MATH 122--Calculus

Professor Matt Miller
miller@math.sc.edu

Section 12 MWF 1:25-2:15 in LeConte 113
Text: Applied Calculus by Hughes-Hallett et. al., second edition,


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  • Class topics, assignments, and homework problems
  • Jan. 10-12. Functions in terms of graphs, tables, and verbal descriptions, linear functions Read sections 1.1 and 1.2. Do problems 1, 2, 3, 1, 3, 5, 6, 7-11, 14, 22, 23 from section 1.1. Learn how to graph functions on your calculator. Know how to change the window size and the spacing of the tickmarks (axis scale). Know how to use the trace key to find coordinates on your graph. Know how to zoom in and how to use these features to find roots, that is, the x-coordinates where y = 0. Do problems 1, 3, 5, 7, 9, 11, 13, 17, 19 from 1.2. Read section 1.3 and begin to work on problems 1-5, 7, 10,11, 13, 15, 19, 21, 29, 38, 41.
  • Jan., 17-19. Average rates of change, economic applications, exponential functions. Finish up section 1.3, and go on to read section 1.4 and do problems 1-4, 7, 9, 13, 23, 24. Read section 1.5 and do problems 1, 2, 3, 4, 5, 6, 13, 14, 15, 21, 29.

  • Jan. 26-30. Exponential growth and decline Class cancelled Monday, 1/26. Continue working on the problems from 1.5 listed above. Then read section 1.6 and ATTEMPT problems 1, 5, 11, 12, 14, 17, 19, 22, 23, 25, 34, 35. Be sure you understand the difference between discrete growth (in steps) and continuous growth, and what we call the rate of growth in each case.
  • Feb. 2-6. Exponential growth and decline (cont.), natural log and exp, regression Finish up the problems from 1.5 and 1.6; then read 1.7 and attempt problems 1-6, 9, 10, 12, 15, 16. Good additional problems are 23, 24, 27. Learn how to do regression (fitting curves to data) on your calculator; do problems 1, 2, 6-8, 11 on p. 79 and following.
  • Feb. 9-13. Review, first exam, instantaneous rate of change Read section 2.1 and do problems 1-3, 6-8, 16, 17, 21, 22, and the problems on the back of the pink answer sheet for quiz #3. When you are doing ordinary graphs be sure your statplots are turned off; you can do this in the Y= menu, the STATPLOT menu, or you can just wipe out all your lists with 2nd MEM 4:ClrAllLists. Get started on the first project.
  • Feb. 16-20. The derivative Do the problems on proportionality, if you have not done so already: 13, 14, 17, 19 from section 1.9 and 39, 40 on p. 72. Finish up the problems from 2.1 and go on to read 2.2 and do problems 1-5, 7-8, 12-13, 16, 18, 20, 25-26, 29abc, 31. Read 2.3 and do problems 1, 2, 3, 5, 6, 7, 9.
  • Feb. 23-27. The derivative and applications Monday is the last day to drop a course with a grade of W, no questions asked. Finish up 2.3 by doing problems 1-3, 5-7, 9, 12, 19, 21; go on to the economics applications of section 2.5. Do problems 1, 2, 4, 5-7, 9. We will come back to section 2.4 later.
  • Mar. 1-5. Applications and formulas Once you have finished with sections 2.5 and 2.6, read section 3.1 and do problems 1-9, 14, 17-20, 25, 27, 31-33, 41. Go on to section 3.2 and do problems 1-3, 6, 10, 11, 13, 16-18, 21, 36. The calculator handout tells you how to combine the graph of a function and the graph of its derivative on a single screen. But remember that formulas are not everything; I'll still expect you to approximate derivatives numerically from tables or graphs, and to sketch graphs even when no formulas are given.
  • March 8-12. Spring Break Enjoy yourselves!
  • March 15-19. Derivative rules and formulas We resume with the chain rule (section 3.3; do problems 1-11 odd, 15-21 odd, 22, 27, 34, 35) and the product and quotient rules (section 3.4; do problems 1, 3, 4, 6-8, 12, 15, 17, 22-23, 25, 31, 35, 38).
  • March 22-26. Second exam, product and quotient rules, concavity, local max and min Be sure to do the problems from 3.4 mentioned above. We'll then do section 2.4 (problems 1, 2, 5, 13, 14, 18, 24) as a prelude to chapter 4. In section 4.1 do problems 1, 3, 4, 5, 9, 13, 26.
  • March 29-April 2. Global max and min, beginning of integration In section 4.2 do problems 20 and 21; in section 4.3 do 7, 9, 11, 15, 16, 17, 19, 23, 24. We will return to applications if time permits, possibly 4.4, which just involves using formulas to do what you did graphically already, and 4.5, which we have touched on, but not really examined closely. But to get to the end, we need to move on, so pick up with 5.1 and do 1, 2, 3, 4, 7, 8, 10, 11, 16, 17.
  • April 5-9. The definite integral We will look at left and right sums using the RSUM program, and how these are related to under and over estimates of integrals. We will interpret these in terms of signed areas. Read section 5.2 and do problems 1-8, 11, 17, 18, 22, 24. Then go on to section 5.3, which has very little that is really new, and do problems 1-3, 5-8, 15, 17, 21, 22, 29, 30. Omit the material on area between two curves. In section 5.4 the calculations are more of the same, but the applications are brought into the spotlight. Omit the material on drug bioavailability. Do problems 1, 3-7, 9, 11, 13, 24. After getting accustomed to using RSUM, we will learn about the built-in calculator methods of integration.
  • April 12-16. Built-in integrators, Fundamental Theorem Read section 5.5 and do problems 1-5, 7, 9-12. Go back and take a second look at the problems from 5.4 and see if they don't come easier now. Feel free to use the built-in integration methods on your calculator. We are skipping chapter 6 and going on to section 7.1. Here you need to do lots of problems for practice: 4, 8, 9, 11, 13, 21, 23, 24, 33, 35, 39, 40-43, 57 for starters, but anything not involving sine or cosine is good. Get to work on your second project.
  • April 19-23. Fundamental Theorem (cont.) and third exam Read section 7.3 and do problems 1, 5, 6, 9, 12, 13, 17, 24. Continue to work on the project and see below for the coverage of the exam.
  • April 26-28. Using antiderivatives with the Fundamental Theorem We will make the connection between definite and indefinite integrals and how to exploit this to make efficient and exact computation of integrals. Finish up the problems of section 7.3, read section 7.4 and do problems xxx. On the last day of class you will receive a printout of all your scores to date, and an estimated grade going into the final.

  • Exams and Projects
  • FIRST EXAM: Wednesday, February 11. This covers sections 1.1 through 1.7 of the text, but not curve fitting (regression). To study for it, be sure you can do the three quizzes perfectly, review the homework of sections 1.5 through 1.7, and for extra practice do problems from p. 69 on in your text: 1, 2, 4-6, 11-15, 17, 23, 34, 44.
  • FIRST PROJECT: Due in class Friday, February 20. The actual project assignment will be distributed on Monday, Feb. 9, but try to form your groups of 3-4 by then. The project will involve data and graphs, regression, (semi) log-plots and loglog-plots, why these are useful, and algebraic conversions from ln(y) = m x + b and ln(y) = m ln(x) + b to y = c e^(mx) and y =a x^m respectively. They will be graded over the weekend of Feb. 21-22 and returned on Feb. 23 in time for you to make your final decision to keep or drop this course. If a group decides that they do not need to see this feedback, the report may be turned in on Feb. 23, but be aware that the grading may then be very slow.
  • SECOND EXAM: Monday, March 22. The exam covers sections 2.1, 2.2, 2.3, 2.5 (omit 2.4 for now), 3.1, 3.2, 3.3. Good review problems for chapter 2 are found on pp. 124-127; I recommend problems 3, 4b, 7-11, 13-14, 16, 20-22, 24, 26, 29, 31. For chapter 3 see pp. 157-158; I recommend problems 1-3, 9, 11-13, 15, 25, 27, 37, 40, 41 (write R=pq in terms of p only, and use nDeriv), 53.
  • SECOND PROJECT: Monday, April 26 is the final deadline, but you will get 5 bonus points for getting it to me on Wednesday, April 21. Help will be available through Thursday, April 22; after that you will be on your own. Problems 1 and 2 on pages 217-218, problem 1 on page 250, and problem 1 on page 275 are acceptable alternatives for the second project.
  • THIRD EXAM: Friday, April 23. The exam will pick up from where we left off with exam two: sections 3.4 (product and quotient rules for derivative formulas), 2.4 (concavity), 4.1, 4.2 (vase problems), 4.3, 5.1-5.5 (VERY IMPORTANT!), 7.1. There is also a sheet on preparation for the exam through this link, and in the envelope hanging by my office door.
  • FINAL EXAM: Saturday, May 1 (9 to noon) In addition to the content of the first three exams we will have sections 3.4, 7.3 and 7.4 on the final exam. The form of most of the questions will closely follow that of the quizzes and exams to date. Previous review guides will also be helpful (see above), but study the exams and quizzes first. I will be available for help by email, appointment late Thursday afternoon and all day Friday, and from 8 to 10 pm in the SCR of Preston Residential College on a first come first serve basis. Graded quizzes (#9) will be available late this afternoon, and graded projects will be available as I complete them; I hope to have them all done by Saturday morning, but I may not be able to have more than the "early" ones done by then since I do have to write the final on Friday! Thanks for your patience, but, like y'all, I am up to my eyeballs in work!

    • Last modified: April 29, 2004