Math 50C --- Homework Assignments

Math 50C: Homework Assignments

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Assignments and activities will be accumulated on this page throughout the semester. Please return often as this page will be updated frequently.

Directions: Please follow these directions on all homework assignments.

It is recommended, but not required, that you do all of your homework on engineering graph paper (available in the bookstore).
On each homework assignment, place your name in the top right corner of the page.
On the first line of the of the first page of your homework, please write down the assignment number, the pages that encompass the assignement, and list each exercise number assigned. For example, the first line of your homework might read:
Assignment #12, Page 150, #1, 3, 5, 7, 8, 10, 11, 23, 45
If an assignment takes more than a page, please staple the pages together with a single staple in the upper left-hand corner.
Simple one or two word answers or choices without explanatory prose are not acceptable. In all cases, use sound writing to justify your response.
Please do not do computation for a problem on one sheet of paper, then refer to a graph or diagram on another sheet of paper near the end of your stapled packet. Keep your work together, compuations and graphs and diagrams in the same general neighborhood on your homework.
Please do not crowd your work on your paper. Space things out and avoid tiny diagrams that are hard to read (please be nice to my old eyes).
Assignments will be handed in during classtime in separate piles: the assignment #1 pile, the assignment #2 pile, etc., so please do not staple two or more assignments together.

Fall 2009

Assignment #1 (Due Aug. 26)
- Read the Syllabus
- All students should see me for a login name and password. The price of admission is a ream of paper. Bring one ream of paper to my office and make sure that I check your name in my gradebook as having received your ream of paper. You can then place your ream of paper under the printer in room PS116.
- After logging onto myCR at http://myCR.redwoods.edu/, click the Account tool, then click the Modify Details button and create a new password. Make sure to write it down somewhere for safety. Next, click the Profile tool and fill in information you want to share. I probably wouldn't enter phone numbers and other information you want to keep private.
- Once you've updated your password and profile, read the welcome message on the Discussion Board and reply to the thread.
Assignment #2 (Due Aug. 31)
- While seated at the computer, read the activity Vectors and Matrices in Matlab and key in the examples in Matlab as you read. You are welcome to try some of the exercises at the end of the activity, but they are not required.
- In this activity, which must be viewed in the latest version of Firefox, download Plotting in Matlab, do the exercises at the end of the activity: #1, 3, 5, and 7. Use cell-enabled mode in the editor to produce each plot then publish your file to HTML. Create a folder in your Drop Box on myCR called assignment2 and upload all of your files into this folder.
Assignment #3 (Due Sept. 2)
- In this activity, which must be viewed in the latest version of Firefox, download Parametric Equations in Matlab, do the exercises at the end of the activity: #1, 2, 5, 7, 8, 11, 13, and 16. Use cell-enabled mode in the editor to produce each plot then publish your file to HTML. Create a folder in your Drop Box on myCR called assignment3 and upload all of your files into this folder.
Assignment #4 (Due Aug. 28)
- In Stewart, Early Transcendentals, read Section 12.1, pages 793-796.
- In Stewart, Early Transcendentals, read Section 12.2, pages 798-804.
- In Stewart, Early Transcendentals, page 805, exercise #4. For each part of this exercise, recopy the figure in pencil, then use a colored pencil to indicate the vector operation and result.
- In Stewart, Early Transcendentals, page 805, exercise #9, 13. Please draw accurate diagrams on graph paper.
- In Stewart, Early Transcendentals, page 805, do exercises 19, and 26.
- In Stewart, Early Transcendentals, page 806, do exercise #36. Include a sketch with your solution.
- In Stewart, Early Transcendentals, page 806, do exercise #37. Please provide an accurate sketch on graph paper for each part.
- In Stewart, Early Transcendentals, page 806, exercises #39, 40, and 43. Please provide a clearly labeled diagram with each solution.
Assignment #5 (Due Sept. 2)
- In Stewart, Early Transcendentals, read Section 12.3, pages 807-812.
- InStewart, Early Transcendentals, pages 812-814, do exercises #3, 7, 9, 11, 15, 19, 21, 27, 37, 45, 49, 51, and 56.
Assignment #6 (Due Sept. 9)
- In Stewart, Early Transcendentals, read Section 12.4, pages 814-820.
- In Stewart, Early Transcendentals, pages 820-821, do exercises #9, 12, 14, 25, 29, 34, 35, 38, 39, and 40.
Assignment #7 (Due Sept. 14)
- In Stewart, Early Transcendentals, read Section 12.5, pages 822-829.
- In Stewart, Early Transcendentals, pages 829-831, do exercises #10, 18, 29, 31, 35, 42, 53, 58, 63, and 65.
Assignment #8 (Due Sept. 14)
- In this activity, which must be viewed in the latest version of Firefox, download Lines in the Plane and Space in Matlab and enter the commands in the narrative while seated at the computer. Make sure you understand the result of each command before proceeding to the next command in the narrative.
- When you finish reading the narrative in Firefox, download Lines in the Plane and Space in Matlab, do all of the exercises at the end of the activity. For each exercise, include the following with your homework (note that this assignment requires submission of hardcopy, not an upload to your drop box):
  - All pencil and paper work required to produce the equations of the lines requested.
  - A printout of the final image.
  - A printout of the M-code used to produce the final image.
Assignment #9 (Due Sept. 16)
- In this activity, which must be viewed in the latest version of Firefox, download Planes in Matlab and enter the commands in the narrative while seated at the computer. Make sure you understand the result of each command before proceeding to the next command in the narrative.
- When you finish reading the narrative in Firefox, download Planes in Matlab, do all of the exercises at the end of the activity. For each exercise, include the following with your homework submission (note that this assignment requires submission of hardcopy, not an upload to your drop box):
  - Include all pencil and paper work required to produce the required equations.
  - A printout of the final image.
  - A printout of the M-code used to produce the final image.
Assignment #10 (Due Sept. 16)
- In this activity, which must be viewed in the latest version of Firefox, download Drawing Cylinders in Matlab and enter the commands in the narrative while seated at the computer. Make sure you understand the result of each command before proceeding to the next command in the narrative.
- When you finish reading the narrative in Firefox, download Drawing Cylinders in Matlab, do all of the exercises at the end of the activity. Create a folder assignment10 in your drop box on myCR, publish your results to HTML, then upload the files to your drop box.
Assignment #11 (Due Sept. 18)
- In this activity, which must be viewed in the latest version of Firefox, download Complex Numbers and Plotting in Matlab and enter the commands in the narrative while seated at the computer. Make sure you understand the result of each command before proceeding to the next command in the narrative.
- When you finish reading the narrative in Firefox, download Complex Numbers and Plotting in Matlab, do all of the exercises at the end of the activity. Create a folder assignment11 in your drop box on myCR, publish your results to HTML, then upload the files to your drop box.
Assignment #12 (Due Sept. 21)
- In this activity, which must be viewed in the latest version of Firefox, download Quadric Surfaces in Matlab and enter the commands in the narrative while seated at the computer. Make sure you understand the result of each command before proceeding to the next command in the narrative.
- When you finish reading the narrative in Firefox, download Quadric Surfaces in Matlab, do all of the exercises at the end of the activity. For each exercise, include the following with your homework submission (note that this assignment requires submission of hardcopy, not an upload to your drop box):
  - Include all pencil and paper work required to produce the required equations.
  - A printout of the final image.
  - A printout of the M-code used to produce the final image.
Assignment #13 (Due Sept. 25)
- In this activity, which must be viewed in the latest version of Firefox, download Velocity and Acceleration in Matlab do all of the exercises at the end of the activity. Publish your results to HTML and upload to your drop box in a folder called assignment13.
Asignment #14 (Due Sept. 25)
- In Stewart, Early Transcendentals, read Section 13.1, pages 849-855. No grade will be given for this assignment, but you should give this section a good read.
- In Stewart, Early Transcendentals, read Section 13.2, pages 857-860.
- In Stewart, Early Transcendentals, pages 861, do exercises #3, 5. Include hand drawn drawings of the curve, position, and tangent vectors for the given t-values.
- In Stewart, Early Transcendentals, page 861, do exercises #15, 16, and 17.
- In Stewart, Early Transcendentals, page 861, do exercises #25. Use Matlab to draw the curve and the tangent line. Obtain a printout of the result and include it with your homework paper.
- In Stewart, Early Transcendentals, page 861-862, do exercise #29c, 31, 39, 47, and 48.
Assignment #15 (Due Sept. 28)
- Download Level Curves in Matlab and do all of the exercises at the end of the activity. Publish your results to HTML and upload to your drop box to a folder called assignment15.
Assignment #16 (Due Sept. 28)
- In Stewart, Early Transcendentals, read Section 14.1, pages 887-897.
- In Stewart, Early Transcendentals, on page 898, without the aid of a computer, determine the domain and range of the function given in Exercise #8. Next, draw the function on the domain D={(x,y): -3<x,y<3}. There might be difficulties with complex numbers on D, so draw your surface with the command mesh(x,y,real(z)). Obtain a printout of the result, then explain on the printout how the picture helps you "see" the domain and range of the given function.
- In Stewart, Early Transcendentals, page 899, do exercises #32, 35, and 36.
- In Stewart, Early Transcendentals, page 899, sketch by hand several level curves of the functions in exercises 41 and 43.
- In Stewart, Early Transcendentals, page 900, use Matlabs's contour command to sketch level isothermals for the temperature function given in Exercise #47. I'd like labels for the contours as well, so sketch the contours with [c,h]=contour(x,y,z), then label them with clabel(c,h).
- In Stewart, Early Transcendentals, page 55, use Matlab's meshc command to sketch both the surface and contours for exercise #55.
- In Stewart, Early Transcendentals, page 900, use Matlab to sketch level surfaces f(x,y,z) = c, for c = 15, 30, and 45, using the function given in exercise #59.
Assignment #17 (Due Oct. 2)
- Download Partial Derivatives in Matlab and do all of the exercises at the end of the activity.
Assignment #18 (Due Oct. 5)
- In Stewart, Early Transcendentals, read Section 14.3, pages 909-919.
- In Stewart, Early Transcendentals, page 920, do exercises #5, 6, 8, 18, 24, and 30.
  1. Note: You can check your answers to differentiation problems using Matlab. This is particularly important on these exercises because you are not provided with the even solutions in your text or student solution manual.
  2. For example, let check exercise #30.
```
>> format compact
>> syms x y z
>> u=x^(y/z)
u =
x^(y/z)
```
    Now, the partial derivative with respect to x:
```
>> ux=diff(u,x)
ux =
x^(y/z)*y/z/x
>> pretty(ux)
 
                                    (y/z)
                                   x      y
                                   ========
                                     z x
```
    Similarly, the derivative with respect to z:
```
>> uz=diff(u,z)
uz =
-x^(y/z)*y/z^2*log(x)
>> pretty(uz)
 
                                  (y/z)
                                 x      y log(x)
                               ================
                                        2
                                       z
```
- In Stewart, Early Transcendentals, page 921, do exercises #39, 41, 43, 55, 67, and 69.
- In Stewart, Early Transcendentals, page 922, do exercise #77.
- In Stewart, Early Transcendentals, page 922, use Matlab to plot each request in exercise #84.
Assignment #19 (Due Oct. 5)
- Work through the activity Tangent Planes in Matlab while seated at the computer, then do the exercise at the end of the activity. Create a folder named assignment19 in your drop box, then upload your result to this folder. For the calculations, include them in your code (and published document) as comments.
Assignment #20 (Due Oct. 7)
- Work through the activity The Differential in Matlab while seated at the computer, then do the exercise at the end of the activity. Create a folder named asignment20 and upload your published file to this folder. Next, obtain a printout of your result, then mark the regions as required in the assignment. Hand this in during class.
Assignment #21 (Due Oct. 7)
- In Stewart, Early Transcendentals, read Section 14.4, pages 923-929.
- In Stewart, Early Transcendentals, on page 930, do exercise #7. Use Matlab to sketch the surface and the tangent plane to the surface at the given point. However, don't bother with the zoom-in instruction given in the text.
- In Stewart, Early Transcendentals, on pages 930-931, do exercises #19, 23, 27, 29, 31, 33, and 37.
Assignment #22 (Due Oct. 9)
- In Stewart, Early Transcendentals, read Section 14.5, pages 931-937.
- In Stewart, Early Transcendentals, on page 938-939, do exercises #5, 9, 13, 15, 23, 29, 33, 39, 43, 45, 47, and 51.
Assignment #23 (Due Oct. 14)
- Sit at a computer and perform the calculations in the activity The Directional Derivative in Matlab, then do the exercise at the end of the activity. Publish your code to a folder named assignment23 in your drop box.
Assignment #24 (Due Oct. 19)
- In Stewart, Early Transcendentals, read Section 14.6, pages 940-950.
- In Stewart, Early Transcendentals, on pages 951-952, do exercises #12, 15, 31, and 37.
- In Stewart, Early Transcendentals, on pages 952, use Matlab to complete exercise #45.
- In Stewart, Early Transcendentals, on pages 952-953, do exercises #47, 52, and 53.
Assignment #25 (Oct. 19)
- Sit at a computer and perform the calculations in the activity The Gradient in Matlab, then perform each of the exercises at the end of the activity. Create a folder named assignment25 in your drop box, then upload your results to this folder. For the calculations, include them in your code (and published document) as comments.
Assignment #26
- Sit at a computer and perform the calculations in the activity Max, Min, and Saddles in Matlab, then perform each of the exercises at the end of the activity.

Assignment #27

In Stewart, Early Transcendentals, read Section 14.7, pages 953-961.
In Stewart, Early Transcendentals, pages 961-962, perform each of the following tasks for exercises #5, 7, 11, and 19.
1. Use Matlab to draw the surface over a domain. Adjust your domain so that the extrema are visible on the surface.
2. Using the same domain as in part (1), use Matlab to create a contour plot with labeled contours. Place a grid on your plot, then use the "Text" and "Arrow" tools off the Figure Toolbar to annotate your plot with the coordinates of the extrema and the type of extrema. Note that there are several ways to use the contour plot.
  - [c,h]=contour(x,y,z), followed by clabel(c,h) gives the default labeled contour plot. However, some find that this places far too many labels on the contours and prefer [c,h]=contour(x,y,z), followed by clabel(c,h,'manual') which allows the user to use the mouse to place labels judiciously.
  - [c,h]=contour(x,y,z,n) will place n contours on your plot, where n is a positive integer. For example, to get 20 contours, you would use [c,h]=contour(x,y,z,20), to get 30 contours, you would use [c,h]=contour(x,y,z,30), etc.
  - You can also force contours at certain levels. For examples to draw the level curves f(x,y)=c, for c=1, 2, 3, 4, and 5, you would exercute [c,h]=contour(x,y,z,[1,2,3,4,5]) or, alternatively, [c,h]=contour(x,y,z,1:5). This allows very selective choice of contours.

Find and analyze extrema using the second derivative test shown in class. Arrange your work in a table as follows:

(a,b)	f(a,b)	f_xx(a,b)	f_xx(a,b)f_yy(a,b)-f²_xy(a,b)	Classification
(1,2)	8	-4	(2)(2)-(1)²=3>0	local maximum

To save paper, you might arrange so that your contour printout is printed near the top of the page, which would allow you to use the bottom half of the page for your calculations. Page Setup off the File menu in the Figure Window will allow you to set up the page with the plot at the top of the page.

Assignment #28
- In Stewart, Early Transcendentals, read Section 15.1 and 15.2, pages 981-994 (Here comes page 1000!).
- In Stewart, Early Transcendentals, read Section 15.3, pages 995-1001. (Yahoo! We just passed page 1000!).
- In Stewart, Early Transcendentals, page 1002-1003, do exercises 9, 10, 17, 19, 25, 27, 28, and 45. You are encouraged to employ fdomain5 and sketch the region of interest in each exercise, be it the indicated volume of a domain of integration.
Assignment #29
- In Stewart, Early Transcendentals, read Section 15.7, pages 1023-1030.
- In Stewart, Early Transcendentals, pages 1030-1031, do exercises #9, 11, 13, and 19.
- In Stewart, Early Transcendentals, pages 1031, do exercise #31. Use fdomain5 to verify each of your setups.
Assignment #30
- In Stewart, Early Transcendentals, read Section 15.8, pages 1033-1037.
- In Stewart, Early Transcendentals, page 1038, do exercises #14, 23, 24, and 32. In each case, use Matlab to sketch the indicated volume (or at least the surfaces bounding the indicated volume).
Assignment #31
- In Stewart, Early Transcendentals, read Section 16.1, pages 1055-1060.
- In Stewart, Early Transcendentals, page 1060, sketch the vector field in Exercises #5 and #6 by hand.
- In Stewart, Early Transcendentals, page 1061, use Matlab to answer Exercise #19. Obtain a printout.
- In Stewart, Early Transcendentals, page 1061, use Matlab to complete Exercise #27.
Assignment #32
- In Stewart, Early Transcendentals, read Section 16.2, pages 1062-1071.
- In Stewart, Early Transcendentals, page 1071, do Exercise #11, two ways:
  1. First, parametrize the given line segement in terms of time t, then evaluate the integral.
  2. Second, parametrize the given line segment in terms of arc length, then evaluate the integral.
- In Stewart, Early Transcendentals, page 1072, do Exercises #15 and 19.
- In Stewart, Early Transcendentals, page 1072, use Matlab to sketch the vector field of exercise #23 and superimpose the given curve C. Use your graph to predict whether the given integral will be positive, negative, or zero, then evaluate the integral and compare the result.
- In Stewart, Early Transcendentals, page 1073, do exercise #40.
- In Stewart, Early Transcendentals, page 1073, do the following for exercise #43.
  1. For part (a), use Matlab to sketch a constant force field of your choice, superimpose the graph of the unit circle, then explain why the field does zero work on the particle as it moves around the unit circle (once, uniformly).
  2. For part (a), let the vector field be defined by F(x,y)=c₁i + c₂j, then evaluate the appropriate integral to show that the work done by the field on the particle as it moves around the unit circle is zero.
  3. For part (b), use Matlab to sketch the given force field for k = 1/2, then superimpose the unit circle. What can you predict from your sketch about the work done by the field on the particle as it moves around the unit circle (once, uniformly)?
  4. Verify your prediction in part (c) by evaluating the appropriate integral.
Assignment #33
- In Stewart, Early Transcendentals, read Section 16.3, pages 1074-1081.
- In Stewart, Early Transcendentals, page 1081, perform each of the following tasks for exercises #3, 5, and 7.
  1. Sketch the vector field on the domain {(x,y): -3 < x,y < 3}.
  2. Examine your sketch. How can you use the sketch of the vector field to determine whether or not the field is conservative?
  3. Check your result of the previous question by answering the questions posed in the text.
- In Stewart, Early Transcendentals, page 1082, do exercises #13 and 21.
- In Stewart, Early Transcendentals, pages 1082-1083, do exercises #33 and 34(a).

David Arnold

Mathematics

Math 50C: Homework Assignments

Fall 2009