key.pdf
Quiz 09 key.pdf
Exam 1 key.pdf
Exam 2 key.pdf

A list of all problems given since 2006: All_Exams.pdf

Homework Assignments and Old Quizzes (not to be turned in):
Quizzes will be given at the following dates (dates my change).
Questions will be based on past quizzes, past midterms, and homework assignements.

## LaTeX Resources

A few resources for learning LaTeX

• Here are a few resources for learning LaTeX:
• ## Basic Course Information

This information is subject to change. Official information will be made available on the syllabus.

• ### Course Description:

This is a one-semester course on Partial Differential Equations (PDEs) which gives an introduction to various topics in PDEs and provides a firm basis for future study. PDEs lie at the heart of an extremely large number of practical and theoretical problems in science, mathematics, and engineering. Furthermore, the unsolved problems are enormously varied, rich, and challenging. Our growing understanding of these equations has yielded a massive amount of progress for human kind. The methods involved are incredibly useful in science, and will require us to develop sophisticated and interesting mathematics to handle them.

• ### Course Outline:

There will be some emphasis on the following topics:
• Classification of linear partial differential equations of the second order
• Fourier series, orthogonal functions, applications to partial differential equations
• Special functions, Sturm-Liouville theory, applications to boundary value problems
• Introduction to Green's functions
• Fourier transforms.
• ### Prerequisites

According to the course catalogue, the prerequists are: MATH 601 or (MATH 308 and MATH 407). More generally, some key topics that will be helpful are:
• Linear algebra: linear systems of equations, matrices and vectors, vector spaces and linear operators, subspaces, scalar product, orthogonality, norm eigenvalues and eigenvectors
• Calculus/analysis: Derivatives and integrals in several dimensions, Taylor expansion
• Complex Analysis
• Ordinary Differential equations: Solutions to first and second order differential equations

## Study Help

Being able to study efficiently is a skill that takes time to develop. It is normal to discover that the study habits and skills that worked for you as an undergraduate need to be updated and improved if you are going to keep from being overwhelmed. It takes time and effort, as well as trial and error, to find which study habits work best for you. Below are some suggestions and resources to get you started. Good luck, and study efficiently!
• Tips on doing homework
1. On the same day the homework is assigned, read over all the problems. This will get you thinking about them early on. The problems will stay in your brain on the "back burner", and you may have more luck later when you sit down to work them.
2. Do all the homework problems, even if you don't get them in on time.
3. Homework is excercise. If you want to get better at sports, you need to excercise everyday. If you want to get better at mathematics, you need to work on problems every day.
• Advice from students for doing better on exams
1. Study with more people. Study in groups or with a partner. Work problems together on a white board. Take turns challenging each other. Being able to explain a problem clearly to someone else is a major step towards understanding it.
2. Pay attention in class and to the instructor's emails.
3. Rework what you didn't understand well.
4. Write down short examples on the notecard.
Note: Notecards are not allowed on exams; the pupose of this tip is to help with studying.
5. Label formulas on your cards.
6. Theorems should be on the notecard.
7. Keep a running list of things for your notecard rather than trying to compile it all at the last minute.
8. Write down formulas completely and correctly.
• Advice on how to predict what is on the exam (in addition to some of the above):
1. Old exams are a hint.
2. Pay attention to problems done in class several times.
3. Take note of quiz questions; one of those might become an exam question.
4. Problems tend to be similar to homework/suggested homework.
• In Class
• Make sure you have read the section we are covering before you come to class.