#### Calculus

#### Calculus

### Calculus Series

## Introduction to Calculus AB

Started

In this series we will cover a rough introduction of calculus, including the ideas of limits, differentiation, and integration. This series will cover these topics at the level of AP Calculus AB, and can serve either as preparation for AP Calculus AB or review for AP Calculus BC.

Piyush M

## Get a 5! - AP Calculus BC/Calc II in a Month

Started

I got a 5 on the AP Calculus BC exam, and you can too. Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2, including a FULL work-through of a real past exam. The first two sessions will serve as a review of differential calculus. Below are what we will cover: INTEGRATION AND APPLICATIONS (UNIT 1) 1. Introduction to accumulation of change 2. Left and right Riemann sums; over and under-approximation 3. Midpoint and trapezoidal sums 4. Definition of indefinite integral using as the limit of Riemann sums 5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals 6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation. 7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds. 8. The reverse power rule, u-substitution, and integration by parts 9. Antiderivatives of all the previously mentioned functions 10. Improper integrals 11. Finding the average value of a function on an interval 12. Connecting position, velocity, and acceleration functions using integrals 13. Using accumulation functions and definite integrals in applied contexts 14. Finding the area between curves expressed as functions of x 15. Finding the area between curves expressed as functions of y 16. Finding the area between curves that intersect at more than two points 17. Volumes with cross sections: squares and rectangles 18. Volumes with cross sections: triangles and semicircles 19. Volume with disc method: revolving around x- or y-axis 20. Volume with disc method: revolving around other axes 21. Volume with washer method: revolving around x- or y-axis 22. Volume with washer method: revolving around other axes 23. The arc length of a smooth, planar curve and distance traveled 24. Calculator-active practice DIFFERENTIAL EQUATIONS (UNIT 2): 1. Modeling situations with differential equations 2. Verifying solutions for differential equations 3. Sketching slope fields 4. Reasoning using slope fields 5. Approximating solutions using Euler’s method 6. Finding general solutions using separation of variables 7. Finding particular solutions using initial conditions and separation of variables 8. Exponential models with differential equations 9. Logistic models with differential equations PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3): 1. Defining and differentiating parametric equations 2. Second derivatives of parametric equations 3. Finding arc lengths of curves given by parametric equations 4. Defining and differentiating vector-valued functions 5. Solving motion problems using parametric and vector-valued functions 6. Defining polar coordinates and differentiating in polar form 7. Finding the area of a polar region or the area bounded by a single polar curve 8. Finding the area of the region bounded by two polar curves 9. Calculator-active practice INFINITE SERIES (UNIT 4): 1. Defining convergent and divergent infinite series 2. Working with geometric series 3. The nth-term test for divergence 4. Integral test for convergence 5. Harmonic series and p-series 6. Comparison tests for convergence 7. Alternating series test for convergence 8. Ratio test for convergence 9. Determining absolute or conditional convergence 10. Alternating series error bound 11. Finding Taylor polynomial approximations of functions 12. Lagrange error bound 13. Radius and interval of convergence of power series 14. Finding Taylor or Maclaurin series for a function 15. Representing functions as power series

Jose Roberto Cossich G

## AP Calculus AB/BC Overview + Practice Questions with 5 Scorer

Started

This series is for prospective AP Calculus AB/BC students. We will be covering all units in AP Calculus BC (which includes all units of AP Calculus AB) and will solve questions from Barron's. All learners are expected to prepare a graphing calculator for every session.

Jeesung L

## AP Calculus AB Head Start

Started

Get a head start on AP Calculus AB before the school year begins. Join multiple sessions to master AP Calculus AB. Units 1-8 will be covered in the series.

Carlos C

## AP Calculus AB/BC

Started

READ FULLY! Hey there! I am Kishan, a rising senior. I enjoy math a lot, particularly calculus - which I developed an interest for in 10th grade. I am currently halfway through teaching myself Calc III and a certified calculus tutor in Schoolhouse. This series is a relatively fast paced course that will cover the entirety of the AP Calculus AB/BC curriculum. We will start from the ground up, introducing ourselves to limits, derivatives, integrals, etc...So, if you are here to learn BC, consider skipping until UNIT 5. Hope you enjoy me as your tutor. I am going to add sessions as we go through the series.

kishan p

## AP Calculus AB/BC Unit 3 intensive learning

4th session

In this series, we will pick up from a series I hosted a while ago that I had to end early. We will be learning all of the topics from unit 3 of the AP Calculus AB/BC curriculum. This series serves as a complete guide for unit 3 and covers EVERY topic in unit 3 according to the syllabus given out by College Board. We will also go over a single topic from unit 4 that is connected to limits in unit 1. Feel free to ask me to cover additional topics from other Units! Additional notes: There will be a quick warm up question each lesson to refresh our minds about last lesson's topics. I will assign homework each lesson via google form but you DO NOT need to do it, it is on you if you feel like you want more practice. If you choose to do the homework, you will receive your grades back from google form. There will be a final exam on ALL of the units we covered before and here(units 1-3). Once again, you do not need to do any test if you do not want to. The test is there just for you to know your current understanding about the topics. Have fun!

Jiarui X

## Differentiation: composite, implicit and inverse functions

3rd session

Welcome to an exciting journey into the fascinating realm of calculus! In this thoughtfully designed series, tailored specifically for high school students, participants will embark on an exploration of the fundamental techniques of differentiation. Throughout our engaging sessions, we'll focus on unraveling the intricacies of composite functions, inverse functions, and implicit differentiation. What You'll Master: Unraveling Composite Functions: Gain proficiency in dissecting and differentiating functions nested within one another. Discover how to navigate through layers of complexity with ease using the powerful chain rule. Navigating Inverse Functions: Delve into the intricacies of inverse functions, learning how to differentiate and manipulate them effectively. Understand their role in solving equations and their significance in real-world applications. Mastery of Implicit Differentiation: Step into the realm of implicit functions, where equations aren't explicitly defined. Master the technique of implicitly differentiating these functions, crucial for tackling advanced calculus problems and scenarios.

WASAY H

## Calculus: Fundamentals of Derivatives, Applications of derivatives and many more

4th session

In this series, we will be looking at one of the most fundamental concepts in calculus- derivatives. We will begin with the basic concepts in this course and work our way up to solving more complex and fun exercises. Come along, it'll be fun:)

Rodas G

## AP Calculus® Summer Bootcamp (2024-25)

25th session

In this series we will be going over the AP Calculus AB/BC curriculum in a lecture-style format with tons of practice along the way. This series is perfect for anyone taking AP Calculus in the upcoming school year as we’ll spend time on various concepts to not only get you ready for AP Calc, but to fully understand it for the AP national Exam. Note: All sessions have not been added, however there are only 4 more (reflected on syllabus). This series will end on August 22, 2024 -- Syllabus: [https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) [](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) Course structure: Instead of using existing lecture notes or following the order of the AP Calc curriculum, I have optimized the structure of our sessions so that we maximize the time learning important concepts and for understanding them. At the end, you will end up learning majority of the course. And by doing the practice problem sets (discussed later), you could master the entire curriculum. Lecture Notes: These will be posted in advance of about 2-3 sessions. You do not have to worry about printing them as they would be very minimal and I promote the idea of writing as I go so we all can stay at a good pace. Please write along as I do so that you can take the complete benefit of our sessions. Practice Problem Set and Homework: While each session will be done with the assumption that you haven't done the practice problems, they are still there for your benefit. However, in my many semesters of being in calculus classes, those who grind practice problems are the most successful. There is almost a direct correlation. Note about structure of sessions: Even though they are just 1hr 15min, I have left 45 minutes after our session for those who want to stay and ask me questions and/or go over additional practice. I will be available entirely from 3pm to 5pm. But for those who are feeling fine can leave freely! [](https://www.dropbox.com/scl/fi/pycxtn037zvay601f15zd/Syllabus-AP-Calc-Summer-2024-Bootcamp-3.pdf?rlkey=imq7wbft89tb08uc96wdb0x60&e=1&st=5bgmngz4&dl=0) Questions/Talk to me: I will dedicate my time to entirely ensuring that every student in my session is able to understand the concepts completely. I will always be available to ensure that you understand the concepts and practice problems. And if you have any other questions about high school, college admissions, etc, feel free to let me know!

Ammar R

## One-on-One AP Calculus AB Tutoring

3rd session

This is meant to be for one learner only. We will go over AP Calculus AB topics starting from basic derivatives. Strong background in algebra and precalculus is required.

Divya N

## Calculus Derivatives and Integrals

Starts

I will be covering derivatives and integrals. Try to unmute your mic and talk about any questions you might have or if you know how to solve the questions

Divyesh N

## 10-day Introduction to Calculus!

10th session

Are you planning to take Calculus classes? In this series, I'll give you the conceptual understanding and the practical strategies that will allow you to succeed in your high school classes, especially for AP Calculus AB and BC. For 10 days, I'll do my best to combine theory with practice, understanding together the material and working together on questions. In the process, I promise you that you will have a lot of fun! All sessions will be very interactive, insightful, and fun! I hope that at the end of the series, you will leave our virtual classroom with a calculus enthusiasm and knowledge that will fuel your high school calculus journey!

Luca G

## Pure Linear Algebra

Starts

This is a full first course on proof-based linear algebra. Sessions are 1h30m daily except for Sunday, so the course is at an accelerated pace. Prerequisites: -Algebra 2 with trig (with Calculus preferred but not required) Syllabus: Unit 1 1. Basic vector operations in R^n Unit 2 2. Vector Spaces and Subspaces 3. Linear independence and Gram-Schmidt 4. Projections and Fourier's Formula Unit 3 5. Linear Transformations, Properties, and Kernel 6. Matrix operations, special matrices, and matrix properties Unit 4 7. Determinants, Linear Systems, and Inverse Matrices 8. LU decomposition 9. Row, Column, and Null Space, Rank and Nullity Unit 5 10. Change of Basis and Matrix Multiplication 11. Eigeneverything and Diagonalizability Unit 6 12+ Special Topics We will use Bronson's "Linear Algebra - Algorithms, Applications, and Techniques" as our main text[](http://ndl.ethernet.edu.et/bitstream/123456789/24629/1/Richard%20Bronson.pdf) in addition to Stanford's Math 51 for supplemental reading (fragments taken under fair use law which will be posted gradually). Note: Required reading of 25 pages a week + Weekly homework (with feedback) + 1 test per unit (with review in-class and the tests graded with feedback).

Jose Roberto Cossich G

## Ultimate AP Calculus AB/BC Summer Series

7th session

Each week, we will go over one unit in the entire AP Calculus AB/BC course. Every session will also include a bunch of previous free-response questions and multiple-choice questions relevant to the topic.

Francis Anthony G

## Multivariable Calculus and Applied Linear Algebra

27th session

Hey everyone, it's finally here! Calculus 3 (the equivalent of the first semester of a full-year course). NOTE: REQUIRED READING OF APPROXIMATELY 25 PAGES A WEEK + WEEKLY HOMEWORK (with feedback) + 1 TEST PER UNIT (in-class and graded with feedback) Prerequisites: - Calculus 1 and 2 (the equivalent of Calc BC) CONTENT COVERED: (UNIT I) Basic Vector Operation 1. Vector geometry in R^n 2. Planes in R^3 3. Span, subspaces, and dimension 4. Basis and orthogonality 5. Cross Products (UNIT II) Partial Derivatives and Applications 6. Multivariable functions, level sets, and contour plots 7. Partial derivatives and contour plots 8. Maxima, minima, and critical points 9. Gradients, local approximations, and gradient descent 10. Constrained optimization via Lagrange multipliers (UNIT III) Basic Matrix Operations 11. Linear functions, matrices, and the derivative matrix 12. Linear transformations and matrix multiplication 13. Matrix algebra 14. Multivariable Chain Rule 15. Matrix inverses and multivariable Newton’s method for zeros (UNIT IV) Further Matrix Properties 16. Linear independence and the Gram–Schmidt process 17. Matrix transpose, quadratic forms, and orthogonal matrices 18. Linear systems, column space, and null space 19. Matrix decompositions: QR-decomposition and LU-decomposition (UNIT V) Motivating the Second Derivative Test 20. Eigenvalues and eigenvectors 21. Applications of eigenvalues: Spectral Theorem, quadratic forms, and matrix powers 22. The Hessian and quadratic approximation 23. Application of the Hessian to local extrema

Jose Roberto Cossich G

## Calculus Review

Starts

End-of-summer course designed to review key concepts of AP Calculus AB + additional topics in preparation for taking AP Calculus BC or any other higher level calculus course in the upcoming school year.

Cencen W

## Rigorous Calculus Course

4th session

In this series we will cover the proofs behind well known theorems in Calculus. Learners will learn the techniques and strategies involved in proving and deriving mathematical theorems, as well as achieve a deeper understanding of each theorem they prove. Learners will engage by answering questions and doing exercises that will guide them to understand the proofs.

Thomas S

## AP Calculus AB: Path To A 5

18th session

Join the AP Calculus Mastery course and master every aspect of Calculus 1. Through rigorous practice, detailed explanations, and interactive discussions, I'll prepare you for a 5 score on the AP Calculus AB Exam. Sessions, typically are 1 hour long, and focus on solving practice problems, supplemented with extra explanations & justifications. The goal is to finish the course before the end of summer but at least finish enough content where you're still a step ahead before the school year begins. I will guide you through each problem, offer clear explanations, and foster collaborative learning. Get ready to excel this summer!

Dhruv Y

## Learn AP Calculus AB + BC over the Summer

22nd session

In this series, we will go over all 10 units of the AP Calculus BC course, covering 1 unit per week. Each week I will host 1 session teaching the units and later in the week, I will host a session where we will solve problems about the unit together.

Sahasra J

## Multivariable Calculus - Integration and Vector Analysis

Starts

Are you interested in learning Calculus 3? Well, this course is the equivalent of a second-semester course, a continuation of my last series. Don't worry though if you weren't there. This series can be taken by anyone who has completed the only prerequisite: Calculus 1 (with integration) and the rest of the necessary background information will be covered or reviewed in the initial sessions. NOTE: Required reading of about 35 pages a week (for units 2 and 3 only)+ weekly homework (with feedback) + 1 test per unit (inside or outside of class depending on time but always graded with feedback within 2 days) Sessions are between 1h15m to 1h30m. Content Covered: (UNIT I) Single-Variable Integration and Vector Analysis 1. Physical interpretations of the integral and the average value of a function over an interval 2. Finding the area between curves expressed as functions of y 3. Finding the area between curves that intersect at more than two points 4. Volumes with cross sections: squares, rectangles, triangles, and semicircles 5. Volume with the disc and washer method: revolving around x-, y-, and different axes 6. Arc length, distance traveled, and unit calculator practice 7. Defining and differentiating parametric vector-valued functions 8. Finding arc lengths of curves given by parametric equations and solving motion problems 9. Defining polar coordinates and differentiating in polar form 10. Finding the area of a polar region bounded by one and multiple polar curves, and unit calculator practice. 11. Finding the surface area of surfaces or revolution, including in polar coordinates. (UNIT II) Multivariable Integration and Applications 11. Formulating Riemann sums 12. The Double Integral and Iterated Integral 13. Applications of The Double Integral 14. Triple Integrals 15. The Jacobian and uv-substitution 16. Integration in Polar, Cylindrical, and Spherical Coordinates 17. Applications of Triple Integrals (Unit III) Multivariable Vector Analysis 18. Scalar-valued Line Integrals 19. Vector-valued line integrals 20. Path Independence 21. Exact Differentials 22. Divergence and Green's Theorem 23 Curl, Stokes' Theorem, and parameterizing surfaces. 24. Flux and Divergence Theorem 25+ (applications to Electrodynamics and other special topics?)

Jose Roberto Cossich G

## Get Ready For AP Calculus AB

8th session

I will be covering Units 1-8 of the Collegeboard AP Calculus AB course. I will be following the Collegeboard curriculum. This course will require around 1-2 hours of work outside of our sessions because I am very briefly running through these topics (each unit has 5-14 topics) as a prep course for AP Calc AB. By the beginning of August, my goal is to cover all of Unit 1, so that you are all prepared for the upcoming school year. During our sessions, I encourage you to ask questions and try your best to participate and work through problems.

Deepthi S

## AP Calculus AB Prep: Full Overview

15th session

We will go through every unit of the AP Calculus AB Exam. There will be both lectures and practice tests to prepare for both the school-year and the AP exam. It will be a fast-paced class, in order to try to cover everything.

Joy L

## Flipped Classroom - AP Calculus AB Summer Crash Course

8th session

This five-week series will function with a flipped classroom - meaning you'll learn topics in your own time, practicing and ask questions during the sessions. This series is designed to be very fast paced and learner-oriented, so expect to be active in sessions and dedicate some time to learning whenever it fits your own schedule! I will not be giving lectures. Communication through microphone is preferred, but I understand completely if you would rather use the chat. Sessions will be twice a week on Wednesdays and Sundays at 7:30 PM PT. The plan is to cover the AP Calculus AB curriculum by mid-August. If you plan on registering as a learner, please read the following: Outside sessions: - Watch videos and do Khan Academy practice problems - Write a problem and solution (this isn't nearly as hard as it sounds, don't fret!) During sessions: - We'll start off by checking in to see if there's any specific questions from learners - Learners will pick a topic from what we're covering that session and give a brief explanation, presenting their practice problem (other learners will try to solve it and give feedback on the problem) - We'll wrap everything up with some more practice problems! This can all sound very intimidating at first, but it'll get easier with practice! AP Calculus AB can be challenging, and I hope that this series helps serve to prepare for that challenge during the school year. Resources are currently TBD. Co-hosts welcome (please DM first)!

Margaret S

## Get Ready For Fall: AP Calc AB/BC First 5 Units!

Starts

In this course, we will go over 2 units a week. This course aims to help you get a head start for the upcoming year and have a solid understanding of many calculus concepts (limits, derivatives, and more)! (The timing for sessions isn't set in stone yet, and I'm also happy to move some things around in order to meet everyone's schedule. More sessions will also be added, we will be going over the first five units!)

Vikram S

### Calculus Sessions

#### Today

## Schoolhouse Calculus Jeopardy 2024

8:00 AM - 10:00 AM

**Dylan P**, **Hind S**, and 1 other

## Help for Seth O

5:00 PM - 6:00 PM

Jai P

## Help for Amira A

6:00 PM - 7:00 PM

Jai P

## Introduction to Integrals: A Calculus Workshop

11:15 PM - 12:15 AM

Nuv A

#### Tuesday, August 13

## Integral Adventures: The Quest for the Antiderivative

3:00 PM - 4:00 PM

Max F

## Understanding Limits and Continuity for AP Calculus AB/BC

3:30 PM - 4:30 PM

Sumedh R