Math 110.417 - Partial Differential Equations

Textbook:  Richard Haberman .   Applied Partial Differential Equations, Fourth Edition.
                  (Plan to cover Chapters 1-5 and 7, and selected material from Chapters 10, 12,  and others. If you have another edition, please check if the homework assignments agree.)
                  Sandro Salsa, Gianmaria Verzini .   Partial Differential Equations in Action: From Modelling to Theory. Fourth Edition.
                 

Course plan:
Characteristics of PDEs, well-posed problems. Separation of variables and expansions of solutions. Fourier series (bounded domain), Fourier transform (infinite domain).
Heat equation and diffusion: IBVP, equilibrium, fundamental solutions, maximum principles
Laplace equation: Sturm-Liouville eigenvalue problems, Green's functions, Poisson's formula, maximum principles, potential theory
The wave equation: Cauchy problem, domains of influence and dependence, Poisson's solution, energy inequalities

Prerequisite: Calculus III. Recommended: 110.405 or 110.415. 4 credits.

Grading Policy: 11 homework assignments (20%), 11 Quizzes (20%)   1 midterm exam (30%) and a final (30%).  The schedule of these exams is given with the homework problems below. There will be no make-up on homework or exams. 

• Homework:
  
  • Homework will be assigned by each Thursday and due on the next Tuesday. There will be 11 assignments, and the lowest score will be dropped in total grade. No late homework will be accepted. To encourage you to do your best in every assignment, the part of your lowest score above 60% will be counted as extra credits to your homework grade. Each assignment has 20 points, with 5 points counting towards completeness and legibility.
  • You are strongly encouraged to collaborate in the analysis and study stage of homework preparation. However, you are required to submit completely original work and must write up your homework for final submission alone. Both parties of copied homework will be assigned a score 0.
• Quizzes take place each Thursday before class (unless otherwise specified). There will be 11 quizzes, and the lowest score will be dropped. NO make-up quizzes.
• Exams: 
  
  • Two exams: Midterm and Final. 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 other parts. Unexcused absences count as zero.
• Grade scale (as typical): >=93% = A; 90-92% = A-, 87-89% = B+; 83-87% = B, 80-82% B-; ....

Academic Support: Besides attending the lectures, the recitation sections and office hours, I encourage you to use the following opportunities for additional academic support:

• Math Help Room*. This free service is a very valuable way to get one-on-one help on the current material of the class from other students outside the course. It is staffed by graduate students and advanced undergraduates. Please see the up-to-date schedule on the website.

Special Aid: Students with disabilities who may need special arrangements within this course must first be registered with the Office of Academic Advising. I will need to have received confirmation from the Office of Academic Advising. To arrange for testing accommodations please remind me at least 7 days before each of the midterms or final exam by email.

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.