# MAT 341

## Applied Real Analysis

### Introduction:

This is a webpage for the summer 2011 MAT 341 course.

My name is S.Ali Aleyasin and I shall be giving the lecture. Your homeworks will be graded by Ying Chi. You can reach her at chying509 AT hotmail DOT com.

The aim of this course is to understand how certain partial differential equations arise (the heat equation and the wave equation, in dimensions one and two), and how to arrive at solutions to these equations by using Fourier series. This course is an introduction to linear partial differential equations, based on the three main examples arising from Mathematical Physics. We follow a pragmatic approach, introducing Fourier series and using them to solve a number of boundary value problems associated with the heat, wave and Laplace equations. Thus, we begin by studying the concept of an orthogonal set of functions, and the representation of arbitrary functions in series of functions from such sets. We then use the method of separation of variables in combination with these representations to obtain solutions to boundary values problems for the operators mentioned above.

The prerequisite for this course is some elemntary knowledge of ordinary differential equations. So do please review that if your ODE is rusty. Also, we'll be dealing with trigonometric series. So you might need to review the basic trigonometric identities.

We meet on Mondays, Wednesdays, and Thursdays, 1800-2015 in Chemistry-128.
If you need help with the course, or if you wish to learn more, do not
hesitate to visit me during my office hours. In case the time does not suit
you, we can make an appointment some other time.

A word of Caution: The usual autumn semester MAT126
runs for 15 weeks. Now, in the summer, we squeeze that into 5 weeks, and there
are no recitations. However, the autumn version has got 3 hours of lecture per week,
while we have 7 hours. This means I should, and I shall, present the same
material and at a higher pace. But it also means that you cannot afford to
lose track. If you experience trouble keeping up with the course, please
contact me immediately. Also, it is strongly recommended that you check out
the Maths Learning Centre (MLC, located in the Math Tower, basement level).
There should always be staffed with plenty of TAs willing to help you.

I am planning to post some suggestions for studying for the midterm and the final, check the webpage around June 21 and July 5.

### Book:

The textbook we use is Powers' Bounday Value Problems; so I am going to post my own homework, you can choose any edition you find!

We shall try to cover selected sections from chapters 1 and 5 (at minimum 1.1-1.5,1.9,1.11; 2.1-2.11; 3.1-3.4,3.6; 4.1-4.5; 5.1,5.3-5.7).

### Final Exam:

The exam is going to be cumulative. But I shall emphasise the material we covered after the midterm. In addition to the first part of the course, I want you to have studied 1.9, 2.5, 2.6, 2.7, 2.8, 2.10 (which I shall teach on Monday), 3.1, 3.2, 3.3, 5.3, 5.4.

### Schedule:

 Week of Sectionscovered HW HW due Comments May 31st 1.1 1.2 1.3 1.4 2.1 2.2 Homework 1 Due next Wednesday. June 8 There will be a short-exam next Wednesday. June 6th 1.5 2.2 2.3 2.4 4.14.2 4.3 June 15th Notes on Fourier Series June 13th 4.5 Homework 2 Due next Monday. June 22th Please be advised that on Thursday we will have the Midterm. June 20th 4.5 Homework 3 Due next Thursday. June 30th June 27th 4.5 July 4th 4.5 Homework 4 Due next Friday. July 8th This is sort of practice exam. Problem 2 is assigned as homework.

### Disabilities:

If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at http://studentaffairs.stonybrook.edu/dss or (631)632-6748. They will determine with you what accomodations are necessary and appropriate. All information and documentation is confidential.

Students who require assistance during emergency evacuation are encouraged to discuss their needs with the lecturer and Disability Support Service. For procedure and information go to the following website: http://www.stonybrook.edu/ehs/fire/disabilities.shtml