Fourier Analysis & Partial Differential Equations

Math 440 Fall 2021     MWF 8:00-8:50 Burruss 34

Instructor: Roger Thelwell Office: Roop 106
Contact: thelwerj@jmu.eduwith "M440 FA21" in subject tel: 568-5103 (office)
Course URL: http://educ.jmu.edu/~thelwerj/440/index.html and on Canvas google voice: check announcements on Canvas
OFFICE HRS: Roop 106 9-10am on MW and 1-2pm WF, and by appt.  
Text: Introduction to Partial Differential Equations by Peter J. Olver, a Springer UTM
Content & Goals:
The goal of this course to gain some understanding of both the theory and applications of Fourier Series & Partial Differential Equations (PDEs). Along the way, we will explore theoretical and applied aspects of the three canonical PDEs: the wave equation, the heat equation, and Laplace's equation. You'll build problem-solving skills as you grapple with the theory and by applying a variety of techniques to boundary-value problems (BVPs) and initial-boundary value problems (IBVPs) for PDEs.

Attendance:
While I won't require attendance, the probability of spectacular failure increases with each missed class. The lectures will supplement the material in the text, but will also contain jewels of information not found there. If exceptional situtations arise that force you to miss class, contact me as soon as possible so as to not fall behind. Please use my office hours if needed, and don't be afraid to send an email or give me a call.

Homework Sets:
Reading and Homework will be assigned throughout the semester. This will be a rigorous course, with inteverals of tedious hand computation and frustrating computer based tasks. Homework sets will be collected several times throughout the semester. You must SHOW your work for full credit and turn in neatly compiled problems. Many problems in PDE can be lengthy. Make it easy for me follow your work - you won't get credit by making me guess! Beware: your chances of passing the exams are poor if you consistently find that you can't complete the homework yourself.

Grading:
The standard scale will be used. 90-100: A- to A range; 80-89: B- to B+ range; 70-79: C- to C+ range; 60-69: D to D+ range; 59 and below: F. An exceptional job on the final project or excellent class attendance and participation could bump borderline cases up to the higher grade. Grades will be calculated as a weighted average from the following categories:

  1. Homework: weekly/bi-weekly assignments will make up 60% of the grade. Scores on these will be Satistfactory (C level), Good (B level), or Excellent (A level). If your submission is scored as not Satisfactory but submitted on time and complete, you will have up to week to revise and resubmit in order to earn a Satisfactory. I will ask for in-class presentations.
  2. Exams: There will be two exams at 15% each, one near the end of September and one near the end of November. Each of these will have a written and oral component. You will be given a list of topics and any questions not already assigned as homework problems at least one week in advance of each of the exams. Scores on these will be Satisfactory (C level), Good (B level), or Excellent (A level)
  3. Final Project: 10%. This will be a 20-30 minute presentation on a PDE topic of your choice. You will present your work between Thanksgiving and Finals week. Graded on the same scale as the exams: Satisfactory (C level), Good (B level), or Excellent (A level).
Honor code
Remember that JMU has a strict honor code. All tests, exams, handouts, and materials for this course, including those posted on Canvas and on faculty and course websites, are the intellectual property of the instructor. Dissemination of any of these items, in whole or in part, through any other agency or website is a violation of the JMU honor code and will be referred to the Honor Council.

Diversity and Inclusion
James Madison University is a community dedicated to diversity and inclusivity. As faculty, we believe that learning environments should support a diversity of thoughts, perspectives, experiences, and identities. We invite you to share anything with us that might help create a more inclusive and welcoming learning environment.

Common JMU Academic Policies
Visit http://www.jmu.edu/syllabus/ for information about: Attendance, Academic Honesty, Adding/Dropping Courses, Disability Accommodations, Disruptive Behavior, Inclement Weather, and Religious Accommodations. If you need to make use of Disability and/or Reglious Accommodations, you must notify me within the first two weeks of the semester.

Nature of the Course Content
(directly from course catalogue)
MATH 440. Fourier Analysis and Partial Differential Equation 3 credits. Offered fall. Elementary applied partial differential equations, the heat equation, Laplace’s equation, the wave equation; Fourier series and boundary value problems. Both theory and problem-solving will be included. Prerequisite: MATH 238 or MATH 336.