[ Course Description | Course Outline | Course Policy | Homework and Sample Tests | Class Schedule ]

Announcements (back to top)

• Class for 8/29 was cancelled due to Hurricane Irene.

Course Description (back to top)

From course catalog: Examples of initial and boundary value problems in which differential equations arise. Existence and uniqueness of solutions, systems of linear differential equations, and the fundamental solution matrix. Power series solutions, Sturm-Liouville theory, eigenfunction expansion, Green's functions.

Prerequisite: Prior knowledge of linear algebra and calculus (at the level of AMS 510).

Required Textbooks

• Differential Equations and Boundary Value Problems: Computing and Modeling, 4th edition, by C. Henry Edwards and David E. Penney, Prentice Hall 2008. ISBN 0131-56107-3. (Earlier editions are OK.)

Supplementary Textbooks

• Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory, by Carl M. Bender and Steven A. Orszag. Springer, 1999. ISBN 0-387-98931-5.

Course Outline (back to top)

The course contains three parts:

1. Linear Differential Equations

   • Introduction to differential equations (1 lecture)

   • Linear first-order equations (1 lecture)

   • Homogeneous linear equations of higher order (1 lecture)

   • Nonhomogeneous linear equations (2 lecture)

   • Systems of linear differential equations (2 lectures)

   • Laplace transform methods (if time permits)

2. Nonlinear Differential Equations and Boundary Value Problems

   • First-order nonlinear differential equations (1 lecture)

   • High-order differential equations (1 lecture)

   • Nonhomogeneous BVPs (1 lecture)

   • Eigenvalue problems and Sturm-Liouville theory (1-2 lectures)

3. Singularities and Power Series Methods

   • Classification of singularities (0.5-1 lecture)

   • Power series methods (1-2 lectures)

   • Approximate solutions near ordinary and regular singular points (3 lectures)

   • Analysis and approximate solutions near irregular singular points (2 lectures)

   • Spontaneous singularities (1 lecture)

   • Introduction to perturbation theory (if time permits)

Course Policy (back to top)

Assignments

Homework assignments are due in class typically two weeks after they are assigned. You are allowed to discuss course materials and homework problems in small groups, but limited to discussion of general ideas only. You must write your solutions completely independently. Under no circumstances may you copy solutions from any source, including but not limited to other students solutions, official solutions distributed in past terms, and solutions from courses taught at other universities. Violation of these rules may result in disciplinary actions.

Exams

The exams (including two tests and the final exam) are closed-book, but you are allowed to bring a one-sided, one-page, letter-size cheat sheet, which you must prepare by yourself.

Attendance

All students are expected to attend all the lectures and exams.

Grading

• Assignments: 30%

• Two tests: 40%

• Final exam: 30%

Homework and Sample Tests (back to top)

Assignments

• Homework #1 (Due 09/14/2011) and sample solution.
• Homework #2 (Due 10/05/2011) and sample solution.
• Homework #3 (Due 10/24/2011) and sample solution.
• Homework #4 (Due 11/07/2011) and sample solution.
• Homework #5 (Due 11/28/2011) and sample solution.
• Homework #6 (Due 12/12/2011) and sample solution.

Sample Tests

• Sample test 1 and sample solution.
• Sample test 2 and sample solution.
• Sample final exam and sample solution.

Class Schedule (back to top)

• Important: All schedules are tentative and are subject to change.

In the reading lists, E&P means Edwards and Penney, and B&O means Bender and Orszag.

University Policies and Academic Integrity (back to top)

Americans with Disabilities Act

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.