** Instructor:** Fei Lu [
feilu## ( ## = @math.jhu.edu) ]

**Class meets: **TTh, 12-1:15, Krieger Laverty Lounge

** Office Hours:** Tue 9:30-10:15, 1:15-2:15; Thr 9:30--10:15, Krieger 301** **

**URL: **
http://www.math.jhu.edu/~feilu/20Spring/PDE417/PDE417.html

**Grader : Junyan Zhang **

**Textbook:** Applied Partial Differential
Equations, Richard Haberman, Fourth Edition.

(Plan to covering Chapters 1-5 and 7, and selected material from
Chapters 10, 12, and others.)

**Grading Policy:**** homework (30%), midterm
exams (30%) and a final (40%). **No make-ups on
homework or exams. See General Information and Syllabus for details and information on
getting help.

- Homework will be assigned by 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 do your best in every assignments, the part of your lowest score above 60% will be counted as extra-credits to homework grade.
- Exams are closed book, closed notes. Midterm: in class on March 12. Final: Wednesday, May 6th, 9:00-12:00, in our classroom. No make-up exams.

- Standard size notebook paper;
**Staple**multiple pages, and**put your name**clearly on the top of the first page. - Present solutions with details. The homework will be graded based on solution, not the final answer.
- Box the final answer for each problem.

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.

Summer 2020 Research Experience For Undergraduates, University of Minnesota Application deadline: Friday, February 7, 2020

week | Topics | Sections | Homework | Due | Other |
---|---|---|---|---|---|

1/28, 1/30 | Heat equation: derivation Boundary conditions |
§1.1-5 | 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. |
2/4 | solution |

2/4, 2/6 | Separation of variables Heat equation |
§2.1-4 | hw2: 2.2.4; 2.3.2(c), 2.3.3(b),2.3.5,2.3.6; 2.4.1(b) | 2/11 | solution |

2/11, 2/13 | Laplace equation Fourier series |
§2.5,3.1 | hw3: 2.5.1(d), 2.5.5(b),2.5.10,3.2.2(d)(g) | 2/18 | solution |

2/18, 2/20 | Fourier series Term by term differentiation |
§3.3-4 | hw4: 3.3.1b, 3.3.2c, 3.3.5c,3.3.18,3.4.1, 3.4.6, 3.4.7 | 2/25 | |

2/25, 2/27 | Fourier series: complex form Inhomogeneous Problems |
§3.5-6 §8.2-3 |
hw5: 3.5.1ab, 3.5.2a,3.5.5,3.4.11,8.2.2d, 8.3.6 | 3/3 | |

3/3, 3/5 | Wave equation | §4.1-5 | 3/10 | ||

3/10, 3/12 | Sturm-Liouville problem/Review | §5.1-3 | Midterm: 3/12 (tentative) | ||

3/17, 3/19 | Spring Break | ||||

3/24, 3/26 | Sturm-Liouville problem Self-adjoint operator |
§5.3-5 | 3/31 | ||

3/31, 4/2 | Sturm-Liouville theorem Rayleigh quotient, Robin BC |
§5.5-6 | 4/7 | ||

4/7, 4/9 | Approximation properties Large eigenvaluses |
§5.8-10 | 4/14 | ||

4/14, 4/16 | Higher dimensional PDEs Bessel functions |
§7.2-4 §7.5-7 |
4/21 | ||

4/21, 4/23 | Fourier Transform Method of characteristic |
§10.2-6 §12.2-5 |
4/28 | ||

4/28,30 | Method of characteristic; | §12.3-6 | |||

5/6-14 | Final Exam - Wednesday, May 6, 9:00-12:00, in our classroom Coverage: ALL. 60% credits for material after midterm. |

** **