An Experiment - Covering Single-Variate Calculus

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An Experiment - Covering Single-Variate Calculus

SAT Score Range

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31 sessions

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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.

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

Tutored by

Shadman S 🇺🇸

Certified in 106 topics

View Profile

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.

Schedule

✋ 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.

SESSION 1

29

Jun

SESSION 1

Orientation

Thu 9:30 PM - 10:30 PM UTCJun 29, 9:30 PM - 10:30 PM UTC

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.

SESSION 2

30

Jun

SESSION 2

Orientation

Fri 9:30 PM - 10:30 PM UTCJun 30, 9:30 PM - 10:30 PM UTC

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.

SESSION 3

1

Jul

SESSION 3

General Calculus Q&A

Sat 9:45 PM - 10:45 PM UTCJul 1, 9:45 PM - 10:45 PM UTC

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!

SESSION 4

2

Jul

SESSION 4

Limits and continuity

Sun 9:45 PM - 10:45 PM UTCJul 2, 9:45 PM - 10:45 PM UTC

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!

SESSION 5

8

Jul

SESSION 5

Limits and continuity

Sat 10:15 PM - 11:15 PM UTCJul 8, 10:15 PM - 11:15 PM UTC

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.

SESSION 6

14

Jul

SESSION 6

Limits and continuity

Fri 9:45 PM - 10:45 PM UTCJul 14, 9:45 PM - 10:45 PM UTC

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!

SESSION 7

15

Jul

SESSION 7

Limits and continuity

Sat 10:15 PM - 11:15 PM UTCJul 15, 10:15 PM - 11:15 PM UTC

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!

SESSION 8

15

Jul

SESSION 8

Limits and continuity

Sat 11:15 PM - Sun, 12:15 AM UTCJul 15, 11:15 PM - Jul 16, 12:15 AM UTC

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!

SESSION 9

16

Jul

SESSION 9

Limits and continuity

Sun 9:45 PM - 10:45 PM UTCJul 16, 9:45 PM - 10:45 PM UTC

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.

SESSION 10

18

Jul

SESSION 10

Office Hours

Tue 9:45 PM - 10:45 PM UTCJul 18, 9:45 PM - 10:45 PM UTC

First office hours! All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 11

24

Jul

SESSION 11

Office Hours

Mon 9:45 PM - 10:45 PM UTCJul 24, 9:45 PM - 10:45 PM UTC

First office hours! All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 12

28

Jul

SESSION 12

Limits and continuity

Fri 9:45 PM - 10:45 PM UTCJul 28, 9:45 PM - 10:45 PM UTC

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.

SESSION 13

29

Jul

SESSION 13

Differentiation: definition and basic derivative rules

Sat 9:45 PM - 10:45 PM UTCJul 29, 9:45 PM - 10:45 PM UTC

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)!

SESSION 14

30

Jul

SESSION 14

Differentiation: definition and basic derivative rules

Sun 9:45 PM - 10:45 PM UTCJul 30, 9:45 PM - 10:45 PM UTC

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.

SESSION 15

31

Jul

SESSION 15

Differentiation: definition and basic derivative rules

Mon 9:45 PM - 10:45 PM UTCJul 31, 9:45 PM - 10:45 PM UTC

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.

SESSION 16

1

Aug

SESSION 16

Office Hours

Tue 10:15 PM - 11:00 PM UTCAug 1, 10:15 PM - 11:00 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 17

4

Aug

SESSION 17

Office Hours

Fri 10:15 PM - 11:15 PM UTCAug 4, 10:15 PM - 11:15 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 18

5

Aug

SESSION 18

Differentiation: definition and basic derivative rules

Sat 9:45 PM - 10:45 PM UTCAug 5, 9:45 PM - 10:45 PM UTC

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.

SESSION 19

7

Aug

SESSION 19

Differentiation: definition and basic derivative rules

Mon 9:45 PM - 10:45 PM UTCAug 7, 9:45 PM - 10:45 PM UTC

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.

SESSION 20

8

Aug

SESSION 20

Office Hours

Tue 9:45 PM - 10:45 PM UTCAug 8, 9:45 PM - 10:45 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 21

11

Aug

SESSION 21

Differentiation: composite, implicit, and inverse functions

Fri 9:45 PM - 10:45 PM UTCAug 11, 9:45 PM - 10:45 PM UTC

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!).

SESSION 22

12

Aug

SESSION 22

Differentiation: composite, implicit, and inverse functions

Sat 9:45 PM - 10:45 PM UTCAug 12, 9:45 PM - 10:45 PM UTC

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!).

SESSION 23

13

Aug

SESSION 23

Differentiation: composite, implicit, and inverse functions

Sun 9:45 PM - 10:45 PM UTCAug 13, 9:45 PM - 10:45 PM UTC

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!

SESSION 24

14

Aug

SESSION 24

Differentiation: composite, implicit, and inverse functions

Mon 9:45 PM - 10:45 PM UTCAug 14, 9:45 PM - 10:45 PM UTC

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.)

SESSION 25

15

Aug

SESSION 25

Office Hours

Tue 9:45 PM - 10:45 PM UTCAug 15, 9:45 PM - 10:45 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 26

19

Aug

SESSION 26

Office Hours

Sat 9:45 PM - 10:45 PM UTCAug 19, 9:45 PM - 10:45 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 27

20

Aug

SESSION 27

Office Hours

Sun 9:45 PM - 10:45 PM UTCAug 20, 9:45 PM - 10:45 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 28

22

Aug

SESSION 28

Office Hours

Tue 9:45 PM - 10:45 PM UTCAug 22, 9:45 PM - 10:45 PM UTC

All questions, on homework, classwork, or just any topic in single variable calculus, are welcome!

SESSION 29

27

Aug

SESSION 29

Differentiation: composite, implicit, and inverse functions

Sun 9:45 PM - 10:45 PM UTCAug 27, 9:45 PM - 10:45 PM UTC

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!

SESSION 30

28

Aug

SESSION 30

Differentiation: composite, implicit, and inverse functions

Mon 9:45 PM - 10:45 PM UTCAug 28, 9:45 PM - 10:45 PM UTC

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!

SESSION 31

4

Sep

SESSION 31

Differentiation: composite, implicit, and inverse functions

Mon 9:45 PM - 10:45 PM UTCSep 4, 9:45 PM - 10:45 PM UTC

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.)

Public Discussion

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Jun 29 - Sep 4

10 weeks

45 - 60 mins

/ session

SCHEDULE

Sundays

9:45PM

Mondays

9:45PM