Math 221PH and Phys 122MA

Integrated Physics and Calculus

Spring 2003

  • Course information (web page) or PDF
  • Daily notes
  • Homework assignments
  • Projects
  • Fun stuff
  • Gradebook

    • Daily notes

    Tuesday, January 21

    Math: In class, we covered some ideas that show up in Section 13.2. The first homework assignment is from Section 13.1. We will cover this material on Wednesday. For now, you should have a first read of Sections 13.1 and 13.2. Try to pick up a sense of the material but don't spend too much time on details until we've gone over some of the ideas in class.

    Wednesday, January 22

    Math: You should work on problems from Section 13.1 and be prepared to ask questions on these in class on Friday.

    Tuesday, January 28

    Math: You should be reading and doing problems from Sections 13.2 through 13.4. Bring questions on this material to class Wednesday. For fun, look at the beautiful sketches of surfaces done by a student at Brown at this web site.

    Wednesday, January 29

    Math: You should really be reading and doing problems from Sections 13.2 through 13.4. In class, we talked about the vector identities involving the dot and cross products and about the triple scalar product. This handout has a few problems related to these. Let me know if you have any trouble downloading or opening this PDF file.

    Friday, January 31

    Math: The Fun Stuff section has a link to a graph of the function f(x,y)=2xy/(x2+y2) that we analyzed in class today.

    Monday, February 3

    Math: You should be reading and doing the problems from Section 14.1.

    Monday, February 10

    Math: The idea of double integrals in polar coordinates is covered in Section 14.2.2 of the text. You should read this and work on the second set of problems assigned from Section 14.2.

    Tuesday, February 11

    Math: The homework from Section 14.2 will be due on Friday so we can answer questions on the problems from this section tomorrow (Wednesday).

    Physics: Homework problems from Section 17.2 will be due on Friday.

    Both: In both math and physics, we have been talking about vector fields. This would be a good time to try out the Vector Field Analyzer. This Java Applet allows you to plot and analyze a two-dimensional vector field. Be patient as the page loads; it takes a minute or two for the Java Applet code to set everything up. After the code is loaded, you will see a plot of the default vector field. You may want to change to some simple example such as F(x,y)=(y,-x). Note that the applet has three "layers" that you can change by clicking on the tabs labeled "Zoom lenses", "DEs/flows", and "Line int's." The "DEs/flows" tab is probably the one you want to start with. Click on the choice labeled "Integral curves" and then click somewhere in the plot region. A blue spot should appear. Clicking on the "Stop and Go" button will start the program drawing a curve that is tangent to the vector field.

    Friday, February 14

    Math: You should read and do problems from Sections 14.3 and 14.4.

    Physics: Work through Examples 16.10 and 17.12, writing up a solution in your own hand. It's OK to follow the equations and derivation in the text, but I'd like you to provide a detailed argument using both words and mathematical analysis.

    Tuesday, February 18

    Math: There are (at least) two errors in the textbook answers for the Section 14.3 problems. For #3, the answer is 96ln(2), not 144. For #27, the answer is +162p, not -162p.

    Friday, April 11

    Math: This would be a good time to try out more features of the Vector Field Analyzer. This Java Applet allows you to plot and analyze a two-dimensional vector field. Be patient as the page loads; it takes a minute or two for the Java Applet code to set everything up. After the code is loaded, you will see a plot of the default vector field. Note that the applet has three "layers" that you can change by clicking on the tabs labeled "Zoom lenses", "DEs/flows", and "Line int's." Go to the "Line int's" tab. Click and drag on the vector field plot to produce a rectangular box. The software will compute the flux, the area, and the ratio of these two. (It also calculates something called "circulation" which we will talk about on Monday.) The values of flux, area, and the ratio are dynamic so if you keep the mouse button down while you drag, the rectangle will be resized and you can watch the values change. Look at what happens if you make the rectangle small. The ratio should approach a constant value. This limit is the flux density.

    Homework assignments

    Section Problems to do Submit Due date Assigned by
    13.1 #1,3,5,7,8,9,10,11,13 #8,10 Monday, Jan 27 MJ
    15.2 #1,8,9 #8 Wednesday, Jan 29 GE
    15.3 #4,7 #4,7 Wednesday, Jan 29 GE
    15.4 #5 #5 Wednesday, Jan 29 GE
    13.2 #1-4,5,6,9,11,13,16 #6,16 Friday, Jan 31 MJ
    13.3 #1,5,6 None MJ
    13.4 #1-4 None MJ
    Vectors #1-4 from handout #3,4 Tuesday, Feb 4 MJ
    16.2 #1,3,4,5,6 #3,5,6 Friday, Jan 31 GE
    16.3 #2,4,7,8,9,14 #4,8,14 Tuesday, Feb 4 GE
    14.1 #1,3,4,5,7,8,9,11 #4,8 Wednesday, Feb 5 MJ
    14.2 #1-15 odd None MJ
    14.2 #16-23 #20,23 Friday, Feb 14 MJ
    17.2 #7,8,10,13,15,24 #8,10,15 Friday, Feb 14 GE
    Chap 16/17 See daily notes. Ex 16.10, 17.12 Monday, Feb 17 GE
    14.3 #1-33 odd #6,30,34 Tuesday, Feb 18 MJ
    14.4 #1,3,10,12,13 #12 Tuesday, Feb 18 MJ
    17.3 #5,9,10 #5,9,10 Friday, Feb 21 GE
    18.1 #1,2,3-25 odd,28 None MJ
    18.4 #1,2,5,8,11,12 #2,8,12 Tuesday, Feb 25 GE
    18.2 #1,2,3,7,8,15,17,21,23 #2,8 Wednesday, Feb 26 MJ
    18.3 #1-19 odd, 21-27 #8,18 Wednesday, Feb 26 MJ
    18.6 #3,4,5,8,9 all Wednesday, Mar 5 GE
    19.1 #2,3,7,12,13,17,18,19,20,27,28,30,32 #3,7,18,20,28,32 Friday, Mar 7 GE
    19.3 #1,2,5,6,10,13 #2,6,10,13 Wednesday, Mar 12 GE
    Gradients #1-8 from handout #4,7 Wednesday, Mar 12 MJ
    20.1 #7,9 None MJ
    20.2 #5,6,9,11,13-18 None MJ
    20.3 #1-9 all #5,6,8 Friday, Mar 14 MJ
    21.2 #3,4,12,13,14 #4,13 Friday, Mar 14 GE
    21.3 #1,3,4,5,8 #3,5,8 Friday, Mar 14 GE
    21.5 #1,2,3,4,6,8 #2,3,4,8 Tuesday, Mar 25 GE
    20.4 #1,3,5,7,9,11,12,13 #12 Wednesday, Mar 26 MJ
    20.5 #1-9 #6,8 Wednesday, Mar 26 MJ
    22.1 #1,5,9,10 None MJ
    22.2 #1-10 None MJ
    22.3 #1-13 odd #10,14 Friday, April 4 MJ
    22.4 #1-7 odd #4 Friday, April 4 MJ
    23.1 #3,5,6,7,9,12,17,18,19,24,25,26 #12,18,19,24,25,26 Friday, April 4 GE
    23.2 #1-15 odd #10,14 Wednesday, April 7 MJ
    23.3 #1,2,3,4,5,7,9,11 #2,8 Friday, April 11 MJ
    24.2 #8,10,13,14,19,20 #13,19,20 Friday, April 11 GE
    24.3 #1,4,6 #4,6 Monday, April 14 GE
    24.4 #3,5,6,8 #3,5,6,8 Wednesday, April 16 GE
    25.6 #1,3,5,7,8,9,10,11,12,13,15,16,17 #1,2 from handout Wednesday, April 16 MJ
    25.7 #1,3,9,11,12,13 MJ
    25.7 #18,19,20 #1,2 from handout Friday, April 25 MJ
    25.1 #2,3,4,5,8,9 #2,3,8,9 Friday, April 25 GE
    25.2 #2,3,5,6,8 #3,5,6 Monday, April 28 GE
    25.4 #2,3,4 #2,3,4 Monday, April 28 GE
    26.1 #7,8,9,15,16 #7,8,9,15,16 Wednesday, April 30 GE
    27.1 #1-8 #4,6 Wednesday, April 30 MJ
    27.3 #1,2 #1,2 Friday, May 2 GE
    27.2 #1-8 #4,6 Monday, May 5 MJ
    27.4 #4,5,10-15 #5,10-15 Monday, May 5 GE

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    Projects

    You will need a PDF viewer to read the files posted here. Visit the Adobe website to obtain a free reader (all major platforms are supported).

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    Fun Stuff

    You can go to http://math.la.asu.edu/~kawski/vfa2/ to play with the Vector Field Analyzer written by Matthias Kawski of the Mathematics Department at Arizona State University. This Java Applet allows you to plot and analyze a two-dimensional vector field. Be patient as the web loads; it takes a minute or two for the Java Applet code to set everything up. After the code is loaded, you will see a plot of the default vector field. You may want to change to some simple example such as F(x,y)=(x,y). Note that the applet has three "layers" that you can change by clicking on the tabs labeled "Zoom lenses", "DEs/flows", and "Line int's." The "DEs/flows" tab is probably the one you want to start with.

    Tom Banchoff of Brown University has written a brief essay entitled "The Best Homework Ever?" It's worth a look to see the beautiful sketches of some surfaces done by an student at Brown.

    On Friday, January 31, we analyzed the discontinuity at (0,0) for the function f(x,y)=2xy/(x^2+y^2). You can go here to see a graph of this function.

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    Gradebook

    To have your scores included in this web version of the gradebook, send me a code name to use.

    This version of the gradebook was lasted updated on May 15, 2003. The course score is computed with the total homework score weighted at 40%, the lab score weighted at 10%, the total exam score weighted at 40% and the final exam weighted at 10%. The lab scores are all listed at 85% until the real lab scores are reported by individual instructors. The averages are computed using scores for all students in the class, not just those displayed here.

      HW                                                                             Exams         Totals       Course  
    Code 13.1 13.2 Vec 14.1 15 16.2 16 14.2 14.3 18.2/3 Grad E16.10 17.2 17.3 18.4 18.6 19.1 19.3 21.2 21.5 20.3 20.4/5 22.3/4 23.1 23.2 23.3 24.2 24.3 24.4 25.1 25.2 25.4 25.6 25.7 26.1 27.1 27.2 27.3 27.4 1 2 3 4 5 HW % L % E % FE Score Code
    Arashi 8 8 5 10 20   15 10 18 19 10 10 12 14 15 24 30 20   18   14 10 30 9 10 15 10 20 15   10 7 18 25 10 10 8 35 53 71 56 83 58 82.2 85 64.2 84 75.5 Arashi
    bodhi 10 9 9 10 18 15 14 10 13 20 10 10 15 11 15 19 30 20 10 20 13 13 14 27 9 8 15 10 15 20 15 15 8 12 25 10 10 10 35 85 64 79 81 75 90.1 85 76.8 63 81.6 bodhi
    jellyfish 8 8 9 10 18 14 15 8 19 20 10 10 15 15 15 24 30 20 25 20 13 13 15 30 10 9 15 10 20 20 15 15 9 20 25 10 10 10 30 100 88 92 94 93 96.4 85 93.4 70 91.4 jellyfish
    miss kitty fantastico 9 7 9 10 18 10 13 9 20 20 10 10 15 10 15 20 15 20   20 14 13 15 28 10 10   10   8 15 15   10 8 10 10 10   80 90 81 68 61 70.2 85 76.0 85 75.5 miss kitty fantastico
    Ralph Wiggum 10 9 10 5 15 15 10 10 19 19 7 10 15     17     9 13 8 11 13 10 8 9 11 10 16 18 13 15     20 8   10 25 73 76 81 69 59 62.7 85 71.6 83 70.5 Ralph Wiggum
    SLady 9 7 8 10 18 9 10 8 16 17 8 0 15 9 12 23 20 20 18 15 13 14 10 18 10 9 10 10 20 18 15 15 7 10 10 8 7 10 20 58 59 60 57 36 76.5 85 54.0 28 63.5 SLady
    squeeze cheese 10 7 9 9 10 9 10 9 17 20 8 10 15 10   15 30 20 9 20   13 12 30 10 10 13 10 20 15 15 15 10 10 25   10 10 35 56 65 76 52 66 80.3 85 63.0 72 73.0 squeeze cheese
    SuckaFree 10 9 10 7 18 12 13 10 18 20 9 10 15 13 15 22 28 19 21 20 11 13 15 30 7 10 15 10 20 20 15 15 7 13 25 10 8 10 20 74 83 84 74 73 90.2 85 77.6 82 83.8 SuckaFree
    Super Saiyan 9 8 3 10 18 15 13 10 19 20 9 10 15 15 13 21 30 19 22 20 13 13 11 30 10 10 15 10 20 20 15 15 7 13 25 10 8 10 35 81 80 87 72 69 92.8 85 77.8 68 83.5 Super Saiyan
    POSSIBLE 10 10 10 10 20 15 15 10 20 20 10 10 15 15 15 25 30 20 25 20 15 15 15 30 10 10 15 10 20 20 15 15 10 20 25 10 10 10 35 100 100 100 100 100 100.0 100.0 100.0 100 100.0 POSSIBLE
    AVERAGE 9 8 8 9 18 13 12 9 17 19 9 9 15 12 14 21 27 19 18 18 12 13 13 25 9 9 14 10 19 17 15 15 8 14   9 9 10 30 74 73 76 70 68 82.6 85.0 72.2 69.4 77.4 AVERAGE

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