Math 417 Partial Differential Equations
Spring 2018

Course Information


Instructor:
  • Jonas Lührmann
  • Email: luehrmann (at) math.jhu.edu
  • Office: Krieger 219
  • Office hours: T 14:00 - 15:30
Course Assistant:
  • Junyan Zhang
  • Email: jzhan182 (at) math.jhu.edu
  • Office hours: W 12:00 - 13:00 at Krieger 211
Lectures:
  • TTh 12:00 - 13:15 at Maryland 104
Textbook:

This course is an introduction to the theory of partial differential equations, with an emphasis on solving techniques and applications. We will largely follow the textbook by Richard Haberman. I strongly recommend to you to read the relevant sections of the textbook before each lecture and to take notes in class.

  • Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, 4th edition, by Richard Haberman


Exams:

There will be a midterm exam and a final exam:

  • Midterm exam: Thursday, March 15, in class
  • Final exam: Tuesday, May 15, 9:00 am -12:00 (noon), Maryland 104

Exams are closed book, closed notes. There will be no make-up exams. For excused absences, the grade for a missed exam will be calculated based on your performance on all remaining exams. If you miss an exam, you will have to provide documentation and a valid excuse. Unexcused absences count as 0.



Grade Policy:

The course grade will be determined as follows:
  • Homework: 30%
  • Midterm exam: 30%
  • Final exam: 40%
Homework:

Weekly homework assignments will be posted to blackboard. Every Thursday the homework sets are collected at the beginning of class and the graded homeworks will be returned the following week. No late homeworks will be accepted. The lowest homework score will be dropped from the final grade calculation.

You are encouraged to do your homework in groups. However, you must write up your solutions on your own. Copying is not acceptable.

Special Aid:
Students with disabilities who may need special arrangements within this course must first register with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accomodations please remind me at least 7 days before the midterm or final exam by email, during office hour or after class.

JHU Ethics Statement:

The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics. You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please ask the instructor.


Tentative Course Schedule

Here is a tentative schedule for this course. Our first goal is to cover Chapters 1-5 from the textbook by R. Haberman. Afterwards we will discuss several selected topics (still to be decided). I strongly recommend to you to read the relevant sections of the textbook before each lecture.

Week
Topics
Sections

Jan 30, Feb 1

Introduction, Derivation of the heat equation, Boundary conditions

Read §1.1-1.5

Feb 6, 8

Separation of variables, Heat equation

Read §2.1-2.4

Feb 13, 15

Laplace equation, Fourier series

Read §2.5, 3.1

Feb 20, 22

Fourier series, Term by term differentiation

Read §3.2-3.4

Feb 27, Mar 1

Fourier series: complex form, Inhomogeneous problems

Read §3.5-3.6, §8.2-8.3

Mar 6, 8

Wave equation

Read §4.1-4.5

Mar 13, 15

Sturm-Liouville Eigenvalue Problems

Midterm exam on Thursday in class

Read §5.1-5.3

Mar 19-25

Spring vacation

Mar 27, 29

Sturm-Liouville Problems (continued), Self-adjoint operators, Rayleigh quotient, Boundary conditions of the third kind

Read §5.3-5.8

Apr 3, 5

Approximation properties, Large eigenvalues, Higher-dimensional PDEs

Read §5.9-5.10 and §7.1-7.4

Apr 10, 12

Higher-dimensional PDEs; Convergence of Fourier series (some proofs)

Read §7.1-7.4

Apr 17, 19

Fourier transform and infinite domain problems

Read §10.1-10.3

Apr 24, 26

Fourier transform and infinite domain problems (continued)

Read §10.4-10.6

May 1, 3

Method of characteristics for wave equations; Course Review

Read §12.1-12.3

Final exam:

Tuesday, May 15, 9:00 am -12:00 (noon), Maryland 104