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Math 534
Honors - Introduction to Partial Differential Equations

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Course Nbr. 17236 --
Spring 2020

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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

Telephone:
(413) 545 6031 or simply Ext. 5-6031 from Campus.
Office: LGRT #1540
#### Main
Book: * **Partial Differential
Equations: An Introduction, by Walter Strauss, Wiley,
Second Edition.*

#### __R____eference 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

__Handouts:__

**1)
The Wave Equation in 1D**

**2) The Wave
Equation in 2D**

**3) Diffusion and Hea****t 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%)

Some
Important Remarks:

##### * 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 (!).

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