Calculus - Mathematics 100

Calculus – Mathematics 100
Brown University – Fall, 2010
Syllabus and Homework Assignments

Homework is due the next class unless otherwise noted. Late homework will not be accepted. (There are no exceptions to this rule.)

Click here to download a Math 100 Review Sheet.

Note to Students
You may freely download Chapters 15 and 16 on Differential Equations and the solutions to the odd problems by clicking on the following links:
Chapters 15 and 16 (Differential Equations) — Ch. 15 Solutions — Ch. 16 Solutions

[1] Wednesday, September 1
Chapters 2 & 3. Review of differential calculus
Important Note: This first homework set reviews material that should be familiar to you. There are a lot of problems, but they cover only material from Math 90 or your high school AP class. If it takes you more than 2 hours to do these problems,then you need to spend time reading and reviewing the relevant sections of the book. [A standard rule of thumb is that a typical college class requires two hours of work outside of class for each hour of class. Math classes often require more.]
Homework (due next class):
Do §2.2 # 38, 39, 86
Do §3.1 # 17, 27–30
Do §3.2 # 18, 30, 47(a,b)
Do §3.3 # 7
Do §3.4 # 8, 17
Do §3.5 # 43, 55
Read for next time: §§ 3.7, 3.8. Also review differential calculus, especially Sections 2.2 and 3.1–3.5.
Homework Solutions

[2] Friday, September 3
   § 3.7. Derivatives of inverse functions, logarithms
   § 3.8. Inverse trigonometric functions
Homework:
   (Homework is due Wednesday September 8 because of Labor Day.)
Do § 3.7 # 5, 8, 9, 21
Do § 3.8 # 1, 5, 14, 15, 23, 42
Read for next time: § 4.6
Homework Solutions

Monday, September 6 — Labor Day — No Class

[3] Wednesday, September 8
§ 4.6. L'Hopitals Rule
Homework (due next class):
Do § 4.6 # 7, 13, 15, 16, 45, 49, 55, 62
Read for next time: §§ 4.8, 5.5
Homework Solutions

[4] Friday, September 10
   § 4.8. Antiderivatives and indefinite integrals
   § 5.5. Techniques of integration — substitution
Homework (due next class):
   This material should be review for you. If you're not completely comfortable with it, you should practice by doing a lot of the odd numbered problems on your own and checking your answers in the back of the book.
Do § 4.8 # 27, 39, 45, 51, 83, 89
Do § 5.5 # 7, 10, 15, 21, 23, 37, 43
Read for next time: §§ 5.2, 5.3, 5.4
Homework Solutions

[5] Monday, September 13
   §§ 5.2, 5.3. The definite integral
   § 5.4. The fundamental theorem of calculus
Homework (due next class):
   This material should be review for you. If you're not completely comfortable with it, you should practice by doing a lot of the odd numbered problems on your own and checking your answers in the back of the book.
Do § 5.3 # 3, 9, 17, 19
Do § 5.4 # 7, 10, 23, 25, 27, 45, 58
   Optional Fun Problems: § 5.3 # 82 (answer is not 40 MPH), § 5.4 # 74
Read for next time: § 6.1
Homework Solutions

[6] Wednesday, September 15
§ 6.1 Volumes by slicing and volumes of revolution
Homework (due next class):
Do § 6.1 # 1, 8, 17, 23, 28, 47
Read for next time: §§ 6.3
Homework Solutions

[7] Friday, September 17
§ 6.3. Lengths of curves
Homework (due next class):
Do § 6.3 # 1, 3, 7, 13, 29
Read for next time: § 6.4
Homework Solutions

[8] Monday, September 20
§ 6.4. Areas of surfaces of revolution
Homework (due next class):
Do § 6.4 # 1(a), 5(a), 13, 15, 28
Read for next time: § 6.5
Homework Solutions

[9] Wednesday, September 22
§ 6.5. Exponential growth and separable differential equations
Homework (due next class):
Do § 6.5# 9, 15, 17, 23, 25, 28
Read for next time: § 6.6
Homework Solutions

[10] Friday, September 24
§ 6.6. Work
Homework (due next class):
Do § 6.6 # 3, 5,9, 19, 23
Read for next time: § 7.1
Homework Solutions

[11] Monday, September 27
§ 7.1. Integration by parts
Homework:
(Homework is due Friday October 1 because of the exam on Wednesday.)
Do § 7.1 # 4, 5, 7, 11, 31, 37, 41
Read for next time: § 7.4
Homework Solutions

Wednesday, September 29
   Hour Exam # 1
   Solutions to Exam #1
   The exam is in Salomon 003. This is not our usual location.
   The exam will cover the material through Friday, September 24.
   That is §§ 3.7, 3.8, 4.6, 4.8, 5.2–5.5, 6.1, 6.3–6.6.

[12] Friday, October 1
§ 7.4. Integration using partial fractions
Homework (due next class):
Do § 7.4 # 1, 3, 6, 11, 17, 21, 49
Read for next time: § 7.5
Homework Solutions

[13] Monday, October 4
§ 7.5. Integral tables and computer algebra systems
Homework (due next class):
Do § 7.5. # 3, 9, 15, 19, 25, 29, 31, 39, 59
Read for next time: § 7.6.
Homework Solutions

[14] Wednesday, October 6
§ 7.6. Numerical integration
Homework (due next class):
Do § 7.6 # 3, 7, 28(a). [Note that #3 and #7 have multiple parts.]
You may omit the parts of Problems 3 and 7 that say "find an upper bound for |E_T|" and "find an upper bound for |E_S|", because we didn't really cover that material in class. Note that you do still need to do the first parts of I(a) and II(a), as well as all of I(b,c) and II(b,c), for Problems 3 and 7.
Read for next time: § 7.7
Homework Solutions

[15] Friday, October 8
§ 7.7. Improper integrals
Homework (due next class):
(Homework is due Wednesday October 13 because of the school holiday.)
Do § 7.7 # 1, 3, 5, 9, 21, 39, 41, 59, 63, 65
Read for next time: § 8.1
Homework Solutions

Monday, October 11 — Brown closed

[16] Wednesday, October 13
§ 8.1. Sequences
Homework (due next class):
Do § 8.1 # 3, 4, 9, 11, 16, 20, 24, 27, 31, 42
Read for next time: § 8.2
Homework Solutions (Errata: Problem #3, the 4^th term should be a₄ = –1/7.)

[17] Friday, October 15
§ 8.1 Sequences and § 8.2 Infinite Series
Homework (due next class):
Do § 8.1 # 59, 61, 68, 70, 85, 97, 98, 115
Do § 8.2 # 1, 4, 5
Read for next time: § 8.2
Homework Solutions

[18] Monday, October 18
§ 8.2 Infinite Series
Homework (due next class):
Do § 8.2 # 7, 12, 15, 20, 23, 26, 27, 33, 43, 47, 59(a,b)
Read for next time: §§ 8.3, 8.4
Homework Solutions (Errata: The series for #27 diverges, because cos(nπ) = (–1)ⁿ, so the series oscillates.)

[19] Wednesday, October 20
§ 8.3 The Integral Test and § 8.4 Comparison Tests
Homework (due next class):
Do § 8.3 # 3, 7, 8, 9, 11, 19, 20, 25, 32
Do § 8.4 # 1, 4, 8
Read for next time: §§ 8.4, 8.5
Homework Solutions

[20] Friday, October 22
§ 8.4 Comparison Tests and § 8.5 The Ratio and Root Tests
Homework (due next class):
Do § 8.4 # 19, 25, 35
Do § 8.5 # 1, 4, 9, 11, 14, 19, 30, 31
Read for next time: § 8.6
Homework Solutions

[21] Monday, October 25
§ 8.6. Alternating Series and Absolute/Conditional Convergence
Homework (due next class):
Do § 8.6 # 1, 3, 6, 13, 15, 18, 21, 24, 39
Read for next time: § 8.7
Homework Solutions

[22] Wednesday, October 27
§ 8.7 Power Series
Homework (due next class):
Do § 8.7 # 3, 4, 5, 6, 11, 23, 34, 35, 39, 40
Read for next time: §§ 8.8
Homework Solutions

[23] Friday, October 29
§ 8.8 Taylor Series
Homework (due next class):
Do § 8.8 # 1, 6, 10, 13, 19, 23, 27
Read for next time: § 8.9
Homework Solutions

[24] Monday, November 1
§ 8.9. Convergence of Taylor Series
Homework (due next class):
Do § 8.9 # 7, 12, 15, 20, 25, 30, 44, 49, 50
Read for next time: § 8.9
Homework Solutions

[25] Wednesday, November 3
   § 15.1. Solutions to Differential Equations and Slope Fields
   In § 15.1, we will only do the first part of the section. We will not cover "Existence of Solutions" or "Picard's Iteration Scheme".
   Click here to download Chapters 15 and 16.
Homework:
   (Homework is due Monday November 8 because of the exam on Friday.)
Do § 15.1 # 1, 2, 3, 4, 7, 8, 10, 17
Read for next time: § 15.2
Homework Solutions

Friday, November 5
   Hour Exam # 2
   Solutions to Exam #2
   The exam is in CIT 227. This is not our usual location.
   The exam will cover the material through Monday, November 1.
   That is §§ 7.1, 7.4–7.7, 8.1–8.9, plus material from the first hour exam.

[26] Monday, November 8
§ 15.2. First Order Linear Equations
Click here to download Chapters 15 and 16.
Homework (due next class):
Do § 15.2 # 1, 6, 13, 15, 16, 17, 20, 24
Read for next time: § 15.2, 15.3
Homework Solutions

[27] Wednesday, November 10
§§ 15.2 & 15.3. Applications of First Order Linear Equations
Homework (due next class):
Do §15.2 # 25, 27
Do §15.3 # 1, 2, 3
Read for next time: § 15.4
Homework Solutions

[28] Friday, November 12
§ 15.4. Euler's Method
Homework (due next class):
Do § 15.4 # 2, 3, 11, 12, 13
Read for next time: § 16.1
Homework Solutions

[29] Monday, November 15
§ 16.1. Second-Order Linear Equations
Homework (due next class):
Do § 16.1 # 7, 15, 25, 28, 41, 46, 55
Read for next time: §§ 16.1, 16.2
Homework Solutions

[30] Wednesday, November 17
§ 16.1. Second-Order Linear Equations
§ 16.2. Nonhomogeneous Linear Equations
Homework (due next class):
Do § 16.1 # 31, 32, 36
Do § 16.2 # 3, 4, 9, 31
Read for next time: § 16.2
Homework Solutions

[31] Friday, November 19
§ 16.2. Nonhomogeneous Linear Equations
Homework (due next class):
Do § 16.2 # 19, 20, 32, 37, 43, 59
Read for next time: § 16.3
Homework Solutions

[32] Monday, November 22
§ 16.3. Applications - Harmonic Motion
Homework:
(Homework is due Monday November 29 because of Thanksgiving.)
Do § 16.3 # 2, 8, 9, 14, 22
Read for next time: § 16.5
Homework Solutions

Wednesday, November 24 — Classes end at noon
Classes that meet will have a further discussion and review of the material on differential equations.

Friday, November 26 — Thanksgiving

[33] Monday, November 29
§ 16.5. Power Series Solutions
Homework (due next class):
Do § 16.5 # 1, 6, 9, 18
Read for next time: § 9.1, 9.2
Homework Solutions

[34] Wednesday, December 1
§ 9.1. Polar Coordinates
§ 9.2. Graphing in Polar Coordinates
Homework (due next class):
Do § 9.1 # 4, 5, 7, 10, 13, 19
Read for next time: § 9.3
Homework Solutions

[35] Friday, December 3
§ 9.2. Graphing in Polar Coordinates
§ 9.3 Areas in Polar Coordinates
Homework (due next class):
Do § 9.2 # 3, 7
Do § 9.3 # 2, 7 , 10, 13
Read for next time: § 10.2
Homework Solutions

[36] Monday, December 6 (Reading Period)
§ 3.5 Parametric Equations
Homework (due next class):
Do § 3.5 # 81, 83, 85, 103, 105, 107
Homework Solutions

Wednesday, December 8 (Reading Period)
Review Sesssion

Friday, December 10 — Final Exam, 2:00–5:00pm — MacMillan Hall 117
Click here to download a Math 100 Review Sheet.

Back to Math 100 Home Page
Back to Top of Math 100 Homework Page