Syllabus for Math 531

Prerequisites: Math 252 and 337

Textbook: Haberman: Applied Partial Differential Equations (with Fourier Series and Boundary Value Problems). Pearson 2013. ISBN 9780321797056

Course Catalog Description: Boundary value problems for heat and wave equations: eigenfunctionexpansions, Surm-Liouville theory and Fourier series. D'Alembert's solution to wave equation; characteristic. Laplace's equation, maximum principle, Bessel's functions.

Prerequisites:
Math 252, 254, and 337 (or equivalent)

1. Math 252: Calculus III
   • Series and Integration of Trigonometric Functions
   • Vectors, Partial derivatives, and Gradients
   • Divergence Theorem or Gauss's Theorem
   • Multivariable Integration
2. Math 254: Linear Algebra
• Linear Independence
• Orthogonality
• Eigenvalues
3. Math 337: Ordinary Differential Equations
• Existence and Uniqueness of Solutions of ODEs
• Solutions of Second Order Linear Differential Equations
• Solving Non-homogeneous ODEs
• Series Solutions of ODEs
• Laplace Transforms for Solving ODEs

Student Learning Outcomes:
At the end of this course students will be able to:

1. Connect significant physical problems with PDEs
2. Learn tools for solving PDEs, including visualization through programming
3. Manage the methods and details for large multi-step problems
4. Explore decomposition of continuous functions with Fourier series
5. Develop intuition for extending finite dimensional vector spaces (254/524) to infinite dimensions
6. Appreciate the complexities and varied techniques for PDEs
7. Connect the subject to diverse mathematicians contributing to the field
8. Use MatLab and Maple software to study the dynamics of a variety of applications.
   

Course Objectives and Expectations on Students:

This course is a 3 unit course designed for students who are majoring in mathematics and ones in the applied sciences. This course is very important for students specializing in dynamical systems.

More to follow.

Scope and Purpose of the Course:

The scope and purpose of this course is being developed.

Course Assessment and Grading

Details of the course and timelines are available on the HW Assignment page.

Grading:

• Homework assignments, including WeBWorK (40%)
• 2 Midterms (40%) (most likely a Take-Home exams only)
• Final (20%) (most likely a Take-Home final)

Accommodation Of Disability: Students with disabilities who may need academic accommodations should notify the professor in writing within the first two weeks of instruction. Students need appropriate forms aproved by SDS (Calpulli Center, Suite 3101). All information will be kept confidential. Students that need evacuation assistance during campus emergencies should also meet with the instructor as soon as possible to assure the health and safety of all students. If you encounter a problem accessing anything in this course, please contact me as soon as possible.

Classroom Behavior And Student Code Of Conduct

1. It is expected that students will conduct themselves within the standards outlined in the student code of conduct,
   disciplinary procedure and student due process. Disciplinary action will be taken by the instructor as necessary. See more information at the SDSU Student Ethical & Civic Responsibility Code.
2. Students are expected to come to class in a timely manner, prepared for the day’s work. Full participation for the entire
   class period in activities, class exercises and discussions is required.
3. Please turn off all cell phones, pagers, etc. You will be released from class with an unexcused absence for making or accepting telephone calls or text messages in the classroom.
4. It is the student’s responsibility to make up missed material. This includes, but is not limited to, obtaining missed lecture notes from another student (not from the instructor), and finding out about any modifications of schedules or assignments announced during class time.
5. WeBWorK assignments are posted with a specific due date. It is the student’s responsibility to complete the assignment on time.
6. Academic dishonesty will result in a grade of zero for the assignment and will be reported to Academic Affairs. It may result in further disciplinary action. Academic dishonesty includes, but is not limited to, cheating, which includes unauthorized collaboration and plagiarism.
7. Missed Exams: Students will receive a ZERO for any missed exam, except for written/documented excuses (illness, personal/family crises, etc.).
8. Even the visual presence of a Cell Phone during an Exam will result in a ZERO for that Exam.

• The instructor will make special arrangements for students with documented learning disabilities and will try to make accommodations for other unforeseen circumstances, e.g., illness, personal/family crises, etc. in a way that is fair to all students enrolled in the class. Please contact the instructor EARLY regarding special circumstances.
• Students are expected and encouraged to ask questions in class.
• Students are expected and encouraged to make use of office hours.

Week 1:

Under Development