Math 111: Calculus (Fall 2022)

Instructor: Robert Chang
Email:
Office: Library 315
Office hours: WRF: 3:00–4:00 p.m.
Midterm: In-class Friday, October 14, 2022
Final Exam: In-person Monday, December 12, 2022
Syllabus.pdf

Hyperlink to current week's schedule. (Updated manually; email me if grossly out-of-date.)

Reference texts: OpenStax Calculus Volume 1 (pdf, html), Volume 2 (pdf, html), and lecture notes by David Perkinson

TA info: Ethan McDonald (ethanmcdonald@) will be running an evening help/group session for all calculus 1 sections 6:30–8:30 p.m. on Thursday evenings at Eliot 314, starting the week of September 8.

Math Help Center/Drop-in Tutoring: SuMTTh 7:00–9:00 p.m. at Library 204 (schedule).

Individual Tutoring: Reed offers one hour per week of free, one-to-one tutoring. Details here.

Examinations: One in-class midterm and one in-person cumulative exam during university scheduled final exam week will be administered.

Submit homework on GradeScope; suggested exercises do not need to be submitted. See Homework 0 for detailed policies and submission guidelines.

You are encouraged to work together, as collaboration is a nontrivial part of learning and of scholarship in general. But, in accordance with the honor principle and basic human decency, you must submit your own write-up with an acknowledgment of collaborators.

Week
Date
Memo
Suggested Exercises
1
8/29
Topics: birds-eye view of calculus
Read OpenStax § 2.1

 
8/31
Topics: limits (tables and graphs)
Read OpenStax § 2.2
Example 2.5, 2.6, 2.39, 2.40
 
9/2
Topics: limits ($\epsilon$-$\delta$)
Read OpenStax § 2.5 up to Checkpoint 2.27
Example 2.39
Homework 0 due Monday, September 5
Homework 1 due Friday, September 9
2
9/5
Labor Day, no class

 
9/7
Topics: limit laws
Read OpenStax § 2.3
Example 2.17–2.22
 
9/9
Topics: squeeze theorem, special limits
Read OpenStax § 2.3, particularly Theorem 2.7
Example 2.24, 2.25; Checkpoint 2.19, 2.20
Homework 2 due Friday, September 16
3
9/12
Topics: continuity, IVT
Read OpenStax § 2.4, skipping the section on discontinuities
Checkpoint 2.21, 2.26
 
9/14
Topics: intro to derivatives
Read OpenStax § 3.1–3.2
Example 3.11, 3.12
 
9/16
Topics: derivatives of polynomials
Read OpenStax § 3.3 up to Theorem 3.4
Example 3.17–3.22
Homework 3 due Friday, September 23
4
9/19
Topics: product and quotient rule
Read OpenStax § 3.3, 3.5
Example 3.32–3.30
 
9/21
Topics: chain rule
Read OpenStax § 3.6
Example 3.48–3.59
 
9/23
Topics: implicit differentiation
Read OpenStax § 3.8
Example 3.68–3.70
Homework 4 due Friday, September 30
5
9/26
Topics: derivatives of $a^x$, $\log x$ and $\sin^{-1}x$
Read OpenStax Example 3.63, Theorem 3.13 and § 3.9
Example 3.64, 3.66, 3.74–3.79
 
9/28
Topics: logarithmic derivative, overview of applications of calculus
Read OpenStax § 3.9
Example 3.81, Checkpoint 3.55
 
9/30
Topics: related rates
Read OpenStax § 4.1
Example 4.1–4.4
Homework 5 due Friday, October 7
Review topics for in-class exam on Friday, October 14
6
10/3
Topics: maxima and minima
Read OpenStax § 4.3
Example 4.12, 4.13
 
10/5
Topics: Mean Value Theorem
Read OpenStax § 4.4
Example 4.14–4.16
 
10/7
Topics: first derivative test
Read OpenStax § 4.5
Example 4.17, 4.18
Homework 6 aka mock exam due Friday, October 14
Practice midterm A and B with solutions
Review topics for in-class exam on Friday, October 14
7
10/10
Topics: second derivative test, L'Hôpital's rule
Read OpenStax § 4.5, 4.8
(focus on $\infty/\infty$ and $0/0$)
Example 4.19, 4.20, 4.38–4.40
 
10/12
Topics: Optimization
Read OpenStax § 4.7
Example 4.32–4.36
 
10/14
In-class midterm

Fall break
No homework due Friday, October 28
9
10/24
Topics: antiderivatives
Read OpenStax § 4.10 (I have not introduced the indefinite integral notation, but you can mentally replace all instances of $\int f(x)\,dx$ with $F(x)$ and understand everything)
Example 4.5
 
10/26
Topics: Summaton notation, Riemann sum and the definite integral
video, notes, read OpenStax § 5.1
Example 5.4
 
10/28
Topics: properties of integral, Fundamental Theorem of Calculus
Read § 5.2 Definition of the integral, properties of the integral, Theorem 5.2 (comparison theorem); § 5.3
Example 5.17–5.22
Homework 7 due Friday, November 4
10
10/31
Topics: net change theorem, indefinite integrals
Read OpenStax § 4.10 (indefinite integrals); § 5.4 (note that net change theorem, Theorem 5.6, is just the second part of the fundamental theorem of calculus, Theorem 5.5)
Example 4.51, 4.52, 5.20, 5.21, 5.24, 5.25
 
11/2
Topics: $u$-substitution
Read § 5.5
Example 5.30–5.39, 5.52–5.54
 
11/4
Topics: area between curves
Read § 6.1
Example 6.3–6.5
Homework 8 due Friday, November 18 (due date not a typo)
I am away for a conference November 7–11. Will be responsive via email.
Videos and lecture notes will be posted below. Zoom office hours can be arranged.
11
11/7
Topics: areas between curves
video, notes, read § 6.1 (skip Example 6.4 and onwards)
Example 6.1–6.3
 
11/9
Topics: volumes by cross-sections aka disk/washer method
video, notes, read § 6.2 (skip the parts involving setting up the integral in terms of $dy$)
Example 6.7, 6.8, 6.10
 
11/11
Topics: volumes by cylindrical shells
video, notes, read § 6.3 (skip the parts involving setting up integral in terms of $dy$)
Example 6.12, 6.13, 6.15, 6.16
Homework 8 and Homework 9 due Friday, November 18
12
11/14
Topics: integration by parts
Read OpenStax II § 3.1
Example 3.1–3.3
 
11/16
Topics: trigonometric integrals
Read OpenStax II § 3.2 (do not worry about ones involving different angles or involving tangents and secants)
Example 3.8–3.12
 
11/18
Topics: trigonometric substitution
Read OpenStax II § 3.3
Example 3.21–3.24
Homework 9 due Monday, November 28
13
11/21
Topics: partial fractions
Read OpenStax II § 3.4
Example 3.28, 3.29, 3.32
 
11/23
Topics: review

Thanksgiving break
Homework 9 due Monday, November 28
14
11/28
Topics: improper integration (infinite interval of integration)
Read OpenStax II § 3.7
Example 3.47, 3.50–3.54
 
11/30
Topics: improper integration (infinite/discontinuous integrand)
Read OpenStax II § 3.7
Example 3.47, 3.50–3.54
 
12/2
Topics: crash course on power series and Taylor's theorem

Homework 10 aka mock exam due Monday, December 12
Practice final exam A and B with solutions
Review topics for in-person final exam on Monday, December 12
15
12/5
Topics: intro to differential equations

 
12/7
Topics: differential equations

Homework 10 aka mock exam due Monday, December 12
Practice final exam A and B with solutions
Review topics for in-person final exam on Monday, December 12

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