Math 102

Spring 2009

Prof. Donnay

Class Materials and Homework Assignments

* indicates a more challenging problem.

 Class# Date Lecture Materials Textbook Reference HW: Practice HW: Hand In. Due Date 1 W 1/20 Introduction. Review of big ideas of calculus. F 1/23 F 1/23 2 F 1/22 Go over Review Sheet. Substitution Rule, worksheet. S.5.5 Any other problems  #1 – 27. S.5.5#2, 3, 4, 5, 6, 9, 12, 18, 19 Substitution worksheet. (will go over this with your group) M 1/25 Substition rule with endpoints; symmetry S. 5.5 Any problems #33-50. S.5.5 # 36, 37, 38, 39, 41*, 42* (symmetry) M 2/2 W 1/27 Area under curve, between curves; slides. Riemann sum worksht Any problems #1-15. S. 6.1 #1, 5, 6, 7, 8, 13. Extra: Solve 5 – x2 = x. M 2/2 F 1/29 Net Change Theorem S5.4 S. 5. 1# 5 (do all parts with n=3 intervals   not with n=6) S. 5.4 #47, 49, 40, 60, 64 (use n=4 intervals) M 2/2 Mathematica 2A Mathematica 2B Must have printout signed by Mathematica TA: Mon 7-9pm or Tue 7 – 8 pm W 2/4 W 2/11 M 2/2 Volume, surfaces of revolution. Worksheet. S. 6.2 S. 6.2. # 2, 3, 4, 5, 7, 8, 49* Do practice quiz3 for Wed and then check answers. M 2/9 W 2/4 Volume by disks. Surface of revolution via Mathematica. S. 6.3 S. 6.3 #2, 3, 5, 8, 29 S. 6.1 #19 (integrate with dy), 21 M 2/9 F 2/6 S. 6.5 #1, 4, 7, 9, 13, 16, 17. For 17: graph T(t). What is the period of sin(Pi *t/12)? M 2/9 M 2/9 Exponential Function, Differentiation Do practice quiz4 for Wed and assess it with AnswerKey. Hand in on Wed. S. 7.2 #3, 4, 7, 8, 9, 11, 13, 33, 35, 37, 39, 65 W 2/11       M 2/16 Mathematica Assignments W 2/18 W 3/4 ?? W 2/11 Exponential Function: Integration Inverse functions, logarithms worksheet. S. 7.2 S. 7.1, S. 7. 3 S.7.1 #3, 5, 6, 23, S. 7.3 #3,  9, 15, 17, 25 S. 7.2 # 73, 74, 75, 76, 81 S.7.1 #13, 14, 21, 24 S. 7.3 # 4, 10, 14, 26, M 2/16 F 2/13 Derivative of Ln wksheet, Integration of Logarithm. S. 7.4 S. 7.4 #2, 4, 7, 8, 27, 69, 71, 73, 75, 78 M 2/16 M 2/15 Applications of Exponential and Logarithm. Population growth, radioactive decay. Worksheet 1, 2, Mathematica Calculations. S. 7. 5. #3, 5, Please try to do these for W 1/17 (although wonÕt hand in till next week) M 2/23 On Wed 2/18, turn in a copy of your score sheet for all the quizzes including Quiz 5. W 2/18. W 2/17 Exponential growth from perspective of differential equations S. 7.5 #1, 4, 6, 8, 10 S. 7.5# 2, 9 , 11  Read Rwanda article Do associated population problems. F 2/19 Modeling via Differential Equations (worksheet) S. 7.5 Instructions for Midterm prep Redo Newspaper problem: article, instructions S. 7.5#10, 13 T(t) = temp of turkey = 75 + Ce^(-kt). Use the info given to determine C and k. Then solve the question. M 2/23 Mathematica Assignment 2D will be due Wed March 4; no lab due this coming week due to exam. M 2/23 Using A + Bsin(kx) in modeling. Inverse Trig Functions S. 7.6 What Makes a Good Answer: do this worksheet for Wed. Bring Index card with your formulas on one side to class on Friday for me to sign. You  can use this on test. W 2/25 S.7.6# 2, 3, 11, 12, 13, 17, 23, 25, 43, 45, 59, 61, 62, 63 F 3/6 – extension now due M 3/16 F  3/6 F 2/27

 18 M 3/02 S. 7.6 S. 7.6# 49, 50*, 71 (independent learning) Finish your 1st connections paragraph; post on Blackboard in the Discussion Board. M 3/16 19 W 3/04 Integration by Parts Integral Tables worksheet (do for FridayÕs class). Use the Integral Tables from the back of the textbook. Please complete the midterm feedback survey at: S. 8.1 #1, 3, 4, 11 M 3/16 20 F 3/06 Using Integral Tables and Mathematica. S. 8. 6 BREAK 21 M 3/16 Improper Integrals Answer Key to worksheet S. 8.8 Using Integral Tables     Integration by Parts Mathematica 2E (due Friday; everything else due Monday)   S. 8.6 1, 2, 3, 7, 8, 9 - for each of these also calculate the integral using Mathematica. Hand in a print out of your results. S. 8.1 #33, 37, 48 S. 8.8 #3, 5, 9, 21 F 3/20 M 3/23 22 W 3/18 S. 8.8 S.8.8 #11, 13, 27, 28, 29, 33 M 3/23 23 F 3/20 Limits; LÕHopitals Rule S. 7.8 24 M 3/23 S. 8.7 Mathematica 2F (due Friday) S. 7.8 #5, 7, 9, 11, 15, 17, 19, 21, 29 S. 5.1 # 6ab, 8.7 #1ab F 3/27 (M 3/30) Change W 4/1 25 W 3/25 Answer Key to Mathematica Integrals S. 8.7 S. 8.7 #3 W 4/1 26 F 3/27 Numerical Integration via Mathematica S. 8.7 Note: the hw for this week will all be due on Wed. rather than on Monday. The Numerical Integration is part of the regular HW assignment. There is no separate Mathematica assignment this week. W 4/1 27 M 3/30 Arc Length S. 9.1 S. 9.1 #1, 3, 7, 37 (Use command NIntegrate or use SimpsonÕs Method to evaluate. You need to determine the a and b of the integral and the formula for the integrand). M 4/6 28 W 4/1 Differential Equations: Separation of variables. Solve dy/dx = y3 x2 for Friday class. S. 10.3 This topic will be on midterm. It is the last topic for the midterm. S. 10.3 #2, 4, 9 (factor the rhs), 11, 14, 39*. M 4/6 29 F 4/3 Application of separable differential equations to biology. S. 10.3     S. 12.1 Do the problems on this Glucose handout – related to #39. Do handout before you try #39. 30 M 4/6 Sequences; writing using formulas. Examples. S. 12.1 S. 12.1 #3, 4, 5, 7, 9, 10, 11, 13, 17, 18 (factor out n3 and cancel), 20, 21, 22, 27, 28, 43, 55, 60, 61, 62 (let f(x) = (2x-3)/(3x+4). Determine if f(x) is increasing), 66, M 4/20 31 W 4/8 32 F 4/10 Test review Instructions for the exam. Midterm 2 Computer Component. You will find the Mathematica file on Numerical Integration useful for the computer test. You are free to cut and paste commands from this file while you work on the exam. 33 M 4/13 S. 12.2 S. 12. 2 #3, 6. For these problems find the first ten partial sums: s1,s2, s3, ..., s10. Try to predict whether the series will converge or diverge. You can use Mathematica with the summation command. Make a graph of the values of sn as a function of n; i.e. plot the points (n, sn). M 4/20 34 Geometric Series; formula and convergence. Mathematica to calculate sums. S. 12. 2 S. 12. 2#11, 12, 13, 15, 17, 18 Each of these is a geometric series. Write out the first few terms of the series by hand. Determine the ÒaÓ and the ÒrÓ.   Write your second Òconnections paragraphÓ and post on Blackboard. M 4/20 35 Bounded or unbounded sequence of partial sums. If a­k does not go to zero, the series diverges. S. 12.3 S. 12.2 #21, 22, 23, 25, 26, 27 S. 12.3 # 1, 2, 16. M 4/20 36 M 4/20 Integral Test, P-Test S. 12.3 S. 12.3# Justify your answers. 3, 4, 6 (do substitution to evaluate integral), 7 (what is f(x) here? ), 8 (does ak -> 0?), 10 (use limit laws), 11, 12, 15 F 4/24   M 4/28 37 W 4/22 Power Series; Approximations to Functions S. 12.11 S. 12.11. #1a (Make the graph using Mathematica), 2a,  Redo problem 1a for f(x) = cos(x) but centered at a = x0 =Pi/2 and up to degree 7. M 4/28 38 F 4/24 More Taylor Series and Power Series. S. 12. 2 #47 (geometric series), 48, 49, 50 For Monday, do as much of the Taylor Polyn worksheet as you can. Also: determine the Taylor Polynomials for f(x) = sin(x) with x0=0. Take n = 1, 3, 5, 7, 9 and try to find the formula for general n.   Most people did not notice that S. 12. 1 was part of last weekÕs hw. So please redo that section and hand it in. If you already did it, just hand in your answers again. S. 12.1 #3, 4, 5, 7, 9, 10, 11, 13, 17, 18 (factor out n3 and cancel), 20, 21, 22, 27, 28, 43, 55, 60, 61, 62 (let f(x) = (2x-3)/(3x+4). Determine if f(x) is increasing), 66, M 4/28 39 M 4/27 S. 12.8 40 W 4/29 Ratio Test. S. 12. 6 For Friday do problems on Ratio Test from the last page of the Review sheet for Final Also S. 12. 8 # 3, 5, 10, 5, 19 (only find radius of convergence for these series. Express your answer as an interval). Do a few from each section for Friday so you can ask me questions about them. I will post an answer key later.   Answer Key to these problems. 41 F 5/1 Further discussion of ratio test. Review Questions for Final. These questions are linked to the List of Topics for Final handout.