Description: Theory of Partial Differential Equations 2
Instructor: Charis Tsikkou. Email
Class Schedule: Tuesdays, Thursdays 02:30-03:45 PM in Armstrong Hall 203
Office Hours: Tuesdays 04:00-05:00 PM, Thursdays 01:00-02:00 PM, and by appointment, in Armstrong Hall 405
Info Sheet containing more or less the stuff on this webpage.
- 35% Final exam
- 25% Midterm exam
- 40% Homework Assignments
- Letter grades will be assigned according to the scheme
- A 90-100% | B 80-90% | C 70-80% | D 60-70% | F 0-60%
- Homework will be assigned once every three weeks, and due two weeks later (please see the course schedule below for exact dates).
- Homework will always be collected at the beginning of the class.
- Late turn-ins will not be accepted.
- There will be one take-home exam, posted: Thursday, March 10, due: Tuesday, March 15.
- No make-up exam will be given.
- Due: Thursday, May 5.
- Final is cumulative.
Course Schedule (subject to changes)
|Tuesday, Jan 12||Introduction to Conservation Laws; Shocks, Entropy Condition||3.4.1|
|Thursday, Jan 14||Examples; Shock and Rarefaction Waves; Entropy Solution||3.4.1 - 3.4.3|
|Tuesday, Jan 19||Riemann's Problem; Separation of Variables; Examples||3.4.4, 4.1.1|
|Thursday, Jan 21||Similarity Solutions; Plane and Traveling Waves; Solitons||4.2.1||HW 1 posted, solutions|
|Tuesday, Jan 26||Examples||4.2.1|
|Thursday, Jan 28||Similarity Under Scaling; Fourier Transform||4.2.2, 4.3.1|
|Tuesday, Feb 2||Plancherel's Theorem; Properties||4.3.1|
|Thursday, Feb 4||Examples||4.3.1|
|Tuesday, Feb 9||Laplace Transform; Examples; Cole-Hopf Transformation||4.3.3, 4.4.1|
|Thursday, Feb 11||Examples; Holder Spaces; Weak Derivatives||4.4.1, 5.1, 5.2.1||HW 2 posted, solutions|
|Tuesday, Feb 16||Sobolev Spaces; Definitions ; Examples||5.2.2|
|Thursday, Feb 18||Elementary Properties||5.2.3|
|Tuesday, Feb 23||Sobolev Spaces as Function Spaces||5.2.3|
|Thursday, Feb 25||Local Approximation by Smooth Functions||5.3.1|
|Tuesday, Mar 1||Global Approximation by Smooth Functions||5.3.2|
|Thursday, Mar 3||Global Approximation by Functions Smooth up to the Boundary||5.3.3||HW 3 posted, solutions|
|Tuesday, Mar 8||Extensions||5.4|
|Thursday, Mar 10||Extension Theorem||5.4||Midterm Exam posted, solutions|
|Tuesday, Mar 15||Problem Solving|
|Thursday, Mar 17||Traces||5.5|
|Tuesday, Mar 22||No Class (Spring Recess)|
|Thursday, Mar 24||No Class (Spring Recess)||HW 4 posted, solutions|
|Tuesday, Mar 29||Traces; Sobolev Inequalities||5.5, 5.6.1|
|Thursday, Mar 31||Gagliardo-Nirenberg-Sobolev Inequality||5.6.1|
|Tuesday, Apr 5||Estimates for W 1,p and W0 1,p, p < n||5.6.1|
|Thursday, Apr 7||Morrey's Inequality||5.6.2|
|Tuesday, Apr 12||Estimates for W 1,p, n < p||5.6.2|
|Thursday, Apr 14||General Sobolev Inequalities||5.6.3||HW 5 posted, solutions|
|Tuesday, Apr 19||Rellich-Kondrachov Compactness Theorem||5.7|
|Thursday, Apr 21||Hardy's Inequality||5.8.4|
|Tuesday, Apr 26||The Dual space H -1; Second-Order Elliptic Equations||5.9.1, 6.1.1|
|Thursday, Apr 28||Weak Solutions; Lax-Milgram Theorem; Energy Estimates||6.1.2 - 6.2.2|
|Thursday, May 5||Final Exam||Final Exam posted, solutions|
The West Virginia University community is committed to creating and fostering a positive learning and working environment based on open communication, mutual respect, and inclusion. If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Accessibility Services (293-6700). For more information on West Virginia University's Diversity, Equity, and Inclusion initiatives, please see http://diversity.wvu.edu.
If you are a person with a disability and anticipate needing any type of accommodation in order to participate in this class, please advise me and make appropriate arrangements with the Office of Disability Services (304-293-6700).