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Calculus • Series

Introduction to Calculus AB

Piyush M

Series Details

Sessions

Public Discussion

This series ended on August 10, 2024. All 1:1 and group chats related to this series are disabled 7 days after the last session.

Series Details

About

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.

✋ ATTENDANCE POLICY

Please try to attend all of the sessions, but message me beforehand if you can't make it!

Dates

August 5 - August 10

Learners

9 / 15

Total Sessions

5

About the Tutor

I'm a rising high school junior from Texas in the United States. I'm here to share my knowledge and experience in math, which is one of my passions. Currently, I'm going into Differential Equations and preparing for various math and computer science competitions like the AMCs and AIME. Aside from those, I do Science Olympiad, Science Fair, Debate, FTC Robotics, and DECA. I also coach middle schoolers in competitive mental math outside of Schoolhouse. I believe that high-quality education should be free and equal for everyone, which is why I'm a tutor on Schoolhouse :) Of course, there is still a lot that I don't know, and I'm here to hopefully learn a bit as well. I want to help everyone feel confident in their subjects, be it math, physics, chemistry, biology, the SAT, and beyond - if you have any questions at all, or need any support in these topics, I am always happy to help you out!

View Piyush M's Profile

Upcoming Sessions

0

Past Sessions

5
5
Aug

Session 1

Limits and continuity

- Definition of limit and continuity
- Types of discontinuities
- Intermediate Value Theorem
- Extreme Value Theorem
- Evaluating limits using graphs and tables
- Evaluating limits using direct substitution
- Evaluating limits using algebraic manipulation
- End behavior and asymptotes
6
Aug

Session 2

Differentiation: definition and basic derivative rules

- Average vs. instantaneous rates of change
- Limit definition of a derivative
- Differentiability criteria for a function
- Common derivatives to memorize
- Derivative rules for addition/subtraction
- Power rule
- Product rule
- Quotient rule
- Mean value theorem/Rolle's Theorem
7
Aug

Session 3

Differentiation: composite, implicit, and inverse functions

- Review of composite functions
- Chain rule
- Implicit differentiation
- Differentiation of inverse functions
- Differentiation of inverse trig functions
- Higher-order derivatives
- L'Hôpital's rule

(NOTE: Curve sketching and related rates are not covered in our discussion of differentiation.)
8
Aug

Session 4

Integration and accumulation of change

- Accumulations of change
- Definition of the integral
- Definite and indefinite integrals
- Definite integrals as "area under the curve"
- Riemann sums
- Average value of a function
- Fundamental Theorem of Calculus
- Reverse power rule
- Common indefinite integrals to memorize
- Using u-substitution to integrate a function

(NOTE: Volumes of solids are not covered in our discussion of integration.)
9
Aug

Session 5

Differential equations

- Definition of a differential equation
- Solving differential equations
- Verifying solutions of differential equations
- Definition of slope fields
- Graphing of slope fields
- Application of slope fields

Public Discussion

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