Last Updated: 8/16/11
Math 110B: Calculus II
Fall 2011 / City College of San Francisco
Instructor: A. Schusteff
Math 110B Page Contents
Homework Assignments
Course Text: Calculus - Early Transcendentals (6th Edition), by James Stewart.
[Note: If you purchased a textbook with "WebAssign", see
this link.]
- §6.1: Read the section, then do exercises #1-9 odd, 15, 25, 29, 31, 41, 42, 45, 50.
If you'd like to experiment with a nice Java Applet that allows you to explore
"area between two curves" problems from the Riemann Sums point of view, visit
this web page by David Little of Penn State University.
- §6.2: #1, 3, 6, 19, 33, 47a, 49, 51, 57, 63.
A very nice treatment of the "disks method" for finding
the volume of a solid of revolution can be found
here.
- §6.3: #1, 3, 5, 8, 21, 28, 29, 43, 44.
[Note: A web page with an excellent
summary of both the "Cylindrical Shells Method" (§6.3) and the "Method of Disks/Washers"(§6.2)
with animations(!)--- showing how the shells (respectively, disks
or washers) arise via revolution about an axis---can be found
here.]
- §6.4: #1,3, 5, 7, 22, 23.
- §7.1: #1-19 odd, 23, 25, 29, 31, 35, 41, 42, 45, 57, 66.
[Note: You can use the
xFunctions
graphing utility to draw graphs
(e.g for problems #41 and #42). It's a java applet that is sometimes
slow to load,
but should run within most web browsers.]
- §7.2: #1, 3, 13, 15, 21-33 odd, 41, 43, 45, 54, 56, 57, 65.
- §7.3: #1-15 odd, 23, 25, 29, 31.
- §7.4: #1, 4, 5, 7, 9, 15, 17, 27-39 odd, 45, 47.
- §7.5: #1-17 odd, 23, 24, 41, 43.
- §7.6: #1-9 odd, 15, 19.
- §7.7: #1-7 odd, 21, 29, 30, 31.
- §7.8: #1-17 odd, 21, 27, 31, 33, 49-59 odd, 69.
- §8.1: #1-9 odd, 13, 15, 17, 31.
- §8.2: #1, 5, 7, 11, 13, 15, 25, 29*, 30*. [Problems with a "*" are challenging and optional.]
- §10.1 Parametrized Curves: #5-21 odd, 22, 23, 24, 27, 28, 40, 41, 49.
NOTE:
Read through
this web page (it may take a few seconds to load)
and take note of the applets therein, which you can use
to help you explore this topic by making up your own parametrized curves
(e.g. while reading the text, doing homework, etc.).
ALSO...Nice graphics, animations, and discussions can be found online
for many interesting
parametrically defined curves. Here are links to a few such curves
from class and homework:
- §10.2: #1-9 odd, 15, 17, 19, 23, 25, 29, 31, 41, 43, 45, 59, 61, 73.
- §10.3: #1-29 odd, 33, 37, 41, 56, 61, 65.
Note: A one page PDF file with two polar graphing grids can be
downloaded here.
- §10.4: #1, 3, 5, 6, 7, 13, 17.
- §11.1: #1-15 odd, 16, 19-39 odd, 43, 63, 65, 68.
- §11.2: #1, 9, 10, 11-31 odd, 35, 37, 41, 43, 49.
- §11.3: #2, 3-25 odd, 32.
- §11.4: #1, 2, 3-9 odd, 17, 21, 31, 37.
- §11.5: #1-7odd, 13-19 odd, 23-29 odd.
- §11.6: #1, 2, 3-13 odd, 21, 23, 27, 31, 33.
Selected Homework Solutions
To view selected solutions from the assigned
course homework
click here.
Recommended Software for Math 110B
Here's a quick reference to some good math software resources
that are very helpful for studying , exploring, and experimenting with topics
in Calculus (and beyond).
- WinPlot is
an extremely versatile, easy to learn and use program. It is completely free.
However, it only runs under the Windows operating system.
To get started using it,
you can view
a tutorial
here.
- xFunctions is a Java applet
that will run in most recent versions of Firefox, Safari, Internet Explorer,
or other Java capable browsers. (Be patient, it may take a minute to
load the Java code into your browser.) XFunctions has eight different "utility
screens" that allow you to:
- View the graphs of many interesting function, and use the mouse to trace
over the curve while reading off x and f(x) values.
- Graph up to eight function on the same screen (in different colors) to
compare behaviors.
- Animate families of functions.
- Plot "parametric curves" (as discussed in section 11.1 of our text).
- Graph a function and its first and second derivative, and trace out tangent
lines and values with the mouse.
- Explore various concepts related to Riemann sums.
- Draw "vector fields" and their "integral curves".
(These concepts arise when studying 110C, and differential equations.)
- Graph surfaces in 3D (studied in Calculus III).
- Here is a
Riemann Sums Java Applet
that has good graphics (the rectangles
are clearly outlined, thus easier to see than the
"XFunctions Riemann Sums Utility"). As often happens, this Java applet
takes a while to load into your browser...be patient, and try
clicking one of the buttons on the lower right to bring up a graph.
(By the way, those buttons are actually labeled...but with
white words on a light gray background, so they're very difficult
to make out. The labels are "left", "midpoint", "right", "random",
"trapezoid", and "Simpson". Any guesses what those buttons might do? :-)
Links of Interest
Many links to math sites of general interest appear on the "Math
Links Page". Here is a shortcut to the Math
110B links.