Fall 2012. MATH5333. Section 001.

### Partial Differential Equations II

Instructor: Luan Thach Hoang
Office: MA 208. Phone: (806) 742-2580 Ext 232. Fax: (806) 742-1112
Homepage: http://www.math.ttu.edu/~lhoang/
Office hours: TWR 2:30 pm - 3:30 pm

Classroom and Time: MA 014, TR 9:30 am - 10:50 am.

Course website: http://www.math.ttu.edu/~lhoang/2012Fall-M5333/

Text: Partial Differential Equations, 2nd edition, by Lawrence C. Evans, published by American Mathematical Society.

Course Description: An introduction to modern theory of partial differential equations (PDE).

• Basic theories of Sobolev spaces which are essential to understanding PDEs.
• Second-order elliptic, parabolic and hyperbolic equations: Weak solutions, Existence, Regularity.
• Various techniques are used to analyze these equations and properties of their solutions.

Course Outline:

• Chapter 5: Sobolev Spaces
• Chapter 6: Second-Order Elliptic Equations
• Chapter 7: Linear Evolution Equations
• Chapter 8: Calculus of Variations

Expected Learning Outcomes: Sobolev spaces: weak derivatives, basic inequalities and embedding theorems. Second order elliptic, parabolic and hyperbolic equations: weak solutions, existence, uniqueness and regularity. Calculus of variations: existence and regularity of minimizers. Many more on properties of the solutions.

Methods of Assessment of Learning Outcomes: Assessment of the learning outcomes will be achieved through homework assignments, two midterm examinations and a final exam.

Grading policy: Homework will be assigned weekly and will count for 30% of the grade. There will be two midterm exams in class, each will count for 20% of the grade. The final exam will count for 30% of the grade. All in-class exams are closed-book. No make-up exams are given unless legitimate documents for excuses are presented to the instructor at least a week in advance.
Grading Scale: A: 90%-100%, B: 80%-89%, C: 70%-79%, D: 60%-69%, F: below 60%.

Attendance Policy: Students are expected to attend every class and are responsible for all information given in class.

Examination Schedule:

• Midterm 1: Thursday Sep. 27.

• Midterm 2: Thursday Nov. 8.

• FINAL EXAM: Friday December 7, 7:30 a.m. - 10:00 a.m., Room MA 014.

Critical Dates:

• Aug. 27: Classes begin.
• Sep. 3: Labor Day. University Holiday.
• Sep. 12: Last day for student-initiated drop on MyTech without penalty. Last day to drop a course and have course charges removed.
• Oct. 29: Last day for student-initiated drop on MyTech with penalty.
• Nov. 21-25. Thanksgiving Holiday.
• Nov. 29-Dec. 5: No exams.
• Dec. 5: Last day of classes.

Academic Misconduct: Academic dishonesty is intolerable and will be punished to the full extent allowed by the University policy.

Civility in the Classroom: Students are expected to assist in maintaining a classroom environment that is conducive to learning.

Students with Disabilities: Any student who because of a disability may require special arrangements in order to meet course requirements should contact the instructor as soon as possible. "I would appreciate hearing from anyone who has a disability that may require special accommodations. I am sure we can work out whatever arrangements are necessary. Please see me during my office hours."

NOTE: When needed, the instructor will communicate with the students using their TTU email addresses. At the beginning of the semester, the instructor will send out a message to confirm the students' email addresses.