Calculus • Series
AP Calculus AB+BC Bootcamp!!!! (For People Taking the Class in 2022-23)
PL
SS
Shadman S
This series ended on October 2, 2022. All 1:1 and group chats related to this series are disabled 7 days after the last session.
Series Details
About
Held every Tuesday+Thursday, starting July 5th!
I am 100% certified in Calculus and I took AP Calculus BC in 2021-2022, receiving a 5 on the exam. I will do my best to create the best first impression of calculus I can, though experienced learners are also welcome to come and review!
In this series, I expect to go over the entire curriculum of AP Calculus BC (but AB students are still welcome to join!), starting all the way from limits going all the way to infinite series! This series is meant to help people with a pre-existing understanding of pre-calculus, but I may review some of the topics in pre-calculus for the first session after orientation (don't worry: you won't need everything from pre-calc!). In any case, afterwards, we will focus on every BC unit for one to two days! If you need any 1-on-1 help, you can contact Shadman! Can't wait to see you all!
For eager people out there:
Here is a link to the AP Calculus AB curriculum on the College Board's official page (includes prerequisites):
https://apstudents.collegeboard.org/courses/ap-calculus-ab
Here is a link to the AP Calculus BC curriculum on the College Board's official page (includes prerequisites):
https://apstudents.collegeboard.org/courses/ap-calculus-bc
Here's a link to our syllabus (and master document on which all resources and materials are posted):
https://docs.google.com/document/d/1_IF7eaN43FBUdRv2kIoUxGFRvDIF-ejEWNjuOwLFHTs/edit?usp=sharing
✋ ATTENDANCE POLICY
You are free to attend/skip whichever sessions you want to an extent. If too many sessions are missed and no attempt is made to let us know why or to catch up, withdrawal is possible.
Dates
May 30 - October 2
Learners
96 / 100
Total Sessions
34
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
34
30
May
GQ
Session 1
General Calculus Q&A
Satrio and I want to hold a general Q&A - come with any BC Calc questions for this session - everything from limits to Taylor series is fair game!!!
4
Jun
GQ
Session 2
General Calculus Q&A
Second Q&A session - we just want to get to know you all more! See what questions you have and talk about math! Come for a fun session!
5
Jul
O
Session 3
Orientation
We will get to know each other + give a basic rundown of all the prerequisites for this class! Towards the end, we will hold a Kahoot! (This session is in the name of fun!!!)
7
Jul
R
Session 4
Review
We will go over precalculus as briefly as possible! We will skim over most of the technicalities of functions, but put emphasis on trigonometry and classes of functions (like rational and basic polynomials)! Towards the end, we will introduce limits! Please be sure to join if you want a refresher on pre-calc before the series officially begins! (*all prerequisites will be mentioned in this session*)
12
Jul
Lc
Session 5
Limits and continuity
Part 1: We will talk about the basic intuition from the last session + one-sided limits and then define continuity. There will be a lot of practice problems for this session, in which we will practice algebraic manipulation among other simplifying methods! Be ready to participate. If there is time, we will also answer questions in the end!
14
Jul
Lc
Session 6
Limits and continuity
Part 2: We will talk about the trig limits as well and the limit definition of Euler's number here. We will also talk about the Squeeze, Intermediate Value Theorem (IVT), and Extreme Value Theorem (EVT) s! There will be some minor proof-writing, but nothing too out of the ordinary! If needed, we may also review part 1.
19
Jul
Dr
Session 7
Differentiation: definition and basic derivative rules
We will talk about the basic principle of differentiation and define *differentiability* as a property (tangent lines!!), similar to continuity. We will also talk about differentiability's connections to continuity, and evaluate basic polynomial derivatives. The end of this session aims to prove the power rule for all natural numbers.
21
Jul
Dr
Session 8
Differentiation: definition and basic derivative rules
We will introduce and prove the product and quotient rules. We will also mention the trig and exponential/logarithm derivatives (only for bases of e), but we might not have time to prove it (maybe in an office hours). Also, we will emphasize differentiation is with *respect* to a single variable.
26
Jul
Df
Session 9
Differentiation: composite, implicit, and inverse functions
First, we will shortly review composite functions. Then, we will introduce and rigorously prove the chain rule (the most crucial rule in differentiation)!! We will also familiarize learners with the idea of differentiation as an operator (IMPLICIT) and work on reviewing all the rules we have learned so far.
27
Jul
Df
Session 10
Differentiation: composite, implicit, and inverse functions
We will fit in a session solely devoted to the differentiation of inverse functions! We will formally prove the power rule and the derivatives of inverse trig functions using implicit differentiation! We will also go over ways to find the derivative of an inverse in general and given a table! Kahoot in the end!!!
28
Jul
Df
Session 11
Differentiation: composite, implicit, and inverse functions
We will fit in a session solely devoted to the differentiation of inverse functions! We will formally prove the power rule and the derivatives of inverse trig functions using implicit differentiation! We will also go over ways to find the derivative of an inverse in general and given a table! Kahoot in the end!!!
30
Jul
Cd
Session 12
Contextual applications of differentiation
We will cover motion problems (differential calculus only) and cover related rates (implicit very important). We will also cover basic geometric theorems for people to effectively use related rates.
2
Aug
Cd
Session 13
Contextual applications of differentiation
We will prove and use L'Hopital's rule to evaluate limits previously inaccessible to us using derivatives. We will also introduce local and global extrema and talk about simple cases: do some graphical local and global extrema evaluation problems.
3
Aug
Cd
Session 14
Contextual applications of differentiation
We will prove and use L'Hopital's rule to evaluate limits previously inaccessible to us using derivatives. We will also introduce local and global extrema and talk about simple cases: do some graphical local and global extrema evaluation problems.
4
Aug
Af
Session 15
Applying derivatives to analyze functions
We will prove Fermat's local extrema theorem and the MVT (Rolle's special case and the general theorem) here!!! Afterward, we will do more complex local minimum problems (algebraically instead of graphically).
10
Aug
Af
Session 16
Applying derivatives to analyze functions
We will explain the relatively straightforward concept of differentiating twice (second derivative) and allude to the possibility of differentiating more than once. We will spend more time on concavity and how it relates to the second derivative and the second derivative test for verifying local minimums and maximums. If we have time, points of inflection (PoI) will be covered in this session (basically critical points of the first derivative), and introduce optimization (with allusions to related rates).
13
Aug
Af
Session 17
Applying derivatives to analyze functions
We will explain the relatively straightforward concept of differentiating twice (second derivative) and allude to the possibility of differentiating more than once. We will spend more time on concavity and how it relates to the second derivative and the second derivative test for verifying local minimums and maximums. If we have time, points of inflection (PoI) will be covered in this session (basically critical points of the first derivative), and introduce optimization (with allusions to related rates).
14
Aug
Af
Session 18
Applying derivatives to analyze functions
We delve further into the topic of optimization and solve some problems on the topic. We will also review basic polynomial instincts - end behavior, graph shape, roots, even vs. odd, etc. Kahoot in the end!!!
16
Aug
Ic
Session 19
Integration and accumulation of change
We will talk about the area under the curve and talk about Riemann sums (left, right, trapezoidal, midpoint). We will also talk about how increasing/decreasing and concave-up/concave-down portions of the graph result in over/underestimates of the Riemann sums. We will not mention the i-word at all :)
19
Aug
Ic
Session 20
Integration and accumulation of change
Shadman will prove the FTC (both parts!!!) and talk about how important of a theorem this is (there is a reason why it is the fundamental theorem of calculus). Afterwards, we will introduce the concept of indefinite integrals and definite integrals, and talk about reverse power rule and introduce the intuition of u-substitution.
23
Aug
Ic
Session 21
Integration and accumulation of change
Integration Techniques - Satrio says, "The most important part of calculus!!!"
After introducing standard integrals (which we will prove along the way/call your attention to the derivatives unit), we will start with u-substitution from the session before. Such an important step that we will spend an entire session on just u-sub.
25
Aug
Ic
Session 22
Integration and accumulation of change
We will introduce the reverse product rule, by which Satrio means integration by parts (IBP). An interesting mnemonic we can use to aid the process will also be introduced, along with a helpful method (tabular method). We will also review polynomial long division, and briefly talk about PFD.
30
Aug
O
Session 23
Orientation
Today we look to a new beginning to this series! I will explain how sessions will commence in light of my school year, and the new way I will teach the class.
3
Sep
Cd
Session 24
Contextual applications of differentiation
We will cover motion problems (differential calculus only) and cover related rates (implicit very important). We will also cover basic geometric theorems for people to effectively use related rates.
4
Sep
Cd
Session 25
Contextual applications of differentiation
We will prove and use L'Hopital's rule to evaluate limits previously inaccessible to us using derivatives. We will also introduce local and global extrema and talk about simple cases: do some graphical local and global extrema evaluation problems.
11
Sep
Cd
Session 26
Contextual applications of differentiation
We will prove Fermat's local extrema theorem and the MVT (Rolle's special case and the general theorem) here!!! Afterward, we will do more complex local minimum problems (algebraically instead of graphically).
13
Sep
Cd
Session 27
Contextual applications of differentiation
We will go over more related rates. Then we will talk about the value theorems, IVT, EVT, and MVT. If we have time there will be some proofs!
17
Sep
Af
Session 28
Applying derivatives to analyze functions
We will explain the relatively straightforward concept of differentiating twice (second derivative) and allude to the possibility of differentiating more than once. We will spend more time on concavity and how it relates to the second derivative and the second derivative test for verifying local minimums and maximums. If we have time, points of inflection (PoI) will be covered in this session (basically critical points of the first derivative), and introduce optimization (with allusions to related rates).
18
Sep
Cd
Session 29
Contextual applications of differentiation
Today we are going to review related rates one last time before we go back to limits for a bit. We will discuss L'Hopital's rule, and since that should be quite short, we should have time to talk about local and global extrema too!
25
Sep
Cd
Session 30
Contextual applications of differentiation
Any discussion of extrema has to lead here. After some graphical and table identification exercises, we will talk about Fermat's theorem. We will take this slowly and easily, but I anticipate ending around Rolle's theorem.
26
Sep
Cd
Session 31
Contextual applications of differentiation
Any discussion of extrema has to lead here. After some graphical and table identification exercises, we will talk about Fermat's theorem. We will take this slowly and easily, but I anticipate ending around Rolle's theorem.
27
Sep
Cd
Session 32
Contextual applications of differentiation
We will extrapolate Rolle's to the MVT! After this, we will do basically tons of MVT practice, and if we need, we will review all the VTs! Also, last session of the unit: stay a bit longer if you have any questions (full review session will be after next unit.)
1
Oct
Af
Session 33
Applying derivatives to analyze functions
Yay for optimization! We already know what extrema are and about Fermat's theorem, so we will talk about critical points now. This means bunch of differentiation practice and root finding :(
2
Oct
Af
Session 34
Applying derivatives to analyze functions
I feel like we should be ready to do inflection points after small review of the last session, so we will definitely talk about concavity (both precalculus and calculus definitions). Then we will go into second-order optimization. :)