MATH 404: Introduction to Partial Differential Equations I
Fall 2020 Course information
| Class Time/Place: | MoWe 5:30pm–6:45pm, online |
| Email: | rostamian@umbc.edu |
| Online office hours: | Tuesdays 11:00–12:00, on Blackboard |
Course content
This is a first course on Partial Differential Equations (PDEs). It provides an overview of the subject from an elementary point of view, and introduces some classic techniques for solving initial and boundary value problem. An integral part of the course is the analysis of physical phenomena such as heat conduction, wave propagation, etc., that lead to mathematical formulations in terms of PDEs.
Prerequisites
You must have completed MATH 225 (Ordinary Differential Equations) and MATH 251 (Multivariable Calculus) with a grade of "C" or better before you can take this class.
Online instruction
This is a fully synchronous remote class which means you will be expected to log in and participate in class sessions at established dates and times for all sessions. The class meets on Blackboard Collaborate on Mondays and Wednesdays between 5:30 and 6:45pm.
Syllabus
The very affordable Dover book Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow will serve as the course's textbook. We will cover most of the book which consists of:
- Chapter 1: Introduction
- Chapter 2: Diffusion-type problems (e.g., the heat equation)
- Chapter 3: Hyperbolic-type problems (e.g., the wave equation)
- Chapter 4: Elliptic-type problem (e.g., (e.g., equilibrium of membranes)
- Chapter 5: Numerical methods (a selection of topics)
Detailed schedule and homework assignments
I will enter homework assignments here after each class. You are expected to work on all the assigned problems and make sure that you can solve them.
Whenever possible, I prefer giving short, in-class quizzes based on the previous week's homework assignments. In those cases I won't collect/grade the homework; I will grade the quiz instead. I will mark an impending in-class quiz in the table below several days in advance. There won't be "surprise" quizzes.
An in-class quiz, however, is not always feasible—in some parts of the course there just aren't short problems suitable for a quick quiz. In those cases, I will collect the homework which may consists of several problems, and will grade a representative subset. Homework assignments which are going to be collected are indicated by a due date in the table below.
Their cumulative score of quizzes and homeworks will determine your course grade. Cut-off scores for the grades of A, B, C, D, F are 85%, 75%, 65%, 55%. There will be no exams.
| Class Schedule | |
|---|---|
| Mon Aug 31 | Lessons 1–4 Introduction: Why PDEs?
Homework #1 due Sep 9 |
| Wed Sep 2 | |
| Mon Sep 7 | Labor Day – no class |
| Wed Sep 9 | Homework #2 due Sep 16 |
| Mon Sep 14 | |
| Wed Sep 16 |
Homework #3 due Sep 23
An easier problem set: hw03-ver2.pdf |
| Mon Sep 21 | |
| Wed Sep 23 | Homework #4 due Sep 30 |
| Mon Sep 28 | |
| Wed Sep 30 | Homework #5 due Oct 7 |
| Mon Oct 5 | |
| Wed Oct 7 | |
| Mon Oct 12 | |
| Wed Oct 14 | Homework #6 due Oct 21 |
| Mon Oct 19 | |
| Wed Oct 21 | Homework #7 due Oct 28 |
| Mon Oct 26 | |
| Wed Oct 28 | |
| Mon Nov 2 | |
| Wed Nov 4 | Homework #8 due Nov 11 |
| Mon Nov 9 | |
| Wed Nov 11 | Homework #9 due Nov 18 |
| Mon Nov 16 | |
| Wed Nov 18 | |
| Mon Nov 23 | |
| Wed Nov 25 | |
| Mon Nov 30 | |
| Wed Dec 2 | Homework #10 due Dec 14 |
| Mon Dec 7 | |
Lecture slides as of Sep 30: slides-heat.pdf
Lecture slides as of Oct 14: slides-wave.pdf
Notes on traffic flow: notes-on-traffic-flow.pdf
Finite difference schemes for the heat equation
heat_explicit.m
heat_implicit.m
Movies from slides-heat.pdf
- Slide 7: refrigerator.mp4
- Slide 13: refrigerator-3d.mp4
- Slide 22: fourier-series-demo1.mp4
- Slide 22: fourier-series-demo2.mp4
- Slide 25: heat-with-hat-function-anim.mp4
- Slide 25: heat-with-hat-function-3d.mp4
- Slide 30: heat-with-insulated-end.mp4
- Slide 39: heat-with-periodic-forcing.mp4
- Slide 46: heat-with-periodic-forcing-on-boundary.mp4
- Slide 77: heat-2d-a.mp4
- Slide 78: heat-2d-b.mp4
- Slide 98: heat-on-disk.mp4
- Slide 104: heat-on-annulus.mp4
Movies from slides-wave.pdf
- Slide 11: string1.mp4
- Slide 12: string2.mp4
- Slide 13: string-piano.mp4
- Slide 22: traveling-blip.mp4
- Slide 33: traveling-wave1.mp4
- Slide 33: traveling-wave2.mp4
- Slide 36: traveling-wave3.mp4
- Slide 36: traveling-wave4.mp4
- Slide 39: traveling-wave5-1.mp4
- Slide 39: traveling-wave5-2.mp4
- Slide 39: traveling-wave5-3.mp4
Miscellaneous notes
Registrar's Office Dates and Deadlines
The Official UMBC Honors Code
By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.
Student Disability Services (SDS)
Services for students with disabilities are provided for all students qualified under the Americans with Disabilities Act of 1990, the ADAA of 2009, and Section 504 of the Rehabilitation Act who request and are eligible for accommodations. The Office of Student Disability Services is the UMBC department designated to coordinate accommodations that would allow for students to have equal access and inclusion in their courses.