# 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

## 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, 2.4
12Thu 9/12/2019Limits Practice, Squeeze TheoremBriggs 2.3
Fri 9/13/2019MML Homework 5 Due
13Mon 9/16/2019Week 3 Review
Begin Infinite Limits
Briggs 2.4
14Tue 9/17/2019Vertical AsymptotesBriggs 2.4MML Homework 6 Due
Quiz 3 in class (Briggs 2.2, 2.3)
15Wed 9/18/2019Finish Vertical Asymptotes, Horizontal AsymptotesBriggs 2.4, 2.5
16Thu 9/19/2019Slant Asymptotes, Begin ContinuityBriggs 2.6
Sat 9/21/2019MML Homework 7 Due
Sun 9/22/2019Lab 1 Out (Sage Version, Maple Version)
17Mon 9/23/2019Week 4 Review
18Tue 9/24/2019ContinuityBriggs 2.6Quiz 4 in class (Briggs 2.4, 2.5, excluding slant asymptotes)
19Wed 9/25/2019Intermediate Value TheoremBriggs 2.6

## 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.

20Thu 9/26/2019Delta/Epsilon Analysis, Intro To Derivatives And Differentiability
Fri 9/27/2019MML Homework 8 Due
21Mon 9/30/2019Week 5 Review
22Tue 10/1/2019Definition of Derivative And Examples
23Wed 10/2/2019Rules of DifferentiationBriggs 3.3
24Thu 10/3/2019Higher Derivatives, The Product Rule/Quotient Rule
Fri 10/4/2019MML Homework 9 Due
25Mon 10/7/2019Week 6 ReviewMML Homework 10 Due
Lab 1 Due
26Tue 10/8/2019Limit definition of `e`Quiz 5 in class
27Wed 10/9/2019Chain RuleBriggs 3.7
28Thu 10/10/2019Chain Rule Practice, Derivatives of Trig FunctionsBriggs 3.5
Fri 10/11/2019MML Homework 11 Due
--Mon 10/14/2019Fall BreakEnjoy!
--Tue 10/15/2019Fall BreakEnjoy!
29Wed 10/16/2019Implicit Differentiation
30Thu 10/17/2019Implicit Differentiation Continued, Derivatives of Inverse FunctionsBriggs 3.8
Sat 10/19/2019MML Homework 12 Due
31Mon 10/21/2019Weeks 7/8 ReviewMML Homework 13 Due
32Tue 10/22/2019Derivatives of Exponential FunctionsBriggs 3.9Quiz 6 in class
33Wed 10/23/2019Derivatives of Log And Inverse Trig FunctionsBriggs 3.9

## 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.

34Thu 10/24/2019Related Rates
Fri 10/25/2019MML Homework 14 Due
35Mon 10/28/2019Related Rates Practice
36Tue 10/29/2019Critical PointsBriggs 4.1MML Homework 15 Due
37Wed 10/30/2019Finish Related Rates Practice, Begin Critical PointsBriggs 4.1
38Thu 10/31/2019Critical Points ContinuedBriggs 4.1
Sat 11/2/2019Quiz 7: Graphing Functions And Minima Take-Home Out
39Mon 11/4/2019Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 1 (Guest Lecture by Professor Schilling)
40Tue 11/5/2019Graphing Functions: Critical Points, Inflection Points, Concavity, Asymptotes Part 2 (Guest Lecture by Professor Schilling)Briggs 4.3, 4.4MML Homework 16 Due
Lab 2 Out (Sage Version, Maple Version)
41Wed 11/6/2019Begin Optimization Problems (Guest Lecture by Professor Kozhushkina)Briggs 4.5
42Thu 11/7/2019Optimization Problems (Guest Lecture by Professor Kozhushkina)Briggs 4.5
Fri 11/8/2019MML Homework 17 Due
43Mon 11/11/2019Week 11 ReviewQuiz 7: Graphing Functions And Minima Take-Home Due
44Tue 11/12/2019Optimization ContinuedBriggs 4.5
45Wed 11/13/2019Optimization ContinuedBriggs 4.5Takehome Quiz 8 Out
46Thu 11/14/2019L'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.

47Mon 11/18/2019More Optimization Hints, Finish L'Hôpital's RuleBriggs 4.7
48Tue 11/19/2019Definite IntegralsBriggs 5.1, 5.2MML Homework 18 Due
Takehome Quiz 8 Due
Takehome Quiz 9 Out
49Wed 11/20/2019Finish Definite IntegralsBriggs 5.1, 5.2Lab 2 Parts 1 And 2 Due
50Thu 11/21/2019Riemann SumsBriggs 5.2
Fri 11/22/2019MML Homework 19 Due
51Mon 11/25/2019AntiderivativesBriggs 4.9MML Homework 20 Due
52Tue 11/26/2019Fundamental Theorem of CalculusBriggs 5.3Takehome Quiz 9 Due
--Wed 11/27/2019ThanksgivingEnjoy!
--Thu 11/28/2019ThanksgivingEnjoy!
53Mon 12/2/2019Fundamental Theorem of CalculusBriggs 5.3MML Homework 21 Due
54Tue 12/3/2019ReviewBriggs 1-5.3
55Wed 12/4/2019ReviewBriggs 1-5.3
56Thu 12/5/2019Review/RaffleBriggs 1-5.3
--Wed 12/11/2019Final Exam (Pfahler 001B 1PM - 4PM)Briggs 1 - 5.3