Math 534 Honors - Introduction to  Partial Differential Equations

                                                            Course Nbr. 80214 -- Spring 2026

                                                                    Prof. Andrea R. Nahmod


Lectures :    Tuesdays and Thursdays 2:30pm-3:45pm  in   LGRT  171

Office Hours: Wednesdays Time TBD and/or by appointment in LGRT 1588. Also: Feel free to email me anytime with any questions you may have at: 

E-Mail:   mylastname at umass dot edu

Telephone:  (413) 545 6031 or simply Ext. 5-6031 from Campus.  Office:   LGRT #1588

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 Thursday February 19th (University follows a 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.

Your grade will be based on:

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 (!).


Mandatory Information:

Accommodation Statement

The University of Massachusetts Amherst is committed to providing an equal educational opportunity for all students.  If you have a documented physical, psychological, or learning disability on file with Disability Services (DS), you may be eligible for reasonable academic accommodations to help you succeed in this course.  If you have a documented disability that requires an accommodation, please notify me within the first two weeks of the semester so that we may make appropriate arrangements.  For further information, please visit Disability Services (https://www.umass.edu/disability/)

Academic Honesty Statement

Since the integrity of the academic enterprise of any institution of higher education requires honesty in scholarship and research, academic honesty is required of all students at the University of Massachusetts Amherst.  Academic dishonesty is prohibited in all programs of the University.  Academic dishonesty includes but is not limited to: cheating, fabrication, plagiarism, and facilitating dishonesty.  Appropriate sanctions may be imposed on any student who has committed an act of academic dishonesty.  Instructors should take reasonable steps to address academic misconduct.  Any person who has reason to believe that a student has committed academic dishonesty should bring such information to the attention of the appropriate course instructor as soon as possible.  Instances of academic dishonesty not related to a specific course should be brought to the attention of the appropriate department Head or Chair.  Since students are expected to be familiar with this policy and the commonly accepted standards of academic integrity, ignorance of such standards is not normally sufficient evidence of lack of intent (http://www.umass.edu/dean_students/codeofconduct/acadhonesty/).

Title IX Statement –

In accordance with Title IX of the Education Amendments of 1972 that prohibits gender-based discrimination in educational settings that receive federal funds, the University of Massachusetts Amherst is committed to providing a safe learning environment for all students, free from all forms of discrimination, including sexual assault, sexual harassment, domestic violence, dating violence, stalking, and retaliation. This includes interactions in person or online through digital platforms and social media. Title IX also protects against discrimination on the basis of pregnancy, childbirth, false pregnancy, miscarriage, abortion, or related conditions, including recovery. There are resources here on campus to support you. A summary of the available Title IX resources (confidential and non-confidential) can be found at the following link: https://www.umass.edu/titleix/resources. You do not need to make a formal report to access them. If you need immediate support, you are not alone. Free and confidential support is available 24 hours a day / 7 days a week / 365 days a year at the SASA Hotline 413-545-0800.