Name (please print):
Math 213, Spring 2006
HW Assignment 8
Instructions
ā¢Write your name on the cover sheet and staple the sheet to the assignment.
Do the problems in order, and make sure that each problem is clearly labelled.
ā¢Deadline: The assignment is due in class on Friday, March 31. (This means that
you have a full 15 days to complete the assignment. There will be another homework
assignment given out Monday after Spring Break, and also due on March 31.)
ā¢Open House: I plan to have an Open House Wednesday and/or Thursday after
Spring Break, at the usual place and time (5 pm, 147 Altgeld).
Reading/review exercise
The generating function method of Section 6.4, which I will cover right after the break,
depends on some knowledge about power series. This is Calculus II material, and you
should review it in preparation for Section 6.4. In particular, review the following:
ā¢Power series (MacLaurin series) expansions of the following functions, along with the
intervals of convergence: ex, ln(1 + x), 1/(1 āx). (See the table on p. 440 of Rosen
for these and some other expansions.)
ā¢Differentiation and integration of power series.
ā¢Addition/subtraction, and multiplication of power series.
ā¢Finite and infinite geometric series. Know the formula for the sums of these.
ā¢Power series expansion of (1 + x)nvia the Binomial Theorem. (See Section 4.4 of
Rosen.)
Note that convergence tests, which are covered ad nauseum in calculus classes, are not rele-
vant here. Also, not particularly important is the explicit computation of a the coefficients
power series expansion for a given function f(x) by the formula an=f(n)(0)/n!.
The important thing is that you know, and be able to recognize, some basic power series
expansions like those listed above, and that you can manipulate these series, e.g., via
differentiation, integration, or multiplication of power series.
This material is covered in Chapter 10 (mainly Sections 10.8 and 10.9) of Edwards/Penney,
or in pretty much any calculus book.
āTurn page for HW 8 Problemsā
