### Math 111

##### Calculus
Fall 2022

Current week   |   Moodle   |   Course information
Instructor: David Perkinson (schedule)
Text: Openstax Calculus Volume 1 (pdf, html).
Office hours: 11–12 M, 3–4 TuTh, or by appointment or drop-in. Office: L388.

Midterm exam: There was a one-hour, closed-book, in-class midterm exam Wednesday, October 12. Review sheet.
Final exam: 9 am--noon, December 12. Review sheet.
Week 1: August 29 - September 2
Monday: Introduction: derivatives, integrals, and the fundamental theorem. (lecture, slides).
• To do list for Wednesday's class:
• Carefully read the Course information sheet.
• Fill out the Office Hour & Mask policy survey.
• Make sure you can access our Moodle page.
• Make sure you can access our Gradescope page. The link and entry code are on our Moodle page.
• Do the homework assignment for this week before class on Wednesday. (You will then have until Friday to figure out how to use Gradescope to turn it in.)
• Do the reading and practice problems for Wednesday (listed under the Wednesday heading, below).

Wednesday: Average speed, instantaneous speed. Definition of the limit. (lecture).
• Reading: Section 2.1. (All references are to our textbook.)
• Practice problems: Examples 2.1, 2.2, and 2.3.

Friday: Limits. (lecture, slides).
Week 2: September 5 - 9
Monday: No class: Labor day.
Wednesday: Limit theorems. (lecture, slides).
• Practice problem: Example 2.40, Checkpoint 2.27.

Friday: Limit theorems; (lecture, slides).
Homework due Friday
Week 3: September 12 - 16
Monday: Limit theorem proof; Cancellation trick; rationalization trick; limit theorem proof. (lecture, slides)
• Reading: Section 2.3 up through Checkpoint 2.16.
• Practice problems: Examples 2.15, 2.17, 2.19.

Wednesday: Continuity, compositions of continuous functions. (lecture, slides)
• Reading: Section 2.4 up through Checkpoint 2.23.
• Practice problems: Examples 2.26, 2.29, 2.30.

Friday: Variations on the definition of the limit. The intermediate value theorem. (lecture)
• Reading: Section 2.2 (subsection on one-sided limits) and 2.4 (subsection on the intermediate value theorem).
• Practice problems: Examples 2.8, 2.9, 2.11, 2.36.
• Turn in: HW3 (Overleaf template)
Week 4: September 19 - 23
Monday: Definition of the derivative. (lecture, slides)
• Practice problems: Example 3.2.

Wednesday: Instantaneous change, tangent lines; first properties of derivatives. (lecture, slides)
• Practice problems: Examples 3.19, 3.21, 3.24, 3.25.

Friday: Proof of derivative theorem. (lecture, slides)
Week 5: September 26 - 30
Monday: Chain rule. Trigonometry review. (lecture, slides)

Wednesday: Implicit functions. Related rates. (lecture, slides)
• Practice problems: Examples 3.68, 3.69, 3.72.

Friday: Related rates. (lecture, slides)
Week 6: October 3 - 7
Monday: Related rates and implicit differentiation examples. (lecture, slides)
• Reading: Sections 3.8 and 4.1
• Practice problems: Section 3.8, Exercises 301, 307; Section 4.1, Exercise 5

Wednesday: Optimization. (lecture, slides)
• Practice problems: Exercises 100–103.

Friday: Optimization. (lecture, slides)
• We have an in-class midterm next Wednesday. Here is a review sheet.
• Practice problems: Example 4.12; Exercise 141.
• Turn in: HW6 (Overleaf template)
Week 7: October 10 - 14
Monday: Optimization and related rates examples. (lecture, slides)
• Reading: Sections 4.1 and 4.3.
• Practice problems: Section 4.1, Exercise 37; Section 4.3, Exercise 127.

Wednesday: In-class Midterm Exam today.

Friday: Curve sketching and the second derivative tests. (lecture, slides)
Week 8: October 24 - 28
Monday: Review of Midterm; Curve sketching. (lecture, slides)
• Practice problems: Exercises 205 and 217.

Wednesday: Least upper bounds, greatest lower bounds. Estimating areas. (lecture)
NOTE: We will have a quiz at the beginning of class on the definition of the limit and the definition of continuity. See the lecture notes for the classes on Friday, Week 1 and Wednesday, Week 3 for the definitions.
• Practice problems: Example 5.4.

Friday: Definition of the integral. (lecture, slides)
Week 9: October 13- November 4
Monday: Definition of the integral. (lecture, slides)
• Practice problems: Section 5.1, Exercise 57.

Wednesday: Definition of the integral. Some first examples. (lecture, slides)
• Reading: Lecture notes from Monday and today.
• Practice problems: None.

Friday: Definition of the integral, continued. (lecture, slides)
Week 10: November 7 - 11
Monday: The fundamental theorem of calculus. (lecture, slides)
• Practice problems: Example 5.20; Exercise 165.

Wednesday: Properties of the integral. Integration practice. (lecture, slides)
• Practice problems: None.

Friday: Integration by substitution. Integration by parts. (lecture, slides)
• Reading: Section 5.5; Lecture notes.
• Practice problems: Example 5.31.
• Turn in: HW10 (Overleaf template)
Week 11: November 14 - 18
Monday: Finish integration by parts. The logarithm. Another version of the fundamental theorem of calculus. (lecture, slides)
NOTE: We will have a quiz at the beginning of class consisting of some subset of the following:
• The definition of the limit of a function.
• The definition of the limit of continuity.
• The definition of the derivative of a function.
• An example of computing the derivative of a particular function directly from the definition of the derivative.
For the first two items see the lecture notes for the classes on Friday, Week 1 and Wednesday, Week 3, and for the last two items, see the lecture notes for the class on Monday, Week 4.
• Practice Problems: None.

Wednesday: More on logarithms. (lecture, slides)
• Practice Problems: None.

Friday: The inverse function theorem and the exponential function. (lecture, slides)
Week 12: November 21 - 25
Monday: The mean value theorem. (lecture, slides)
• Reading: Lecture notes and Section 4.4.
• Practice problems: None.

Wednesday: The fundamental theorem of calculus. (lecture, slides)
• Practice problems: None.

Friday: Thanksgiving break. No class today.

Week 13: November 28 - December 2
Monday: Differential equations. (lecture, slides)
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