Last Updated: 1/18/10

Page Contents

• Homework Assignments
• Selected Homework Solutions
• Links of Interest for Math 110C
• Recommended Software

Homework Assignments

We'll be covering Chapters 12-16 of the text.  Homework is assigned daily and the previous weeks assignments are collected each Monday. I'll periodically update this list. Here are the homework assignments so far:

• §12.1: #1, 3, 4, 5, 7, 10, 11, 13, 17, 21-31 odd.
• §12.2: #1, 2, 4, 5, 7, 11-21 odd, 25, 32, 37, 38.

  HW Packet 1: Homework assigned from §12.1 - §12.2 is due on Monday, January 25.

• §12.3: #1, 2, 3-29 odd, 35-45 odd, 49.
• §12.4: #1, 5, 8-17 all, 31, 35, 43, 49.

HW Packet 2: Homework assigned from §12.3 - §12.4 is due on Monday, February 1.

• §12.5: #1-7 odd, 13, 16, 19, 23, 27, 35, 37, 39, 43, 45, 47, 49, 53, 65, 67.

HW Packet 3: Homework assigned from §12.5 is due on Monday, February 8. (Also try to start working on Quadric Surfaces...see §12.6 below.)

• §12.6: #5-19 odd, 21-28 all, 31, 33, 35, 45, 46, 49.

As part of your study of Quadric Surfaces (§12.6) please read through and experiment with the excellent Interactive Gallery of Quadric Surfaces. This site has an interactive web page for each of the six types of quadric surface, where you can:

• Click and drag within the graphics window to rotate the surfaces to any viewpoint you like AND
• Click and drag the "blue boxes" along the "red slider intervals" to see each of the three "families of coordinate plane slices" swept out before your eyes.

[Note: If the text is too small to read comfortably, you can enlarge it by pressing cntl-+ in Windows, or Cmd-+ on a Mac.]

HW Packet 4: Homework assigned from §12.6 is due on Tuesday, February 16. (Also try to start reading §13.1 on Parametrized Curves/Vector-Valued Functions.

• §13.1: #1, 3, 7, 9, 14, 15, 17, 20-24 all, 29, 31, 33, 37, 39.

Note: Two nice and useful tools for interactively exploring parametrized curves can be found at the following links: The "Parametric Paths (3-D Graphing)" webpage and the "Motion in 3-D" webpage. Each page contains a Java applet (which can be SLOW to load...be patient!).

The first link has a fairly straightforward interface where you can enter three different parametrized curves, which can be graphed in three colors with respect to a single coordinate axis frame. The coordinate axes (and their scales) are clearly indicated. You'll need to thoughtfully choose the "bounds" of your viewing window to avoid having much of the view of your graph truncated. You can also click and drag the graph and "rotate" it in 3-D.

The second link also allows you to type in your vector-valued function <x(t),y(t), z(t)>, click on the "GRAPH" button, and see the curve rendered. However, in this applet, if you press the ">>" button, the parametrized curve will be "swept out" before your eyes, complete with velocity vector (in red) and acceleration vector (in green)! Like the first applet, you can click and drag the image to change your viewpoint. But be forewarded! This applet is a bit unusual in the way they've implemented "rotating the image". Usually things are set up so that when you click and drag on the graph, you move the graph as an object. But in this applet, think of the cursor as the position of your eyes...when you drag the cursor, you're changing your viewing position (and thus, only indirectly, the position of the object). This will probably appear strange at first...until you get the hang of it.

HW Packet 5: Homework assigned from §13.1 is due on Monday, February 22.

• §13.2: #1, 3, 5-8 all, 9, 17, 18, 19, 21, 25, 29, 33, 39, 49.

HW Packet 6: Homework assigned from §13.2 and the exercises on the class handout "Four Parametrizations of the Circle, and Two of its Involute" is due on Monday, March 1. It's advisable to read §13.3 as well...there are a lot of concepts (relating the geometry to the calculus) therein.

• §13.3: #1, 2, 3, 11 (Hint: Parametrize the curve by using x as the parameter, i.e. use the equations of the two surfaces to express y and z in terms of x), 13, 17, 43, 53.
• §13.4: #33, 35. (Note: For both these problems, compute the acceleration a(t) and verify the vector equation: a=a_TT+a_NN. Also, these problems can involve a lot of algebra, so work carefully and allow a good amount of paper for simplifying computations!)

HW Packet 7: Homework assigned from §13.3 and §13.4 is due on Monday, March 8

• §14.1: #2, 5, 7-29 odd, 30, 31, 32, 34, 41-47 odd, 55-60 all, 63, 74. NOTE: For real-valued functions of two variables, this java applet will render screen images of both the graph of the function AND its level sets. (However, the graph and the level sets are not both shown on the same screen, you'll have to click the dark gray button at the bottom of the window to toggle between the two views.)
• §14.2: #1, 5, 7, 9, 13, 24. (Hint: For #24, try approaching (0,0) along a "cubic curve" of the form x=cy³ for two different choices of c.)

HW Packet 8: Homework assigned from §14.1 - §14.2 is due on Monday, March 15.

• §14.3: #3-9 odd, 10, 11-21 odd, 39, 40, 45, 51, 57, 61, 73, 74, 95.

No homework from §14.4

• §14.5: #1-7 odd, 13, 15, 19, 25, 27, 31, 35, 39, 49.

HW Packet 9: Homework assigned from §14.3 and §14.5 is due on Monday, March 22.

• §14.6: #1, 4, 7, 9, 11, 13, 19, 21, 25, 27, 37, 38, 41, 49, 61.
• §14.7: #2, 3, 4, 5, 7, 9, 13, 29, 33, 35, 43.

HW Packet 10: Homework assigned from §14.6 and §14.7 is due on Monday, April 5.

• §15.1: #1, 3, 5, 9, 11.
• §15.2: #1, 5, 13, 15, 17, 21, 25, 27, 30.

HW Packet 11: Homework assigned from §15.1 and §15.2 is due on Monday, April 12.

• §15.3: #1, 5, 9, 13, 17, 21, 25, 43, 45, 49, 61.
• §15.4: #1-15 odd, 21, 25, 27, 29.
• §15.5: #1, 3, 5, 7.

HW Packet 12: Homework assigned from §15.3 through §15.5 is due on Monday, April 19.

• §15.6: #1, 3, 5, 13, 27-33 odd.
• §15.7: #1-15 odd, 19, 21, 25, 27.
• §15.8: #1-17 odd, 21, 23, 27, 29, 35, 39.
• §15.9: #1, 3, 5, 9, 10, 13, 15, 17, 21.
• §16.1: #1-11 odd, 15, 17, 21, 23, 25, 29, 31.
• §16.2: #1, 5, 7, 13, 17, 18, 21.
• §16.3: #1, 3, 9, 17, 19, 23.
• §16.4: #1-13 odd, 19.

Selected Homework Solutions

To view scanned images of handwritten solutions to a selection of assigned course homework click here. 

Links of Interest for Math 110C

• Basic Vector Concepts: This link opens a web page for a Java applet which allows you to explore various concepts involving vectors in the 2-dimensional plane---for instance: vectors as "directed line segments"; vector equality; the opposite of a vector; scaler multiplication of vectors; the sum and difference of two vectors; etc. In each case, you can "click and drag" the end of the arrow to interactively adjust the "ingredients" in the diagram. Unfortunately, some of the text has errors, which may cause confusion. In particular, the 4th "button" along the top right of the applet window should be labelled "A = N*B", and the text for that item should read "N*B" instead of "N*A".
• Java Applets for Graphing Parametrized Curves and Surfaces: This link opens a web page with links to a number of Java applets which allow you to graph parametrized curves and parametrized surfaces (using rectangular, cylindrical, or spherical coordinates).
• Vector Fields:  The VECFIELD applet will draw a vector field with horizontal component f(x,y) and vertical component g(x,y).  Here's a brief rundown:
1. You enter the "viewing window dimensions" by clicking on the "Enter Limits" button at the bottom left of the applet window.  Use the mouse to click in each box and enter your chosen left, right, bottom, and top limits. NOTE: The "step" box controls the distance bewteen points where arrows are drawn.  In order to get picture that is "readable" you may need to set this to a larger value than the default. Also, you may want to scale your vectors down by a fixed factor (e.g. 1/10) so all the arrows aren't overlapping.  (It's somewhat of an art to render a vector field picture that is "readable").
2. Press the "Enter Expression" button at the bottom of the applet window. Click on the box labeled "f(x,y)" to enter the horizontal component of your vector field, then click the box labeled "g(x,y)" to enter the vertical component.
3. Press "Draw!" to see what you get.  (It may look like a mess...or a bunch of tiny "point arrows" so small that the picture doesn't convey the "flow" of the vector field.  There may also be erratic lines here and there (arising from division by zero somewhere?).  As was said above, creating good vector field pictures is somewhat of an art.  Try adjusting the value of "step" in the "Enter Limits" pop-up window.  Also try scaling both components of your vector field to eliminate/minimize overlapping arrows.
• Further links for Math 110C appear within the "Math Links Page". Here is a shortcut.

 
 

[ Page Contents | A. Schusteff Home ]

Recommended Software for Math 110C

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 Internet Explorer, Netscape, 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).
• The Implicit Function Graphing Tool is a Java applet that will render the graphs of implicitly defined functions of two variables, x and y, in the xy-plane. It's easy to use and is based on a simple to understand algorithm (see the "How it works..." link on the webpage). If the applet doesn't seem to work, make sure you are entering your implicit equations in the required format (see the "Entering Functions" link).