642:527–Fall 2008

- Instructor: Professor E. Speer, Hill Center 520, 732&ndash445&ndash1313, speer at math.rutgers.edu
- Office hours:
- Monday 1:40–3:00 PM, Hill 520
- Tuesday F 3:20–4:40 PM, Hill 520
- Wednesday 10:20–11:40 AM, Hill 520
- Or by appointment or chance in Hill 520

- Text: Greenberg, Michael, D.,
*Advanced Engineering Mathematics*(second edition). Upper Saddle River: Prentice Hall, 1998. - General: 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: solution of ordinary differential equations by power series methods (in particular, the method of Frobenius), Laplace transform methods, and phase plane methods; vector spaces of functions, Hilbert spaces, and orthonormal bases; Fourier series, Fourier transforms, and Sturm-Liouville theory; solution of the linear differential equations of physics—the heat, wave, and Laplace equations—by separation of variables.
- Prerequisites:
We assume familiarity with
- Single and multivariable calculus;
- Ordinary differential equations (as in Greenberg, Chapters 1, 2, and 3 and Sections 4.1–2, although the material in chapter 4 will be reviewed);
- Linear algebra (roughly Greenberg Chapter 8 and Sections 9.1–5, 10.1–5, and 11.1–2, although not all of this material will be used in detail).

- Homework: Homework problems will be assigned weekly through postings on the web page, and will normally be due on Tuesdays.
- Exams: There will be two in-class exams, tentatively scheduled for
**Thursday, October 9**and**Thursday, November 13**. The final exam will be held**Friday, December 19, from 8:00 AM to 11:00 AM**. Make-up exams will be given only in the case of well-documented illness or major emergency or (only with permission in advance) of a major outside commitment. - Grading: Grading will be based on a
weighted average of homework and exams:
Homework 20% Class exams 20% each 40% Final exam 40%