Calculus • Series
An Experiment - Covering Single-Variate Calculus
PL
SS
Shadman S
This series was cancelled by the tutor on September 5, 2023. We're very sorry–you can explore more Calculus series here. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
We will cover every topic normally covered in AP Calculus BC, and some more topics if there is enough demand.
The catch? I don't plan to do this bound to any standardized curriculum. This can be as intensive or as light as learners want; I plan to try teaching this way to a small group of people, and then try this on a broader scale. There will be no lesson plan for most sessions; I will try to be as flexible as possible and questions, while they will be prepared before the class, will be fit according to whichever topic I happen to be talking about, written by me for the class (though questions from other sources can inspire my questions).
Seeing as this will be in a summer, the series will be a little fast-paced; for this reason, I recommend having a very good base in math topics covered before calculus, such as geometry and algebra, before joining this series as a learner. Despite the lack of a concrete base curriculum, I will have a set order in which I plan to teach things, that is to say there will be an always flexible syllabus keeping track of our progress. There will be weekly assessments, but they are purely for you to see your own progress. I hope that you will all enjoy this series!
Link to syllabus sheet: https://docs.google.com/document/d/17ee7-E5A1PwpRF5iJCtlOB90xVRmNRoZxJbBlgLDFjs/edit?usp=sharing
✋ ATTENDANCE POLICY
You must attend every session, unless you give me 24 hours prior notice with valid reason. After either two absences in a row or three total absences, whichever comes first, a learner may be withdrawn from the series. Office hours will be offered for those who have missed my primary sessions; if you missed a certain session, showing up to the weekly office hours session that week, even if you did not given me 24 hours advance notice, will absolve you of any unexcused absences that week, so long as you spend your time wisely in the office hours.
Dates
June 29 - September 4
Learners
5 / 5
Total Sessions
31
About the Tutor
PL
SS
Hey there! I'm a current undergraduate freshman at Stony Brook University, and I love the STEM fields most out of all my subjects in school! With that being said, though I tutor mostly competitive math nowadays, I also tutor high school math and science. I also join many sessions on Schoolhouse, because there are so many things to learn and enjoy in Schoolhouse - though I haven't joined many series recently, I had a lot of fun in Taeho's Korean Camp last summer! Outside of Schoolhouse, I love to play basketball and Pokemon.
View Shadman S's Profile
Upcoming Sessions
0
Past Sessions
31
29
Jun
O
Session 1
Orientation
Let's see each other for the first time! I'll introduce myself, and I hope each of you will introduce yourselves - we will get to know each other over a summer, so what's better than starting off on the right note?
We'll go over the (tentative) syllabus as well as the expectations I have for all of you. In this session, we will also decide some things together: what time works best for all of us? Which days of the week should I hold sessions? How much homework, if any, should I give? If time permits, the remaining portion of the session will be spent talking about some beginning concepts of calculus.
30
Jun
O
Session 2
Orientation
Let's see each other for the first time! I'll introduce myself, and I hope each of you will introduce yourselves - we will get to know each other over a summer, so what's better than starting off on the right note?
We'll go over the (tentative) syllabus as well as the expectations I have for all of you. In this session, we will also decide some things together: what time works best for all of us? Which days of the week should I hold sessions? How much homework, if any, should I give? If time permits, the remaining portion of the session will be spent talking about some beginning concepts of calculus.
1
Jul
GQ
Session 3
General Calculus Q&A
Today, instead of starting right away with some calculus topic, I want to set forth some questions we can solve without calculus, but point heavily in the direction of calculus. Nothing better than a motivating session to officially start our series!
2
Jul
Lc
Session 4
Limits and continuity
Let's try to hit limits today! Of course, not without considering some fundamental properties of functions: continuity, "differentiability" (without outright mentioning derivatives). We will also classify broad types of functions (rational, polynomial, exponential) as continuous/differentiable. First of our free-style lessons!
8
Jul
Lc
Session 5
Limits and continuity
First, we'll go through some algebraic and trigonometric limit solving techniques! Then, we will cover the squeeze theorem in depth and show two important trigonometric limits that might otherwise be difficult to compute.
14
Jul
Lc
Session 6
Limits and continuity
If we didn't do it last time, we'll prove the trigonometric limits in this session. Then, we will do more difficult limits, and finally we'll talk about the definition of a limit!
15
Jul
Lc
Session 7
Limits and continuity
I will talk about the definition of a limit! This includes an introduction to quantifiers in first order logic, some intuitive motivation for how to define a limit, and how to speak the motivation into math language. I will also try some easier limit proofs with you guys!
Lc
Session 8
Limits and continuity
I will talk about the definition of a limit! This includes an introduction to quantifiers in first order logic, some intuitive motivation for how to define a limit, and how to speak the motivation into math language. I will also try some easier limit proofs with you guys!
16
Jul
Lc
Session 9
Limits and continuity
After some rigorous limit proofs, we'll talk one last time about continuity and differentiability. This time, we'll talk about what differentiability really means - and how it implies continuity. We will also talk about orders of continuity and differentiability as a fun little end to this unit.
18
Jul
OH
Session 10
Office Hours
First office hours! All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
24
Jul
OH
Session 11
Office Hours
First office hours! All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
28
Jul
Lc
Session 12
Limits and continuity
After some rigorous limit proofs, we'll talk one last time about continuity and differentiability. This time, we'll talk about what differentiability really means - and how it implies continuity. We will also talk about orders of continuity and differentiability as a fun little end to this unit.
29
Jul
Dr
Session 13
Differentiation: definition and basic derivative rules
We will officially talk about the definition of a derivative! Motivation included in this session, as well as the rules of differentiation as an operator (more on that later)!
30
Jul
Dr
Session 14
Differentiation: definition and basic derivative rules
We will try differentiation of basic polynomials and rationals in this function and try to define the power rule by ourselves. For now, we will assume the real number case: our definition will be best used for the rational case.
31
Jul
Dr
Session 15
Differentiation: definition and basic derivative rules
We will try differentiation of basic polynomials and rationals in this function and try to define the power rule by ourselves. For now, we will assume the real number case: our definition will be best used for the rational case.
1
Aug
OH
Session 16
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
4
Aug
OH
Session 17
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
5
Aug
Dr
Session 18
Differentiation: definition and basic derivative rules
In this session, we will prove the trig derivatives, then we will prove the product and quotient rules. We will also start mentioning antiderivatives more - in that we need to talk about how to reverse all the derivatives we've been doing.
7
Aug
Dr
Session 19
Differentiation: definition and basic derivative rules
In this session, we will prove the trig derivatives, then we will prove the product and quotient rules. We will also start mentioning antiderivatives more - in that we need to talk about how to reverse all the derivatives we've been doing.
8
Aug
OH
Session 20
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
11
Aug
Df
Session 21
Differentiation: composite, implicit, and inverse functions
We bring back the limit definition of e - and use it to differentiate natural log and exponential functions. Then we will begin a proof of the chain rule (rigorous!).
12
Aug
Df
Session 22
Differentiation: composite, implicit, and inverse functions
We bring back the limit definition of e - and use it to differentiate natural log and exponential functions. Then we will begin a proof of the chain rule (rigorous!).
13
Aug
Df
Session 23
Differentiation: composite, implicit, and inverse functions
Chain rule proof part 2! (sorry, this proof is both important and long...).
In any case, we will be finished with the chain rule by the halfway point of this session. After that, we will go back to trig derivatives, but now targeting all six functions, using our new derivative rules!
14
Aug
Df
Session 24
Differentiation: composite, implicit, and inverse functions
Today, we will first review the differentiation techniques we just learned. Then, we will begin to cover implicit differentiation - which is, really, even more review + some algebra! (I think this will be a very good session.)
15
Aug
OH
Session 25
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
19
Aug
OH
Session 26
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
20
Aug
OH
Session 27
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
22
Aug
OH
Session 28
Office Hours
All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!
27
Aug
Df
Session 29
Differentiation: composite, implicit, and inverse functions
This is where we need to touch bases on what we've learned so far! We will review all the derivatives and antiderivatives we've memorized so far, and practice some implicit differentiation questions (the only truly comprehensive differentiation questions). We will learn to differentiate inverse functions, but nothing else new!
28
Aug
Df
Session 30
Differentiation: composite, implicit, and inverse functions
This is where we need to touch bases on what we've learned so far! We will review all the derivatives and antiderivatives we've memorized so far, and practice some implicit differentiation questions (the only truly comprehensive differentiation questions). We will learn to differentiate inverse functions, but nothing else new!
4
Sep
Df
Session 31
Differentiation: composite, implicit, and inverse functions
This is where we need to touch bases on what we've learned so far! We will review all the derivatives and antiderivatives we've memorized so far, and practice some implicit differentiation questions (the only truly comprehensive differentiation questions). We will learn to differentiate inverse functions, but nothing else new!
(Note: I will start referring to anti-differentiation as "integration", but I mean anti-differentiation. While they may appear similar, their definitions are fundamentally different.)