640:527: Methods of Applied Mathematics

Class meets: TTH6 (5:00-6:20), Hill Center, Room 124

Text: M.Greenberg Advanced Engineering Mathematics (second edition); Prentice, 1998 (ISBN# 0-13-321431-1))

Instructor: Daniel Ocone

Office Hours: Hill 518: 3:00-4:30 Tuesday and Thursday or by appointment.

Syllabus: Click here.

Course description

This is a first semester graduate course appropriate for students in mechanical and aerospace engineering, biomedical engineering, other engineering, and physics. The topics to be covered are: power series and the method of Frobenius for solving differential equations; nonlinear differential equations and phase plane methods; perturbation techniques; vector space of functions, Hilbert spaces and orthonormal bases; Fourier seres and integrals; Sturm-Liouville theory; Fourier and Laplace transforms; separation of variables for solving the linear differential equations of physics, the heat, wave, and Laplace equations.

Prerequisites: Topics the students should know, together with the courses in which they are taught at Rutgers, are: Introductory Linear Algebra (640:250); Multivariable Calculus (640:251); Elementary Differential Equations (640:244 or 640:252); Advanced Calculus for Engineering(Laplace transforms, sine and cosine series, introductory pde)(640:421).

Students who are not prepared for this course should consider taking 640:421.

Grading: Grades will be determined out of 500 points as follows:

100 points (20%) graded homeworks and quizzes;
100 points (20%) for each of the two midterms;
200 points (40%) for the final exam.