Mathematics 1508LA       Calculus II       Fall, 1997

Current homework assignments

Due Thursday, 12 March

The homework due on the final Thursday of the course will not be collected and graded, but you should be prepared to work the following in recitation.

Section 7.4, #10-14,33-36,42
Section 7.6, #4,6,8,10,27,30,33,34
Section 7.7, #1-4,10,11,12,26

Current contests

  • A prize will be awarded to the first student to find a solution of section 4.6, # 4.8 "When is UGA math accidentally correct?" Note: Only finite integrals, please. A prize will also be awarded for the most interesting solution, whether or not first.

  • A prize will be paid to the student who finds the best patterns for the sum of kp for
    k =1..N, and for all p. You are allowed to call on Maple for this one, but it is up to you to find the pattern. No deadline (other than the end of the term).

    • Past homework assignments

    Due Thursday, 15 January

    To prepare for the test on 16 January, the following problems from Grossman were suggested:

    Section 4.2, # 4,6,8,18,20
    Section 4.3, # 3,12,21,22,25,26,28
    Section 4.4, #11,12,18,19,27,30,33,40
    Section 4.5, # 2,6,21,24,28,35

    Due Thursday, 22 January

    Section 4.6, # 5-8, 27, 33, and the following variant of #33:
        F(x) = int(1/(1+t^3), t=x..3);
    with
        x0 = 1.

    Also, students were to do problems at the level of the test I gave in 1995.

    Finally, students should know how to plot graphs with Maple and to use the commands diff and int .

    Due Thursday, 29 January

    Section 4.7, # 18,20,27,38,50

    Section 4.8, # 3,4,5

    Find the averages of the following functions on the given intervals.

        a) f(x) = 1 + x3, 0 < x < 2.
        b) f(x) = 1 + x3, -1 < x < 1.
        c) f(x) = x2sin( pi x3), 0 < x < 7.

    Section 5.1, # 8,9,12,20,25

    Section 5.2, # 9-14,21,24,25

    Work through the Maple worksheet illustrating the important geometric relationships which exist between the graphs of f, the derivative of f and the integral of f. In particular, do the problem at the end of this worksheet.

    Due Thursday, 5 February

    Section 5.3, #4,5,6,15
    Section 5.4, #8,10,20,24
    Section 5.5, #3,7,9

    Due Thursday, 12 February

    To prepare for the test on 13 February, please examine the following on-line materials:

  • A Java applet illustrating the notion of arc length. This is a completely interactive program which shows what arc length is all about, without requiring any Maple code or calculation on your part.
  • A Maple worksheet on arc length. (Only the part "Arc length for a graph y = f(x)" and the first two sections of the exercises.)
  • A Maple worksheet on the theorem of Pappus.
  • A Maple worksheet on some simple differential equations and their applications. (Only the parts "The solution of the basic growth/decay law" and "Some applications of the basic growth/decay law" and Exercise 1.)

    • Also, the following problems from Grossman are suggested:

    Section 5.6, all drills, and #13-15
    Section 8.6, all drills (for review of polar coordinates)
    Section 8.7, all drills, and #30,31,36,37,39
    Section 6.4, #26-28,43,44
    Section 6.6, #6,8,9,17
    Section 6.3, #15-19, 25,28,30,31, 38,43

    Due Thursday, 19 February

    Section 16.2, #2,10,18

    Also, work through the Maple worksheet on Growth, decay, and exponential functions, and do the exercises there.

    Due Thursday, 26 February

    Section 16.3, #3,4,5,17,20,32
    Section 16.4, #4,6,8

    Also, please work through the worksheet discussing a differential equation for diffusion, and do the exercises there.

    To prepare for the test on 3 March, please examine the following on-line materials:

  • The worksheet discussing a differential equation for diffusion, including the exercises there;
  • The section "Direction Fields for a Differential Equation" in the Maple worksheet on differential equations written by Prof. Herod,

    • and be prepared to solve any differential equation in Grossman, sections 16.1-16.6.

    Due Thursday, 5 March

    Section 7.2, # 2,5,14,20,
    Section 7.3, #6

    Contest results

  • A prize was awarded to Martin Urda for finding by hand the best upper and lower bounds for the area bounded by: the x-axis, the y-axis, the line x=2, and the graph of the function 1/2sqrt(x).

    A newsgroup called git.math.class.harrell has been created on the Georgia Tech computer system. Please use it to post questions and comments for the other students or the professor.

    Link to:
  • Evans Harrell's home page
  • The School of Math on-line resources 
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