Math 534 Honors - Introduction to  Partial Differential Equations

                                                            Course Nbr. 17236 -- Spring 2020

                                                                    Prof. Andrea R. Nahmod

Lectures :    Tuesdays and Thursdays 11:30am-12:45am  in   LGRT  145

Office Hours: Wednesdays 1:00PM-2:30PM or by appointment (in LGRT 1540). Also: Feel free to email me anytime with any questions you may have at: 

E-Mail:   mylastname at math dot umass dot edu

Main Book:   Partial Differential Equations: An Introduction,  by Walter Strauss, Wiley, Second Edition. 

Reference text (optional): Partial Differential Equations in Action: From Modelling to Theory by Sandro Salsa, (UNITEXT; Springer) 3rd ed. 2016 Edition.  

Syllabus:  An introduction to PDEs (partial differential equations), covering the some of the most basic and ubiquitous equations modeling physical problems and arising in a variety of contexts. We shall study the existence and derivation of explicit formulas for their solutions  —when feasible and study their behavior.  We will also learn how to read and use specific properties of each individual equation to analyze the behavior of solutions when explicit formulas do not exist. Equations covered include:  heat/diffusion equations;  the Laplace’s equation; transport equations and the wave equation. Along the way we will discuss topics such as  Fourier series, separation of variables, harmonic functions and potential theory,  maximum principle, energy methods, etc.   Time-permitting, we will discuss some additional topics. The final grade will be determined on the basis of homework, attendance and class participation, a midterm and final projects.

Special Announcements: No class on Tuesday February 18th (University follows Monday schedule due to President's Day).

Assignments:   Homeworks will be assigned and collected regularly. 

No late homeworks will be generally accepted (in case of illness please contact me before due date).  

All assignments and their `due dates' will be posted on this web page by clicking in

                                                                HOMEWORK, etc.       

Handouts:

1)  The Wave Equation in 1D

2)  The Wave Equation in 2D

3) Diffusion and Heat Flow in 1D, 3D and higher D

4) Wave Equation on R and the Causality Principle.

5)  The Energy Method and Uniqueness for the Wave Equation on R.

6) Maximum Principle and Stability; and Energy Method for the Heat/Diffusion Equation on [0, L]

7)** The Weak Maximum Principle and Comparison Principle (from Sandro Salsa's book)

8)  Diffusion/Heat Equation on R^d (Notes for Section 2.4 and more)

9) Wave Equation on the Half-Line (also first part of Section 3.2 in Strauss)

10) Wave with a Source  (also Strauss section 3.3)

Grading Policy. Modified on March 23rd, 2020 given COVID-19 and remote instruction. 

Your grade will be based on:

•  Homework and class participation (subjectively given)  (30% + 10%)
  
•  A set of special homework and projects to be turn in at the end of classes typed in Latex. The full list will be available to you the last day of classes  and due  uploaded in Moodle the day and time of your final exam. The problems will be released as we move along and posted at the end of the homework under Special Projects (60%)
  

* Due to the amount of material to be covered, the pace might be fast at times. And since later sections depend on ideas covered earlier, it is important not to fall behind.

* You are expected to read the sections we will be covering in lecture before/after you come to class. We will not have time to cover all the examples from the text, but you are still expected to read the whole section yourself and be familiar with it.  You are always welcome to discuss the material with me.  

* Please let me know in advance of any special circumstances which may prevent you from attending classes.

* Help each other out and discuss difficulties, but do your own work (!).