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).
- Reading: Section 2.3.
- 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)
- Reading: Section 3.1.
- Practice problems: Example 3.2.
Wednesday:
Instantaneous change, tangent lines; first properties of derivatives.
(
lecture,
slides)
- Reading: Section 3.3.
- 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)
- Reading: Section 3.8.
- 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)
- Reading: Section 4.3.
- Practice problems: Exercises 100–103.
Friday:
Optimization.
(
lecture,
slides)
- We have an in-class midterm next Wednesday. Here is a review sheet.
- Reading: Section 4.3.
- 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)
- Reading: Section 4.5.
- 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.
- Reading: Section 5.1.
- 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)
- Reading: Section 5.1
- 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)
- Reading: Section 5.3.
- Practice problems: Example 5.20; Exercise 165.
Wednesday:
Properties of the integral. Integration practice.
(
lecture,
slides)
- Reading: Lecture notes.
- Practice problems: None.
Friday:
Integration by substitution. Integration by parts.
(
lecture,
slides)
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.
- Reading: Lecture notes.
- Practice Problems: None.
Wednesday:
More on logarithms.
(
lecture,
slides)
- Reading: Lecture notes.
- 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)
- Reading: Lecture notes.
- Practice problems: None.
Friday:
Thanksgiving break. No class today.
Week 13: November 28 - December 2
Monday:
Differential equations.
(
lecture,
slides)
Wednesday:
Population models I.
(
lecture,
slides)
Friday:
Population models II.
(
lecture,
slides)
Week 14: December 5 - 9
Monday:
Population models III.
(
lecture,
slides)
Wednesday:
Review for the final
exam.
Friday:
No class today.
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