Math 110.417 - Partial Differential Equations

Lecture Schedule and Homework Assignments | General Information and Syllabus

Instructor:     Fei Lu [ feilu##   ( ## = @math.jhu.edu) ]
Class meets:   TTh, 3-4:15, Croft Hall G02.
Office Hours: Tue 2-3; Thr 8:00-9:00 (TBD),   Krieger 218
URL:          http://www.math.jhu.edu/~feilu/25Spring/PDE417/PDE417.html
TA : Lam Doan, ldoan5- at - jhu.edu

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 (SV) . Partial Differential Equations in Action: From Modelling to Theory. Fourth Edition.

Grading Policy: homework (20%), Quiz (20%), midterm exams (30%) and a final (30%). No make-ups on homework or exams. See General Information and Syllabus for details and information on getting help.

Homework will be assigned each Thursday and due on the next Tuesday. No late homework will be accepted. There will be 11 assignments, and the lowest score will be dropped in total grade. To encourage you to do your best in every assignment, the part of your lowest score above 50% will be counted as extra credits to your homework grade. Each assignment has 20 points, with 6 points counting towards completeness and legibility.
Quizzes occur each Thursday before class (unless otherwise specified). There will be 11 quizzes, and the lowest score will be dropped. NO make-up quizzes. The quizzes will be available on GradeScope on Thursday from 1 am to 2 pm on quiz days. Each quiz has 5 true/false questions, and you will have 10 minutes to complete it once you start it.
Exams are closed books, closed notes. Midterm: 3/13, in-class. Final: TBD. No make-up exams.

Please turn in homework assignments in the following format:

Present solutions with details. The homework will be graded based on the solution, not the final answer.
Box the final answer for each problem.

Announcements:
Jan.21: The Directed Reading Program is an effort, run by graduate students in our department, designed to allow undergraduate students to experience mathematics beyond the standard curriculum and to expose them to what doing and learning mathematics might feel like. To that end, the program pairs undergraduate students with graduate student mentors for one-on-one weekly meetings. The program culminates in short presentations given by the undergraduates at an end-of-semester party open to all. Moreover, students can earn 1 mathematics credit by successfully completing the program.

Tentative schedule ( Most of the content will be updated before each class )

week	Topics	Sections	Homework	Due
1/21, 1/23	Heat equation: derivation Boundary conditions Equilibrium	§1.1-5 LecNote LecNote	hw1: 1.2.9ab, 1.4.1g, 1.4.11, 1.5.3 For 1.5.3(b): show that the two vectors are orthogonal and normal. Recommend: 3Blue1Brown@Youtube What is a partial differential equation? Video in class: Heat Flow in a Non-uniform Rod	1/28
1/28, 1/30	Separation of variables Heat equation	§2.1-4; Quiz 1 LecNote	hw2: 2.2.4, 2.3.2(c), 2.3.3(b), 2.3.5, 2.3.6, 2.4.1(b), 2.4.6	2/4
2/4,2/6	Laplace equation Minimax Principle and energy method	§2.5,3.1; Quiz 2 LecNote	hw3: 2.5.1(d), 2.5.5(b),2.5.10, 3.2.2(d)(g)	2/11
2/11, 2/13	Fourier series Term by term differentiation	§3.3-4 ; Quiz 3 LecNote	hw4: 3.3.1b, 3.3.2c, 3.3.5c,3.3.18,3.4.1, 3.4.6, 3.4.7 Video in class: Gibbs Phenonmenon (Hojun Lee's simulation)	2/18
2/18, 2/20	Fourier series: complex form Inhomogeneous Problems	§3.5-6 §8.2-3 ; Quiz 4 LecNoteTu LecNoteTr	hw5: 3.5.1ab, 3.5.2a,3.5.5,3.4.11,8.2.2d, 8.3.6	2/25
2/25, 2/27	Wave equation	§4.1-5 ; Quiz 5 LecNote	hw6: 4.2.1a, 4.3.1,4.4.3b,4.4.4, 4.4.7, 4.4.12 Video in class: Wave equation (Hojun Lee's simulation)	3/4
3/4, 3/6	Sturm-Liouville problem Self-adjoint operator	§5.1-5 ; Quiz 6 LecNote	hw7: 5.3.3, 5.3.4 ac, 5.3.5, 5.3.8, 5.3.9, 5.4.5 Video in class: Sturm-Liouville Eigenvalue Problem and its Numerical Solution	3/11
3/11, 3/13	Midterm Review		Midterm 3/13 Midterm sample solution
3/18, 3/20	Spring Break;
3/25, 3/27	Sturm-Liouville theorem Rayleigh quotient, Robin BC	§5.5-8; Quiz 7 LecNote	hw8: 5.5.1cef, 5.5.8, 5.6.1a,5.6.2, 5.8.1b, 5.8.8abd, 5.8.9,	4/1
4/1, 4/3	Approximation properties Higher dimensional PDEs	§5.10; Quiz 8 LecNote LecNote 4/7	hw9: 5.10.2a, 5.10.3, 5.10.7 Video in class: Mean square error	4/8
4/8, 4/10	Higher dimensional PDEs Bessel functions Fourier Transform	§7.2-7; Quiz 9 LecNote §10.2-3 LecNotes	hw10: 7.3.3, 7.4.1, 7.5.9, 7.6.4,7.7.10,7.7.12b Video in class: Vibrating membrane (Qingci An's simulation)	4/15
4/15, 4/17	Fourier Transform Green's function	§10.3-5 ; Quiz 10 LecNotes	hw11: 10.3.13,10.4.4,10.4.8, 10.5.1,10.5.12	4/22
4/22,4/24	Green's function Review	§9.2-3; Quiz 11	hw12: 10.6.10,10.6.11c, 9.2.1ab, 9.3.2,9.3.3, 9.3.4 Hw12 is not collected. But it will be covered by Quiz11.
4/28-5/2	Reading week. Final Exam, Wed. May 7th, 9am-12pm. Coverage: ALL. 60% credits for material after midterm.