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
Date
Lectures (click for notes)Readings/LinksAssignments/Deliverables

Functions

We 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: f(x) = x + 4 (also in the set of years). In this course, we will focus on real-valued functions; that is, functions that taken in a single real value and which output a single real value (of which the above +4 ageing function is an example). We will discuss how to represent real valued functions, how to make new functions from template functions, and some special families of real-valued functions (linear, polynomial, trigonometric, exponential/logarithmic).

1Mon 8/26/2019Course Sneak Preview, Background Knowledge Assessment, Beginning FunctionsBriggs 1.1Submit Personal Survey on Microsoft Teams
2Tue 8/27/2019Functions: Function Representations/Notation, Domain/Range, SymmetryBriggs 1.1
3Wed 8/28/2019Finish symmetry, Function Composition / TransformationsEnroll in MyMathLab(MML) using these directions, and go through orientation
4Thu 8/29/2019Practice Compositions / TransformationsGeogebra Transformations Interactive Tool
Fri 8/30/2019MML Homework 1 Due
Sun 9/1/2019Practice with Transformations Tool
5Mon 9/2/2019Week 1 ReviewMML Homework 2 Due
6Tue 9/3/2019Inverse Functions, Exponential/Logarithmic FunctionsBriggs 1.3Quiz 1 in class (Briggs 1.1-1.2)
7Wed 9/4/2019Exponential/Logarithmic Functions
8Thu 9/5/2019Finish Logarithms, Trig Functions And Their Inverses
Fri 9/6/2019MML Homework 3 Due

Limits

In 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!

9Mon 9/9/2019Week 2 Review
More Trig
Briggs 1.4
10Tue 9/10/2019Limits OverviewBriggs 2.2MML Homework 4 Due (Out of 12, any more is extra credit)
Quiz 2 in class (Briggs 1.3, 1.4)
11Wed 9/11/2019Evaluating Limits, Limit LawsBriggs 2.3, 2.4Lab 1: Functions, Out
12Thu 9/12/2019Limits Practice, Squeeze Theorem, Infinite LimitsBriggs 2.3
Fri 9/13/2019MML Homework 5 Due
13Mon 9/16/2019Week 3 Review
Begin End Behavior
Briggs 2.4MML Homework 6 Due
14Tue 9/17/2019End Behavior (Limits At Infinity)/Asymptotes of FunctionsBriggs 2.5Quiz 3 in class (Briggs 2.2, 2.3)
15Wed 9/18/2019ContinuityBriggs 2.6Lab 1: Functions, Due
16Thu 9/19/2019Week 4 Review
Intermediate Value Theorem
Briggs 2.6Lab 2: Limits, Out
17Mon 9/23/2019Limit definition of e
18Tue 9/24/2019Delta/Epsilon Analysis of LimitsBriggs 2.7Quiz 4 in class

Derivatives

Now 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.

19Wed 9/25/2019Intro To Derivatives And DifferentiabilityBriggs 2.1, 3.1
20Thu 9/26/2019Week 5 Review
Intro Derivatives Continued
Briggs 3.2
21Mon 9/30/2019Basic Rules of DifferentiationBriggs 3.3Lab 2: Limits, Due
22Tue 10/1/2019Rules of Differentiation Continued, Higher-Order DerivativesBriggs 3.3Quiz 5 in class
23Wed 10/2/2019The Product Rule/Quotient RuleBriggs 3.4
24Thu 10/3/2019Week 6 Review
Derivatives of Trig Functions
Briggs 3.5
25Mon 10/7/2019Derivatives of Trig FunctionsBriggs 3.5
Lab 3: Derivatives, Out
26Tue 10/8/2019Begin Chain RuleBriggs 3.7Quiz 6 in class
27Wed 10/9/2019Finish Chain RuleBriggs 3.7
28Thu 10/10/2019Week 7 Review
Implicit Differentiation
Briggs 3.8
--Mon 10/14/2019Fall BreakEnjoy!
--Tue 10/15/2019Fall BreakEnjoy!
29Wed 10/16/2019Derivatives of Inverse Functions
30Thu 10/17/2019Week 8 Review
Limit definition of e revisited
Briggs 3.9Quiz 7 in class
Sun 10/20/2019Lab 3: Derivatives, Due
31Mon 10/21/2019Derivatives of Exponential/Logarithmic FunctionsBriggs 3.9
32Tue 10/22/2019Derivatives of Inverse Trig FunctionsBriggs 3.10Quiz 8 in class

Applications of The Derivative

Now 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.

33Wed 10/23/2019Related Rates Part 1Briggs 3.11
34Thu 10/24/2019Week 9 Review
Related Rates Part 2
Briggs 3.11
35Mon 10/28/2019Critical PointsBriggs 4.1
36Tue 10/29/2019Critical PointsBriggs 4.1Quiz 9 in class
37Wed 10/30/2019Rolle's Theorem, Mean Value TheoremBriggs 4.2
38Thu 10/31/2019Week 10 Review
Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 1
Briggs 4.3, 4.4Quiz 10 Graphing Functions Take-Home Out
39Mon 11/4/2019Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 2Briggs 4.3, 4.4
40Tue 11/5/2019Begin Optimization ProblemsBriggs 4.5Quiz 11 in class
41Wed 11/6/2019Optimization ProblemsBriggs 4.5
42Thu 11/7/2019Week 11 Review
Local Linearity
Briggs 4.6
43Mon 11/11/2019Local Linearity Continued, Begin Newton's MethodBriggs 4.8
44Tue 11/12/2019Finish Newton's MethodBriggs 4.8Quiz 12 in class
Lab 4: Optimization, Newton's Method Out
45Wed 11/13/2019L'Hôpital's RuleBriggs 4.7

Introduction To Integration

We 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.

46Thu 11/14/2019Week 12 Review
Riemann Sums Part 1
Briggs 5.1
47Mon 11/18/2019Riemann Sums Part 2Briggs 5.2
48Tue 11/19/2019Begin Definite IntegralsBriggs 5.2Quiz 14 in class
49Wed 11/20/2019Finish Definite IntegralsBriggs 5.2
50Thu 11/21/2019Week 13 Review
The Antiderivative
Briggs 4.9
Sun 11/24/2019Lab 4: Optimization, Newton's Method Due
51Mon 11/25/2019The Antiderivative ContinuedBriggs 4.9
52Tue 11/26/2019The Fundamental Theorem of CalculusBriggs 5.3Quiz 15 in class
Lab 5: Integration And Fourier Out
--Wed 11/27/2019ThanksgivingEnjoy!
--Thu 11/28/2019ThanksgivingEnjoy!
53Mon 12/2/2019The Fundamental Theorem of Calculus ContinuedBriggs 5.3