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
• Selected Homework Solutions
• Recommended Software
• Links of Interest

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:

• the cycloid;
• the epicycloid;
• the trochoid (see Problem #40);
• Lissajous figures (see Problem #49).
• §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.
  NOTE: Here are two links with nice graphics more and info on the "Koch Snowflake" discussed in Problem #5 on page 761 of our text:: Wikipedia web page for Koch "Snowflake"; and MathWorld web page for Koch "Snowflake".
• §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.

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Selected Homework Solutions

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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? :-)

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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.

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