Schedule
Outlined below is the schedule for the course, including lecture topics and assignment due dates. All assignments are due at 11:59PM on the date specified. The specific dates of different topics are subject to change based on the pace at which we go through the course. For the same reason, the homeworks and quiz topics will only be listed a week in advance.
The assigned textbook for the course covers most of the topics we will go over in the class, but I will sometimes add external links to other resources if I feel the textbook is lacking in a particular area, or if there is a fun application for you to play with beyond what's offered in the textbook.
Lecture | Lectures (click for notes) | Readings/Links | Assignments/Deliverables | |
FunctionsWe start the course with a review about some topics from functions. A function is an object which, given an input from some set of objects, returns an output from another set of objects. For example, if I want to know how old someone will be in four years, then I input their (possibly decimal valued) age in years (from the set of years), and the function will output that age plus 4: | ||||
1 | Mon 8/26/2019 | Course Sneak Preview, Background Knowledge Assessment, Beginning Functions | Briggs 1.1 | Submit Personal Survey on Microsoft Teams |
2 | Tue 8/27/2019 | Functions: Function Representations/Notation, Domain/Range, Symmetry | Briggs 1.1 | |
3 | Wed 8/28/2019 | Finish symmetry, Function Composition / Transformations |
| Enroll in MyMathLab(MML) using these directions, and go through orientation |
4 | Thu 8/29/2019 | Practice Compositions / Transformations | Geogebra Transformations Interactive Tool | |
Fri 8/30/2019 | MML Homework 1 Due | |||
Sun 9/1/2019 | Practice with Transformations Tool | |||
5 | Mon 9/2/2019 | Week 1 Review | MML Homework 2 Due | |
6 | Tue 9/3/2019 | Inverse Functions, Exponential/Logarithmic Functions | Briggs 1.3 | Quiz 1 in class (Briggs 1.1-1.2) |
7 | Wed 9/4/2019 | Exponential/Logarithmic Functions |
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8 | Thu 9/5/2019 | Finish Logarithms, Trig Functions And Their Inverses | ||
Fri 9/6/2019 | MML Homework 3 Due | |||
LimitsIn this section, we take our first foray into problems involving dividing zero by zero, which form the foundation of the rest of calculus. In more concrete terms, we ask what happens to the output of a function when we can get as close as possible to a particular input for a function. This works even if the function isn't defined at the input we're approaching! | ||||
9 | Mon 9/9/2019 | Week 2 Review More Trig | Briggs 1.4 | |
10 | Tue 9/10/2019 | Limits Overview | Briggs 2.2 | MML Homework 4 Due (Out of 12, any more is extra credit) Quiz 2 in class (Briggs 1.3, 1.4) |
11 | Wed 9/11/2019 | Evaluating Limits, Limit Laws | Briggs 2.3, 2.4 | Lab 1: Functions, Out |
12 | Thu 9/12/2019 | Limits Practice, Squeeze Theorem, Infinite Limits | Briggs 2.3 | |
Fri 9/13/2019 | MML Homework 5 Due | |||
13 | Mon 9/16/2019 | Week 3 Review Begin End Behavior | Briggs 2.4 | MML Homework 6 Due |
14 | Tue 9/17/2019 | End Behavior (Limits At Infinity)/Asymptotes of Functions | Briggs 2.5 | Quiz 3 in class (Briggs 2.2, 2.3) |
15 | Wed 9/18/2019 | Continuity | Briggs 2.6 | Lab 1: Functions, Due |
16 | Thu 9/19/2019 | Week 4 Review Intermediate Value Theorem | Briggs 2.6 | Lab 2: Limits, Out |
17 | Mon 9/23/2019 | Limit definition of e | ||
18 | Tue 9/24/2019 | Delta/Epsilon Analysis of Limits | Briggs 2.7 | Quiz 4 in class |
DerivativesNow we are able to introduce the first real workhorse of calculus: the derivative. This allows us to estimate the "tangent slopes" of functions. More concretely, it tells us how quickly functions are changing at different inputs. We will spend a lot of time building up the nuts and bolts on toy functions in this section before we move onto the applications. | ||||
19 | Wed 9/25/2019 | Intro To Derivatives And Differentiability | Briggs 2.1, 3.1 | |
20 | Thu 9/26/2019 | Week 5 Review Intro Derivatives Continued | Briggs 3.2 | |
21 | Mon 9/30/2019 | Basic Rules of Differentiation | Briggs 3.3 | Lab 2: Limits, Due |
22 | Tue 10/1/2019 | Rules of Differentiation Continued, Higher-Order Derivatives | Briggs 3.3 | Quiz 5 in class |
23 | Wed 10/2/2019 | The Product Rule/Quotient Rule | Briggs 3.4 | |
24 | Thu 10/3/2019 | Week 6 Review Derivatives of Trig Functions | Briggs 3.5 | |
25 | Mon 10/7/2019 | Derivatives of Trig Functions | Briggs 3.5 | Lab 3: Derivatives, Out |
26 | Tue 10/8/2019 | Begin Chain Rule | Briggs 3.7 | Quiz 6 in class |
27 | Wed 10/9/2019 | Finish Chain Rule | Briggs 3.7 | |
28 | Thu 10/10/2019 | Week 7 Review Implicit Differentiation | Briggs 3.8 | |
-- | Mon 10/14/2019 | Fall Break | Enjoy! | |
-- | Tue 10/15/2019 | Fall Break | Enjoy! | |
29 | Wed 10/16/2019 | Derivatives of Inverse Functions | ||
30 | Thu 10/17/2019 | Week 8 Review Limit definition of e revisited | Briggs 3.9 | Quiz 7 in class |
Sun 10/20/2019 | Lab 3: Derivatives, Due | |||
31 | Mon 10/21/2019 | Derivatives of Exponential/Logarithmic Functions | Briggs 3.9 | |
32 | Tue 10/22/2019 | Derivatives of Inverse Trig Functions | Briggs 3.10 | Quiz 8 in class |
Applications of The DerivativeNow that we are through the nuts and bolts of derivatives, we move onto some applications of derivatives. We will talk about how we can use derivatives to come up with accurate sketches of functions by understanding their "critical points" and "concavity." We will also see how to use some of these features to understand optimization problems (e.g. what's the largest volume enclosure I can create from a fixed amount of material?). We will end by finally being able to address the question of what infinity divided by infinity is. | ||||
33 | Wed 10/23/2019 | Related Rates Part 1 | Briggs 3.11 | |
34 | Thu 10/24/2019 | Week 9 Review Related Rates Part 2 | Briggs 3.11 | |
35 | Mon 10/28/2019 | Critical Points | Briggs 4.1 | |
36 | Tue 10/29/2019 | Critical Points | Briggs 4.1 | Quiz 9 in class |
37 | Wed 10/30/2019 | Rolle's Theorem, Mean Value Theorem | Briggs 4.2 | |
38 | Thu 10/31/2019 | Week 10 Review Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 1 | Briggs 4.3, 4.4 | Quiz 10 Graphing Functions Take-Home Out |
39 | Mon 11/4/2019 | Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 2 | Briggs 4.3, 4.4 | |
40 | Tue 11/5/2019 | Begin Optimization Problems | Briggs 4.5 | Quiz 11 in class |
41 | Wed 11/6/2019 | Optimization Problems | Briggs 4.5 | |
42 | Thu 11/7/2019 | Week 11 Review Local Linearity | Briggs 4.6 | |
43 | Mon 11/11/2019 | Local Linearity Continued, Begin Newton's Method | Briggs 4.8 | |
44 | Tue 11/12/2019 | Finish Newton's Method | Briggs 4.8 | Quiz 12 in class
Lab 4: Optimization, Newton's Method Out |
45 | Wed 11/13/2019 | L'HÃ´pital's Rule | Briggs 4.7 | |
Introduction To IntegrationWe now look at the other major half of calculus, which is integration. We introduce this concept as the ability to find the "area under a complicated curve" as the limit of a sum of very small simple areas we know how to compute, which is more precisely referred to as a Riemann Sum, or a Definite Integral. In this way, we will be able to address what 0 times infinity is. Amazingly, we will see that integration turns out to be the "dual" of differentiation, in the sense that we can compute definite integrals by doing derivatives in reverse. | ||||
46 | Thu 11/14/2019 | Week 12 Review Riemann Sums Part 1 | Briggs 5.1 | |
47 | Mon 11/18/2019 | Riemann Sums Part 2 | Briggs 5.2 | |
48 | Tue 11/19/2019 | Begin Definite Integrals | Briggs 5.2 | Quiz 14 in class |
49 | Wed 11/20/2019 | Finish Definite Integrals | Briggs 5.2 | |
50 | Thu 11/21/2019 | Week 13 Review The Antiderivative | Briggs 4.9 | |
Sun 11/24/2019 | Lab 4: Optimization, Newton's Method Due | |||
51 | Mon 11/25/2019 | The Antiderivative Continued | Briggs 4.9 | |
52 | Tue 11/26/2019 | The Fundamental Theorem of Calculus | Briggs 5.3 | Quiz 15 in class
Lab 5: Integration And Fourier Out |
-- | Wed 11/27/2019 | Thanksgiving | Enjoy! | |
-- | Thu 11/28/2019 | Thanksgiving | Enjoy! | |
53 | Mon 12/2/2019 | The Fundamental Theorem of Calculus Continued | Briggs 5.3 |