Current reading and homework assignments

• Due Thursday, 6 December:

  Reading

  • SHE, Sections 8.5. Note: We will not discuss denominators of degree higher than 2.
  • Prof. Herod's worksheet on methods of integration
  • Prof. Loss's class notes on complex numbers
  • Prof. Harrell's lectures on complex numbers
  • Prof. Cain's class notes on complex numbers
  Exercises
  • SHE, p. 477, #1,9,14,18,36
  • Use integration by parts to evaluate int(sin(m*Pi*x)*cos(n*Pi*x), x=0..2);
    Separately consider the cases where m and n are unequal integers and where m=n.
  • evaluate int(1/(a*x^2 + b^x + c),x); where:
    1. a = 2 b = 1, c = 2
    2. a = the number of members in your immediate family, b = your age in years, and c = your score on the last test
    3. Same as b), but permute the values and insert minus signs in every possible way.
    4. Same as c), but for int((2*x - 1)/(a*x^2 + b^x + c),x);
    5. Same as c) and d), but use complex numbers (we will talk about this on Monday).
  • Find all complex roots of the following polynomials, and factorize them.
    1. 2 z² - 6 z + 6
    2. z³ - 3 z² + 9 z + 13
       Hint: (-1)³ - 3 (-1)² - 9 + 13 = 0
    3. z² + 2 z - i
       Hint: In Monday's lecture we learn that (1/sqrt(2) + i/sqrt(2))² = i.
  • Consider the complex numbers z = 3 + 4 i and w = -1 + i, and find all of the following in standard form, (real part) + i (imaginary part):
    1. z + w, z - 2 w, z w, z w* (We'll use * for complex conjugate here, because it prints more easily on a web page than an overbar.)
    2. |z|, |w|, |z - 2 w|, and |z w|
    3. 1/z, 1/w, |1/z|, |1/w|
    4. z/w, w/z, z/w*, z*/w, (z/w)*, and (z/w*)*
    5. i z/w, (i z/w*)*, |(i z/w*)*|, |z/w|
  • Locate all the numbers you calculated in the previous problem in the "complex plane."
  • Use Euler's formula and/or the "polar form" of complex numbers (explained in Wednesday's lecture) to calculate:
    1. a cube root of i
    2. a cube root of -8i
    3. (sqrt(3) + i/2)²²
  • Do the exercises in Prof. Cain's class notes on complex numbers.

  For final review

  • Take the School of Math practice tests for 1501. At this stage they are all appropriate for final review.
  • Watch this space for more.

Past homework assignments

• Due Thursday, 23 August:

  Reading

  • SHE (Salas, Hille, Etgen), chapter 1, all
  • Look at the worksheet with the basic Maple commands you will need in this course. Familiarize yourself with the plot and substitute commands. (In case you have not yet acquired Maple, click here for a version you can read but not operate.)
  Exercises
  • SHE, p. 11, # 6,7,8,13,15,27-29,44,45,49,57
  • SHE, p. 19, # 15,19, 20,28,29,45, 51,52, 61, 63
  • SHE, p. 27, # 17-35, 40,41,58
  • SHE, p. 35, # 3,4,7,11,19-23,31-46
  • SHE, p. 45, # 3-16, 29-31
• Due Thursday, 30 August:

  Reading

  • SHE, sections 2.1-2.4.
  • Look at two worksheets with the basic Maple commands you will need in this course. (worksheet 1, worksheet 2). Familiarize yourself with the plot and substitute commands. (In case you have not yet acquired Maple, click here or here for versions you can read but not operate.)
  • Look at Prof. Heil's notes on limits.
  Exercises
  • Prof. Cain's Maple worksheet, #1-5.
  • Use Maple to sketch the graphs on p. 35, #31-43. For this week's quiz, you should know the code to sketch the graph of a function. For example, a correct Maple answer for #38 might be:
    > plot(sqrt(9-x^2), x=-3..3);
  • SHE, p. 51, # 1-10,23-25,31,39,40,48,50
  • SHE, p. 57, # 4,9, 10
  • SHE, p. 68, # 5-11, 17-22
  • SHE, p. 78, # 5-12; be able to evaluate these limits both by hand and by Maple. Also: # 27-29, 52, 55, 56
  • SHE, p. 87, # 1,3,5,6,19-23,39,40,44,45

There was a test on Friday, 7 September.

• Due Thursday, 6 September:

  Reading

  • The test will cover SHE, sections 1.1-3.1.
  Exercises
  • SHE, p. 97, # 10-14,23, 24,40,43,52
  • SHE, p. 105, # 1-3,17,20,21,27,28,41
  • SHE, p. 110, #1,2,7,9-14
  • SHE, p. 125, # 1-6, 13-15, 19,20,21
• Due Thursday, 13 September:

  Reading

  • SHE, sections 3.2-3.4
  Exercises
  • SHE, p. 135, # 1-6,23-28,33,34,35,41,42,49
  • SHE, p. 141, #6-10,17,18,25,26,50,51,53,65,66
  • SHE, p. 152, # 1,2,7,23,25,45,46,51,60,63
  • Also, be able to do all the calculations in these exercises with Maple.

• Due Thursday, 20 September:

  Reading

  • SHE, sections 3.5-3.9
  • Another Maple worksheet by Prof. Cain
  • Some Maple worksheets by Prof. Herod (optional):
    • Slopes, tangent lines, and normal lines
    • Method of bisection
    • Newton's method
  Exercises
  • SHE, p. 161, # 5,6,19-25,37-42,52,53,68,73,74,75
  • SHE, p. 169, # 5-15,39,40,47,58
  • SHE, p. 175, # 1,2,3,11, 12,18, 21,22,47
  • SHE, p. 181, # 1,2,7,10,17
  • SHE, p. 189, # 3-5,19,22,26,31-34,38
  • Prof. Cain's Maple worksheet, #1-4.

There was a test on Friday, 28 September.

• Due Thursday, 27 September:

  Reading

  • SHE, sections 10.1-10.4
  • Prof. Carlen's on-line notes on exponential functions
  • Prof Loss's on-line notes on exponential functions
  Exercises
  • SHE, p. 589, #10,11,15,16,33,34
  • SHE, p. 595, #1-3,9,10,19,20
  • SHE, p. 604, #3-6,24,31,33,34,52,53
  • SHE, p. 606, Project 10.3, 1-3
  • SHE, p. 611, #2,3,6,11,37
  • Experiment with the spreadsheet about the Newton-Raphson method (optional - requires microsoft Excel or compatible software).
  • Experiment with the spreadsheet about compound interest (optional - requires microsoft Excel or compatible software).

• Due Thursday, 4 October:

  Reading

  • SHE, sections 4.1-4.5
  • Look over another worksheet by Prof. Cain
  Exercises
  • SHE, p. 199, #1,2,11,30,40
  • SHE, p. 206, #5-8,22,37
  • SHE, p. 215, #1-7,22-26,35,36,45,48,49
  • SHE, p. 232, #1,4,44,46
• Due Thursday, 11 October:

  Reading

  • SHE, sections 10.5, 4.4-4.8
  Exercises
  • SHE, p. 223, #4-10,21,22,24-26,42,45,46
  • SHE, p. 617, #1-5, 17-19,44-46
  • SHE, p. 239, #1-5,17,20-23,29,30
  • SHE, p. 246, #2-6,21-24,38
  • SHE, p. 255, #1-3,8,13,23,57
  • Be able to sketch any of these graphs with Maple, using the command plot.

• Due Thursday, 18 October:

  Reading

  • SHE, Section 5.1
  Exercises
  • SHE, p. 266, #1-10,19,20

• Due Thursday, 25 October:

  Reading

  • SHE, Sections 5.1-5.3
  Exercises
  • SHE, p. 266, #9,10,17,31,33,34
  • SHE, p. 276, #1,2,4,9-11,18,19,25
  • SHE, p. 284, #4,6,10,19,20,27,37,38,51

• Due Thursday, 25 October:

  Reading

  • SHE, Sections 5.1-5.3
  Exercises
  • SHE, p. 266, #9,10,17,31,33,34
  • SHE, p. 276, #1,2,4,9-11,18,19,25
  • SHE, p. 284, #4,6,10,19,20,27,37,38,51

• Due Thursday, 1 November:

  Reading

  • SHE, Sections 5.4-5.6
  Exercises
  • SHE, p. 290, #3-8,11-15,36
  • SHE, p. 297, #1,2,5,8,15-18,20,21,23-26,35,39,42,44,48
  • SHE, p. 306, #3,8-11,23-27,32,34,37,49-52,63,65,66,69,77
• Due Thursday, 8 November:

  Reading

  • SHE, Sections 5.7,5.8,7.1-7.6
  Exercises
  • SHE, p. 311, #1-6, 17-19
  • SHE, p. 317, 9-13,22,23,28
  • SHE, p. 373, #3,5,7,35,36
  • SHE, p. 381, #17-20
  • SHE, p. 390, #2,8,18-22,51,57,61
  • SHE, p. 399, #16,22,32,36,42,67

• Due Thursday, 15 November:

  Reading

  • SHE, Sections 7.7,6.1-6.3
  • A helpful worksheet on the u substitution.(You are not yet responsible for the material on integration by parts.)
  • A helpful worksheet on solids of rotation. (You are not yet responsible for the material on the surface area.)
  Exercises
  • SHE, p. 415, #1,4,7,15,22,28,30
  • The half-life of C¹⁴ is 5730 years. The charcoal drawings at Lascauxwere dated by the carbon-dating method: Modern charcoal was prepared from the same wood as is believed to have been used by the ancient artists, and was found to have 6.68 alpha decays per gram-minute. Charcoal from the cave was found to have 0.97 alpha decays per gram-minute. How old is the ancient charcoal? (I.e., finish the word problem from the end of Friday's lecture.)
  • SHE, p. 427, #2,4,19-22,33,44,55-57,61,62
  • SHE, p. 324, #3,4,15-17,31,32,35
  • SHE, p. 335, #4-7,13,15, 23-26,27,29,35,36,39,45
  • SHE, p. 343, 5-9, 15-19

• Due Thursday, 22 November:

  Reading

  • SHE, Sections 6.4-6.6
  Exercises
  • If Uncle Bud, who was graduated from Tech back in 1961, is there at the Thanksgiving table, remind him about the method of cylindrical shells and see how high he jumps!
  • On Tuesday your recitation will review the test and, time permitting, SHE p. 349, #6,7,15,16,26 and SHE p. 356, #3,4,15,16,18.

• Due Thursday, 29 November:

  Reading

  • SHE, Sections 6.6,8.1-8.4
  Exercises
  • SHE, p. 361, #3,17
  • SHE, p. 453, #4-10,27,28,29,38,49
  • SHE, p. 462, #1,4,6,8,11,49,52.
  • SHE, p. 468, #2,4,5,29,32,35,36,37,46

Gluttons for more math? Check out the contest page.

• The 1501 home page
• Evans Harrell's home page
• The School of Math on-line resources

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