MATH 221 Homework

Homework Assignments

12/10
  1. Come to class tomorrow with a list of topics you would like to review for the final exam. We will start by brainstorming in-class review topics, based on your lists.
  2. Exercises 8.8: 1, 2, 3, 4, 6, 7, 9, 12, 13, 14, 17.
12/09
  1. Read Section 8.8 (Probability, Mean, and Median) for discussion in class tomorrow.
  2. Exercises 8.7: 1, 3, 4, 9, 10, 13, 14, 16, 17, 20, 21, 27, 28, 29.

12/05
  1. Read Section 8.7 (Distribution Functions) for discussion in class on Monday.
  2. Hand in Exercises 17.1: 15, 41; Exercises 17.2: 30. Due 12/10.
  3. Complete your project and hand it in next Thursday. Due 12/12.
12/04
  1. Read Section 17.2 for discussion tomorrow. (You should find some of this material familiar after today’s class.)
  2. Section 17.2: 1, 4, 6, 8, 9, 12, 13, 14, 17, 19, 22, 23, 25, 27, 29, 30, 31, 33, 35, 36, 44
12/03
  1. Section 8.3: 13, 15, 16, 19, 21, 23, 31, 39, 43, 45.
12/02
  1. Reread Section 8.3 for discussion tomorrow. You should try to get to the end of the section this time, although we may not complete our discussion of it in one day.
  2. Section 17.1: 1, 5, 7, 11, 15, 21, 23, 39, 41.
  3. Section 8.3: 1, 3, 5, 7, 9, 10, 13, 15, 16, 19.
  4. (Reminder) Hand in Section 4.8: 17; Your 1-page project progress report. Due 12/03.

11/26
  1. Read Section 8.3 (Area and Arc Length in Polar Coordinates) for discussion after Thanksgiving. You can omit the book’s discussion of area, and concentrate on the definition of a polar curve and on arc length.
  2. Hand in Section 4.8: 17; Your 1-page project progress report. Due 12/03.
  3. Have a good break!
11/25
  1. Read Section 17.1 (Parametrized Curves) as far as the boxed equation “Parametric Equation of a Line in Vector Form” for discussion in class on Tuesday. This will give you a review of vector notation and how it is used to describe parametric curves (albeit in 3 dimensions).
  2. Section 4.8: 1, 5, 9, 11, 17, 19, 23, 27, 28, 33, 35, 37, 39, 45, 46, 47, 50, 61, 66, 67.

11/21
  1. Read Section 4.8 (Parametric Equations) for discussion in class on Monday.
  2. Use class time today to work on your projects in your project groups. (This could also be a convenient time to discuss the project with, and gain insight from, other groups.)
  3. Hand in Section 11.7: 29, 30; Section 11.8: 32. Due 11/26.
11/20
  1. Section 11.9: 6-10, 14, 19, 20, 23, 24, 25.
  2. Continue working on your projects.
11/19
  1. Re-read Section 11.9 (Analyzing the Phase Plane).
  2. Continue working on your projects.
11/18
  1. Read Section 11.9 (Analyzing the Phase Plane) for discussion in class tomorrow.
  2. Begin work on your second project. (You can find a description of the project on the Additional Notes and Files page.) A progress report is Due Tuesday, December 3; the completed project is due on the last class meeting day: Thursday, December 12. Due 12/12.
  3. Section 11.8: 1, 3, 7, 9, 11, 13, 14, 16-20, 28-32.

11/14
  1. Read Section 11.8 (Systems of Differential Equations) for discussion in class on Monday.
  2. Section 11.7: 1, 3, 7, 9, 19, 23, 25, 27, 29, 30, 31, 35, 39, 40.
  3. Your second project will be to complete Projects 2 and 3 from Chapter 11 in the textbook (pages 661-663). I will provide more details next week, but you can start thinking about Project 2 (SARS Predictions for Hong Kong) now, if you wish. (You should wait on Project 3 until we have covered the relevant section of the book on Monday.) I will assume you are working in the same teams as you did for your first project unless I hear otherwise from you.
  4. Hand in Section 11.1: 8; Section 11.4: 28, 48. Due 11/19.
11/13
  1. Read Section 11.7 (The Logistic Model) for discussion in class tomorrow.
  2. Section 11.5: 1, 3, 5, 7, 9, 11, 18, 21, 25, 27, 28.
11/12
  1. Read Section 11.5 (Growth and Decay) for discussion in class on Wednesday.
  2. Section 11.4: 1(b)(c)(g)(j)(l), 5, 13, 23, 25, 28, 29, 31, 32, 41, 48, 59, 60, 61, 62.
11/11
  1. Read Section 11.4 (Separation of Variables) For discussion in class tomorrow.
  2. Section 11.1: 3, 5, 8, 15, 17, 19, 21, 23, 25, 29, 31, 35, 37.
  3. Section 11.2: 3, 4, 9. (You may find it helpful to look at Section 11.2 for these questions, but see first if you can answer them just thinking about the example we saw in class today. There is also a link to a Desmos slope field generator on the “Useful Links” page, in case you find it useful.)

11/07
  1. Read Section 11.1 (What is a Differential Equation?) For discussion in class on Monday.
  2. Section 7.4: 1, 3, 5, 7, 8, 10, 12, 14, 15, 29, 31, 37, 39, 41, 47, 49, 53.
  3. Hand in Section 7.1: 134; Section 7.2: 78; Section 7.4: 24 (including your anti-derivative computation). Due 11/12.
  4. Extra credit Use the method of partial fractions to compute {\displaystyle \int \frac{1}{x^4 + 1}\,dx}. I will need to see full computations, not just the answer obtained from a calculator or the Internet. A correct solution will earn an amount of extra credit equal to one regular homework.
    (Hint: x^4 + 1 = (x^2 + \sqrt{2}x + 1)(x^2 - \sqrt{2}x + 1).) Due 11/12.
11/06
  1. Re-read Section 7.4 (Algebraic Identities and Trigonometric Substitutions) for discussion in class tomorrow. This time, you should also read the section on the Method of Partial Fractions carefully.
  2. Section 7.4: 20, 21, 24 (and also try to compute the anti-derivatives), 55, 57, 61, 63.
11/05
  1. Read Section 7.4 (Algebraic Identities and Trigonometric Substitioutions) for discussion in class tomorrow. (Concentrate on the section on Trigonometric Substitutions, which begins on page 380.)
  2. Section 7.2: 1, 2, 7, 9, 13, 15, 19, 21, 23, 29, 33, 37, 41, 43, 47, 52, 53, 54, 55, 57, 59, 61, 63, 65, 66, 69, 73, 75, 77, 78, 79.
11/04
  1. Read Section 7.2 (Integration by Parts) for discussion in class tomorrow.
  2. Section 7.1: 1, 9, 15, 17, 19, 27, 35, 41, 47, 53, 55, 57, 61, 67, 69, 70, 73, 79, 81, 85, 91, 95, 97, 105, 115, 117, 121, 125, 129, 135, 139.

10/31
  1. Read Section 7.1 (Integration by Substitution) for discussion in class on Monday.
  2. Section 6.4: 1, 3, 9, 17, 25, 27, 39, 43, 50, 52.
  3. Hand in Exercises 6.1: 30; Exercises 6.2: 74; Exercises 6.3: 34. Due 11/05.
10/30
  1. Read Section 6.4 (Second Fundamental Theorem of Calculus) for discussion in class tomorrow.
  2. Section 6.3: 1, 5, 11, 17, 19, 21, 27, 28, 30, 31, 33, 34, 37, 39, 42, 43, 49.
10/29
  1. Read Section 6.3 (Differential Equations and Motion) for discussion in class tomorrow.
  2. Catch up on any of the assigned problems from Seections 6.1 and 6.2 that you have not yet completed.
10/28
  1. (Re)read Sections 6.1 and 6.2 for discussion in class tomorrow.

10/23
  1. Prepare questions you would like the class to discuss tomorrow in preparation for Monday’s midterm.
  2. Section 6.2: 1, 7, 11, 17, 23, 25, 39, 49, 51, 53, 52, 55, 61, 63, 67, 71, 74, 77, 81, 82, 85, 87, 89, 91, 95.
10/22
  1. Read Section 6.2 (Constructing Anti-derivatives Analytically) for discussion in class on Wednesday.
  2. Section 6.1: 1, 3, 11, 13, 15, 19, 21, 29, 30, 31, 33. 35, 36.
10/21
  1. Read Section 6.1 (Anti-derivatives Graphically and Numerically) for discussion in class on Tuesday.
  2. Section 5.3: 1, 3, 5, 7, 8, 9, 11, 15, 18, 19, 21, 24, 27, 31, 37, 42, 49-51.
  3. Begin reviewing the material we have covered so far this semester, in preparation for the midterm exam, which will be given in class one week from today, 10/28.

10/17
  1. Section 4.3: 1, 7, 8, 10, 17, 21, 28, 32, 33, 35, 38, 41, 42, 45, 50, 55, 56,
  2. Read Section 5.3 (The Fundamental Theorem and Interpretations) for discussion in class on Monday.
  3. Hand in Project 1. Due 10/21.
  4. Hand in Exercises 3.10: 13; Exercises 4.3: 41. Due 10/22.
10/16
  1. Section 4.2: 1, 5, 6, 14, 18, 22, 26, 28, 30, 31, 33, 34, 37, 40, 44, 45, 46, 48, 49, 50, 59, 60, 62.
  2. Read Section 4.3 (Optimization and Modeling) for discussion in class on Thursday.
10/15
  1. Section 3.10: 1, 3, 5, 11, 13 (don’t just give the answer; use the Mean Value Theorem to justify it); 19, 23, 30, 31, 33, 37, 39, 41.
  2. Read Section 4.2 (Optimization) for discussion in class on Wednesday.
10/14
  1. Section 3.9: 1, 4, 5, 8, 10, 12, 19, 21, 22, 23, 25, 38, 43, 45, 47, 48.
  2. Read Section 3.10 (Theorems about Differentiable Functions) for discussion in class on Tuesday.
  3. Keep working on your projects, which are ue one week from today. Due 10/21.

10/10
  1. Section 3.8: 1, 3, 5, 9, 15, 17, 18, 19, 20, 29, 33.
  2. Read Section 3.9 (Linear Approximation and the Derivative) for discussion in class on Monday.
  3. Hand in Your 1-page project progess report. Due 10/10.
  4. Hand in Exercises 3.6: 46, 58; Exercises 3.8: 20; Exercises 1 and 6 from the Euler’s Formula (Exponential and Trigonometric Functions) worksheet. Due 10/15.
10/09
  1. Section 3.6: 1, 5, 7, 13, 19, 23, 33, 37, 39, 41, 43, 44, 45, 46, 49, 52, 53, 57, 58, 59, 67, 70, 72, 75, 81.
  2. Section 4.1: 35, 37, 41, 43, 47, 49. Again, let me know if you would like to spend time in class on some problems like this.
  3. Read Section 3.8 (Hyperbolic Functions) for discussion in class on Thursday.
10/08
  1. Section 3.5: 1, 3, 7, 11, 17, 29, 31, 39, 43, 49, 51, 53, 54, 57, 59, 60, 62, 63, 65, 68, 69, 73.
  2. Section 4.1: 1, 3, 5, 7, 9, 11, 27, 29. (The definition of critical point is on page 187; the definition of inflection point is on page 190.) Let me know if you would like to spend time in class on some problems like this.
  3. Read Section 3.6 (The Chain Rule and Inverse Functions) for discussion in class tomorrow.
10/07
  1. Section 3.4: 3, 5, 21, 23, 27, 30, 43, 53, 55, 57, 61, 66, 68, 69, 71, 75, 77, 78, 79-82, 86, 89, 91, 97, 100.
  2. Read Section 3.5 (The Trigonometric Functions) for discussion in class on Monday.
  3. Continue working on your project with your group. Remember, your 1-week progress report is due on Thursday of this week. Due 10/10.

10/03
  1. Section 3.3: 1, 7, 11, 19, 25, 29, 32, 34, 35, 36, 45, 46, 51, 55, 57, 59, 60, 66, 67, 71.
  2. Read Section 3.4 (The Chain Rule) for discussion in class on Monday.
  3. Read the part of Section 1.3 on Inverse Functions (pages 23-25). We will use this material when we study Section 3.6, so let me know by Monday if you would like some further review of inverse functions in class. Due 10/07.
  4. Hand in Exercises 3.2: 46; Exercises 3.3: 60. Due 10/08.
10/02
  1. Section 3.2: 1, 9, 11, 14, 19, 21, 23, 24, 27, 29, 31, 33, 39, 41, 43, 45, 46, 48.
  2. Read Section 3.3 (The Product and Quotient Rules) for discussion in class tomorrow.
10/01
  1. Section 3.1: 1, 3, 4, 5, 9, 15, 19, 23, 33, 35, 41, 42, 55, 67, 68, 69, 73.
  2. Read Section 3.2 (The Exponential Function) for discussion in class tomorrow.
  3. If you haven’t done so already, send me the list of people in your project group.
09/30
  1. Section 2.5: 1, 2, 3, 5, 14, 16, 19, 23, 25, 29, 30, 32, 33, 35, 37, 38.
  2. Section 2.6: 3, 4, 6, 7, 10, 13, 16, 23-27.
  3. Read Section 3.1 (Powers and Polynomials) for discussion in class tomorrow.
  4. Send me the list of people in your project group. (One e-mail per group would be sufficient.)

09/26
  1. Section 2.4: 8, 11, 13, 19, 22, 25, 29, 34, 40, 41. (You may find it helpful to read some of the examples in Section 2.4 as you do these problems; it is not necessary for you to do so if you can do the problems anyway.)
  2. Read Sections 2.5 (The Second Derivative) and 2.6 (Differentiability) for discussion in class on Monday. Send me a question on the reading by Sunday evening. Due 09/29.
  3. Hand in Exercises 2.3: 28, 44; Exercises 2.4: 22. Due 10/01.
09/25
  1. Section 2.3: 3, 7, 11, 15, 19, 23, 28, 31, 35, 40, 43, 44, 45.
  2. Read Section 2.4 (Interpretations of the Derivative) for discussion in class tomorrow.
09/24
  1. Section 2.2: 1, 3, 5, 9, 10, 11, 13, 14, 17, 19, 21, 23, 30, 31, 33, 37, 39, 47, 49, 51, 52, 54, 55, 56.
  2. Read Section 2.3 (The Derivative Function) for discussion in class tomorrow.
  3. I will ask you next week to send me the members of your first project group. Don’t send me names yet, but you could start thinking about who you would like to work with. I would like groups of 3 whenever possible; I will accept groups of 2 if necessary. (But if there are lots of groups of 2, I reserve the right to re-form them into groups of 3.)
09/23
  1. Section 2.1: 1, 3, 4, 5, 7, 9, 15, 16, 17, 19, 20, 24, 25, 27, 29, 30, 33, 34, 35, 37.
  2. Read Section 2.2 (The Derivative at a Point) for discussion in class tomorrow.

09/19
  1. Catch up on all homework from Chapter 1.
  2. Read Section 2.1 (How Do We Measure Speed?) for discussion in class on Monday.
  3. Hand in Exercises 1.8: 52, 84. Due 09/24.
09/18
  1. Exercises and Problems for Section 1.8: 1, 2, 3, 5, 9, 11, 13, 16, 18, 19, 23, 27, 35, 36, 47, 49, 52, 73, 75, 84, 87, 89, 91, 93, 98, 101.
09/17
  1. No new reading or problems tonight, but you can re-read parts of Sections 1.7 and 1.8 in light of today’s discussion if you like, and see if you have a deeper understanding of them (or any new questions) as a result of that discussion.
09/16
  1. Read Section 1.8 (Limits). You do not have to send me a question, but feel free to do so. You may find this to be a challenging section, if you have never seen the formal definition of limit before. Don’t be concerned: we will spend a few days discussing the concept.
  2. Exercises and Problems for Section 1.7: 1, 2, 5, 6, 16, 17, 18, 19, 25, 27, 31, 32, 35, 37, 39, 40, 42, 45, 46, 47.

09/12
  1. Read Section 1.7 (Introduction to Continuity). Send me a question by Sunday evening. Due 09/15.
  2. Exercises and Problems for Section 5.4: 32, 37, 38, 43, 46, 65, 69, 73, 77, 78.
  3. Exercises and Problems for Section 8.1: 1 through 4, 13, 15, 18, 19, 21, 25, 28, 29, 35, 37, 40, 41. (Note In any of these problems, if you are asked to evaluate an integral of a polynomial, try to do so exactly with the short cut we learned in class; for the integral of any other function, evaluate it numerically with Desmos or some other technology, and give an estimate for the size of your error.)
  4. Hand in Section 8.1: 2, 4, 28. Due 09/17.
09/11
  1. Read Section 8.1 (Areas and Volumes). You do not have to send me a question, but feel free to do so if there is something you would particularly like to discuss in class.
  2. Exercises and Problems for Section 5.4: 1 through 6, 10, 11, 15, 21, 23, 24, 25 (find an approximation to the integral, using 35 subintervals).
09/10
  1. Read Section 5.4 (Theorems about Definite Integrals). You do not have to send me a question, but feel free to do so if there is something you would particularly like to discuss in class.
  2. Exercises and Problems for Section 5.2: 1, 4, 11, 13, 14, 17, 23 (find an approximation using 4 subintervals), 29, 31, 35, 37, 41, 46, 47, 51, 53, 54, 55.
09/09
  1. Read Section 5.2 (The Definite Integral). This is a particularly important section, and there is a lot of notation to work through, so send me a question on the reading when you finish it this evening. Due 09/09.
  2. Exercises and Problems for Section 5.1: 9, 11, 13, 14, 15, 25, 26, 30, 31.

09/05
  1. (Re)read the start of Section 1.1 in the textbook (Functions and Change), up to and including “Difference Quotients and Delta Notation” on page 5.
  2. Read Section 5.1 in the textbook (How Do We Measure Distance Travelled?, starting on page 272).
  3. Exercises and Problems for Section 5.1: 1 through 8.
  4. Hand in: “Calculus with Technology” problem 2 (volume of a cone); Section 5.1: 2, 7. Due 09/10.
    When writing up homework solutions, do not just give me equations. You should try to write your mathematics as the textbook does:

    • use complete English sentences, with equations as clauses in those sentences as appropriate;
    • carefully define any variable you introduce in your solution;
    • state your conclusion clearly and accurately.
09/04
  1. If you have not done so already, finish your list of topics from Chapter 1 that you would like to review in class, and e-mail it to me. Due 09/05.
  2. Our textbook defines “Function” on page 2. What, if anything, is the difference between the book’s definition and the one I gave in class?
  3. Look at the two problems on the “Calculus with Technology” handout, and the six problems on the “Meta-problem Sheet”. You can try to solve some of them if you like, but whether you actually solve them or not, try to answer the meta-problem: what do all of these problems have in common?
09/03
  1. Read through the course syllabus and let me know if you have any remaining (or new) questions.
  2. Review the two proofs without words that we covered in class today, and make sure you are convinced by them. (Be prepared to ask about them in class tomorrow, if not.)
  3. Study the remaining two proofs without words (the two for sums of cubes), and be ready to discuss them in class tomorrow. You can find the handout on the “Additional Notes and Files” page on this website.
  4. Look through Chapter 1 of the textbook (A Library of Functions) quickly, and make a note of anything that doesn’t seem familiar to you. Send me an e-mail with a list of topics that you think we need to review in class. Due 09/05.


Kevin Mcleod

08/31/2019