Spring 2012 Course Syllabus: Math 689-002

Course Title:	Advanced Applied Mathematics II: Ordinary Differential Equations
Textbook:	It may be useful to own one of the following recommended texts but it is not required. Copies will be available on reserve in the library. Primary Textbook: Boundary Value Problems of Mathematical Physics, Volumes I and II. By Ivar Stakgold. SIAM Classics in Applied Mathematics vol 29. ISBN: 0-89871-456-7. Also Useful: (1) Green’s Functions and Boundary Value Problems. Third edition. By I. Stakgold and M. Holst. ISBN 0-470-60970-2. (2) Principles and Techniques of Applied Mathematics. By B. Friedman. ISBN 0-486-66444-9. (3) Applied Mathematics. By J.D. Logan. ISBN 0-471-74662-2.
Prerequisites:	Math 545 or Math 645, Math 613, and Math 631

Weeks	Sections	Topic
1	1	Introduction. Linear two-point boundary value problem for an ODE. Examples. The inner product and adjoint operator.
2-3	2	Introduction to distributions (generalized functions). Test functions. The Dirac delta function. Green’s functions. Examples of the use of the Dirac delta function.
4-6	3	General, linear, second order boundary value problems. Solution in terms of the Green’s function. Discussion of the role of boundary conditions. Self-adjoint and non self-adjoint problems. Problems of general order. The Fredholm alternative and the modified Green’s function. Applications and examples.
7-9	4	General theory of eigenfunction representations. Sturm-Liouville eigenvalue problems and their occurrence in the solution of PDE’s. Overview of spectral theory of linear operators. Spectral representation. Eigenfunction expansion of the Green’s function and modified Green’s function.
10-12	5	The eigensystem of a general non self-adjoint operator. Discrete and continuous spectrum. Singular problems. Applications and examples.
13-14	6	Approximation of eigenvalues and eigenfunctions by variational methods. The Rayleigh-Ritz method. Applications and examples.

IMPORTANT DATES
FIRST DAY OF SEMESTER	January 17, 2012
LAST DAY TO WITHDRAW	March 20, 2012
LAST DAY OF CLASSES	May 2, 2012
FINAL EXAM PERIOD	May 3-9, 2012

Grading Policy

Assignment Weighting
Homework	60 %
Midterm	10%
Final Exam	30%

Important Departmental and University Policies

• Academic Integrity Code is Strictly Enforced
• Prerequisites Requirements are Enforced
• Attendance is Required in Lower-Division Courses
• Exam Policies (No Make Up Exams and More)
• Cell Phone and Pager Use Prohibited in Class
• Drop Date (March 20, 2012) is Strictly Observed
• Complete DMS Course Policies (math.njit.edu/students/undergraduate/policies_math)

Prepared by Prof. Michael Booty, December 14, 2011