Basic Ground Rules:
Final grade based on six equal parts: Final exam (equals two parts), three
midterm exams,
everything else. Everything else includes regular homework, computer
homework, the occasional quiz in recitation, lecture points, etc..
Homework will be
assigned before each Thursday, and will
be due at Thursday's lecture the following week.
You will almost always need to use the computer to do some
of your homework.
Homework will contain instructions for reading. Make sure you do the
reading before the class for which it is assigned. I will assume you
have done so.
Make use of my office hours, Math Center, Maple Center,
Electronic newsgroups (upenn.math.math104), Sunday Night Reviews
(schedule to be announced soon) etc..
Grading notes: At the end of the semester, everyone who has not withdrawn from the
class will get a grade. Incompletes will not be given to avoid F's.
LATE WORK (homework, Maple, etc..) will NEVER be accepted.
Exams:
- First midterm: Thursday October 6 (Review, Chapter 6 and some of
8)
- Midterm rules: You may bring a standard-size sheet of paper with
notes written on both sides. No calculators or any other electronic
devices are allowed.
- Here are some practice problems for the
first
midterm (note that numbers 1-10 near the end are last year's first
midterm). Some of the answers (I'll try and get to the rest over the
weekend) are here.
- Second midterm: Thursday, November 3 (Chapter 8, Chapter 9 (and
section 7.2))
- Third midterm: Thursday, December 1
(Chapter 10)
- Final exam: Wednesday, December 14, 9-11 am in the Nursing
Auditorium.
Ways to get help:
Class notes:
Homework and class notes:
Bonus problems and solutions:
- Bonus problem #1: Suppose that three points on the parabola
y = x2 have the property that their normal lines
intersect at a common point. Show that the sum of their
x-coordinates is 0. Is this if and only if?
Bonus problem #2:
Consider a square with side length
L. Let R be the region inside the square
consisiting of all points that are closer to the center of the
square than to any side of the square. What is the area of R
?
This is an interesting problem -- the hard part is to draw a good
picture of the region and get equations for its (curved) sides. (Can you
do it with Maple?)
Bonus problem #3:
Prove that (explain why) log3(11) is an irrational number.
A speedy solution, by Joshua Jackson:
Suppose log3(11) = n
where n = a/b, and a and b are both
(nonzero) integers (this would define
n as a
rational number.) Then
log3(11) = a/b
b log3(11) = a
log3(11b) = a
3a = 11b
So, for log3(11) to be a rational number, there must exist
nonzero
integers a
and an integer b for which the above statement is true.
Because the prime factorization of any number is different from that of
any other number, and 3a and 11b are
examples of numbers that have been
simplified to their prime factors, there cannot be integers a and
b for
which 3a = 11b, and so
log3(11) cannot be a rational number.
Therefore, log3(11) is an irrational number.
Bonus problem #4:
A cylindrical glass of
radius r and height L is
filled
with water and then tilted until the water remaining in the glass exactly
covers its base.
- (a) Determine a way to "slice" the water into parallel
rectangular
cross sections and then set up a definite integral for the
volume of the water in the glass.
- (b) Determine a way to "slice" the water into parallel cross-sections
that are trapezoids and then set up a definite integral for the
volume of the water.
- (c) Find the volume of water in the glass by evaluating one of the
integrals in part (a) or part (b).
- (d) Find the volume of water in the glass from purely geometric
considerations.
- (e) Suppose the glass is tilted until the water covers half the base.
In what direction can you "slice" the water into triangular cross
sections?
Rectangular cross-sections? Cross-sections that are segments of circles?
Find the volume of water in the glass.
- Here are two pictures that may help:
Maple worksheets from class:
- September 29 (intro to Maple)
- October 18 (Excel spreadsheet for
trapezoidal rule)
- Here is a link to a Maple worksheet
showing how to solve differential equations and how to draw slope fields
that you might find useful. It concerns the example y' = 2(y
- y2).
Solutions to homework and in-class problems