MATH 142 -- Calculus II

Professor Matt Miller
miller@math.sc.edu

All sections: MWF 9:05-9:55 in BA 502, lab sessions TuTh in LC 303A

Required text: Calculus by Varberg, Purcell, Rigdon, eighth ed.

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  • Class topics and problems
  • Jan 13-17. Logs and exponentials
    Read section 7.1 and do problems CR (Concepts Review) 1-4, and PS (Problem Set) 1-3, 6, 8, 11, 13, 15, 18-20, 31, 34, 37-39, 46, 49. Read section 7.2 and do problems CR 1-4, PS 1-3, 5, 6, 17, 19, 21, 25, 34, 36, 39, 40. Read section 7.3 and do CR 1-4, PS 2, 3, 7, 9, 13-15, 17, 20, 23, 25, 28, 29, 31-33, 37, 38, 44.
  • Jan 22-24. Exp. growth, other transcendental functions
    Finish up section 7.3; then go on to 7.4 and do CR 4, PS 1, 13, 23, 37, 41, 46. Over the weekend read 7.5 and do CR 1-4, PS 1-2, 5-9, 11-12, 15, 26-29. Omit the discussion of the logistic model (which will be a lab topic most likely) and the applications to finance. There will be a quiz on 7.1-7.3 on Friday, Jan. 24. Since classes before 10:00 am on Friday, 24 Jan. have been cancelled, I recommend that you try to read and get started on the problems of 7.5 on your own. Here is a bit more explanation, written by Dr. Girardi and slightly modified by myself on the model of exponential growth and decay. Biology students should pay particular attention to the paragraph on per capita growth rate (1/P)(dP/dt) vs. net growth rate dP/dt.
  • Jan 27-31. Inverse trig functions and techniques of integration (I)
    Read 7.5 and do CR 1-4, PS 1-2, 5-9, 11-12, 15, 26-29. Omit the discussion of the logistic model (which will be a lab topic) and the applications to finance. Read 7.7 and do CR 1-4, PS 1-5, 7-8, 11 (be careful -- is your calculator set on radians?), 16, 19-21, 29-31, 36, 37, 39, 41-43, 48-50, 53, 55, 56, 58, 72. You already know the idea of 8.1; all you have to do is work a zillion problems until you get good at it. Begin with CR 1-4, PS 3-7, 11, 13, 14, 17, 19-24, 29-30, 39, 47, 49-52; if these aren't enough, do all the odds, and if you need more practice do all the evens.
  • Feb 3-7. Techniques of integration (II), Exam 1
    We continue with 8.2, trigonometric integrals: do CR 1-4, PS 1, 3, 5, 7, 8, 13, 14, 17, 19, 27, 31. Here are some additional review problems (section 7.9): CT 2, 5, 6, 9, 17, 39, 40, STP 3, 10, 14-15, 18, 25-28, 30-31, 33, 38.
  • Feb. 10-14. Techniques of integration (III)
    We pick up with section 8.3 on substitutions to deal with radicals. Do CR 1-4, PS 1, 3, 5, 6, 10, 14, 15, 17-19, 21, 23, 25. We will spend two days on this section, and then move on to 8.4, integration by parts, which is the most important technique we will learn after u-substitution. In 8.4 do CR 1-4 and PS 1, 5, 6, 9, 11, 13-15, 17, 19, 20, 27, 37, 41, 45, 46, 48, 55, 59, 60, 70, 81.
  • Feb. 17-21. Techniques of integration (IV)
    After practicing integration by parts a little more we will move on to yet another method for dealing with integrals that have fractional integrands, in this case rational functions (fractions involving polynomials, but no radicals, etc.), called "partial fractions". We will only do the easiest case in class, and leave the rest to the lab. Do 8.5 CR 1-3, PS 1-3, 5-7, 11, 13-14, 17-18, 41-42 (hint: get all the x or y stuff on one side, including the dx or dy, and get the t stuff, including dt, on the other side; then integrate both sides and use properties of ln and exp). Finally we will finish the week with sections 9.1 and 9.2. In 9.1 do CR 1-3, PS 2-8, 10, 11; in 9.2 do CR 1, 2, 4, and PS 1, 3, 5, 11.
  • Feb. 24-28. Indeterminate forms, improper integrals, probability
    Note that the deadline to drop the course with a W is Monday, February 24. In 9.3 do CR 1-4, PS 1-5, 8, 10-12, 14, 17, 18, 23, 25. Also do 31, 33, and on page 426 do 3-5. You may leave computation of variances to the lab, as these are usually messy to do by hand. Do the circled problems on the blue sheet.
  • Mar 3-7. Probability, improper integrals of the second type, Taylor polynomials
    Finish the problems of 9.3 and the blue sheet: page 413, problems 4, 5, 6, 9-11, page 422, problems 5, 8, 9, 10, 13-15. Go on to 9.4, CR 1-4, PS 1, 2, 5-7, 10, 16, 19, 21, 29. Over the break (yes, make a copy of the pages, and do them in the car, or on the plane, or on the beach), do 11.1 CR 1, 2, PS 1, 3-7, 15, 17.
  • Mar 17-21. Taylor polynomials and series
    Memorize the formula for the Taylor polynomial of order n centered at a (p. 480) and the error on p. 482, and know how to use these. In 11.1 do PS 33-36, 39, 41, 43-45, 46. In 10.8 memorize the Maclaurin series 1, 2, 4, 5, 6, and 9 at the end of the section. Then do CR 1-4, PS 3, 4, 11, 17, 20, sin(x) with a = 13 * pi / 6, 22, 23, 27, 29, 38, 40. Here are some additional review problems: p. 398, 17, 18; p. 399, 15, 7, 9, 11-13, 22, 28, 34, 35, 3740, 42; p. 425, CR 1, 2, 4, 5, 10, 12, 13, 15-17, 20, STP 1, 2, 4, 7, 8 10, 13, 16, 19-23, 28-29, 31-34, 39-40; p. 426, 5ab, and find the median; blue sheet p. 414, 12, 13; blue sheet p. 422, 4 (and any problems you have not already done on the blue sheet).
  • Mar 24-28. Exam 2, power series
    If you have not already done the problems from 10.8 do them now. Then do the problems 1, 2, 3, 5, 7, 9, 11, 13, 14, 15, 25 from section 10.7. Again, you should memorize the Maclaurin series 1, 2, 4, 5, 6, and 9 at the end of 10.8. This includes knowing the interval of convergence! Review integration by re-doing 8.2 #21, 43; 8.4 #13, 14; 8.6 #34, 35; 9.5 #7. Then read 10.6 and give CR 1-3 and PS 1-3, 5, 7, 8, 14, 15, 17 a try (I haven't lectured on this, but will do so on Monday; in any case, it's pretty easy so I encourage you to plunge right in.)
  • March 31-April 4. Convergence tests for numerical series
    Continue working on the problems of 10.6; also revisit the problems of 10.7 now that you know what the interval of absolute convergence is (but don't worry about the endpoints for now). Start working on 10.1 CR 1, 2, 4, PS 1, 2, 7, 10, 12, 16, 17; and 10.2 CR 3, 4, PS 1, 2, 5, 6, 8, 12.
  • April 7-11. Convergence tests (cont.)
    Finish up problems from 10.1 and 10.2. Do CR 2-4 and PS 1, 3, 4, 5, 7, 11-13, 17, 19 from 10.3 and CR 1-4, PS 1-3, 5-8 from 10.4. Finally do 11, 13, 15, 16, 18, 20, 23-25, 30 from 10.4 and read over 10.5.
  • April 14-18. Alternating series, Exam 3
    Do CR 1-3, PS 1, 2, 5, 7, 8, 9, 13, 15, 17, 21 from 10.5. To review for the exam, beyond the problems already assigned, and the quiz problems, I recommend 12, 18, 20, and 29 from 10.5; 4, 12, 19, 26 (hint: use that ln(n) is less than sqrt(n)), 28 from 10.4; 3, 9, 10 from 10.2 (use any of the tests even if they come later in the chapter); 6, 9, 11 from 10.6; 7, 30, 32 from 10.8; 11-14, 17-21, 27, 31, 33, 35, 43, 49, 50, 52abc from page 476.
  • April 23-25. Polar coordinates
    In 12.6 do CR 1-3, PS 1, 3, 7, 9, 11, 12, 14, 15, 17-19, 25, 27, 28. In 12.7 do 3-6, 9, 11, 17, 21, 28, 29, 31, 33, 35. In 12.8 do CR 1-3, and find the area enclosed by the curves you graphed in 12.7 PS 5, 6, 9, 11, 17, 21, 28-29 (for these last two take theta from 0 to 2*pi), 31 (for theta from pi/6 to 2*pi), 33, 35. Finally, do 12.8 PS 18, 19.
  • April 28-30. Review, and class evaluations
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  • Exams
  • Fri Feb 7: FIRST EXAM (This is the correct date!)
    Text sections 7.1-7.3, 7.4 (lightly), 7.5, 7.7 (concentrate on arcsin and arctan), 8.1 (concentrate on formulas 1-3, 5-7, 9, 11, 13, 14 on p. 372), 8.2 (concentrate on type 1, ex. 1 and 2, type 2, ex. 3).
  • Mon Mar 24: SECOND EXAM
    Text sections 8.3-8.5 (but note that these integral types may lead back to material you learned in chapter 7 and 8.1, 8.2), 9.1-9.4, probability, 11.1. Although 10.8 will not be on the exam, doing the problems from that section will solidify your understanding of 11.1.
  • Fri Apr 18: THIRD EXAM
    Text sections 10.8, 10.6-10.7, 10.1-10.5
    Evening Review Session: Thursday, 17 April, 7-9 pm, LeConte 405
  • Mon May 5 (9 am - noon): FINAL EXAM
    Text sections all the above plus 12.6-12.8. If you have questions about the final, call or email me to set up an appointment for some time on Thursday (but not 1:00-3:00), Friday (but not 10:00-12:00), Saturday or Sunday. Sunday evening I will be available at the Preston Seminar Room or SRC from 8 until 10.


    • Last modified: April 24, 2003