Text: Greenberg, Michael, D., Advanced Engineering
Mathematics (second edition). Upper Saddle River: Prentice Hall,
1998. A copy of the text will be placed on reserve in the Mathematical
Sciences Library in Hill Center.
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
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 some of
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. The first assignment will be due Wednesday, 9/14;
the next few assignments after that will also be due on Wednesdays.
Academic integrity: You are strongly encouraged to discuss
homework problems with me or with other students. On the other hand, after
you have finished discussing a problem, you must write your solution
independently, not in concert with others. If you consult any source other
than Greenberg (such as a web page, solutions from a previous semester,
etc.), and material from that source contributes significantly to the
preparation of homework, you must acknowledge this by citing that
source; moreover, the work you turn in must be written up in your
own words, not copied from a source. Failure to observe these restrictions
will be treated as a violation of the Rutgers Academic Integrity Policy.
Exams: There will be two in-class exams, tentatively scheduled for
Monday, October 10 and Monday, November 21. The date and
time of the final exam will be determined later. Make-up exams will be
given only in the case of well-documented illness or major emergency or
(onl y with permission in advance) of a major outside commitment.
Grading: Grading will be based on a
weighted average of homework and exams: