Beyond Calculus




Limits and Continuity


Applications of Derivatives


Applications of Integrals

Beyond Calculus is designed for students currently taking Calculus.

About the Author

Welcome to Beyond Calculus



Developed by Jake Chipps



Why Use This Site?

Beyond Calculus is an online video-based textbook that provides support to students taking AP Calculus AB. Are you sitting at home wracking your brains over your homework, and need help? Try watching the videos in whatever section you are stumped. Is your math class going too fast? The instructional videos on this site may just provide the understanding you need to excel. Cramming for the AP exam or a final? Why not review by going through this e-book? You will find instructional videos here rather than academic text.

How to Use This Site

Each section of Calculus A and B is organized in the table of contents. Click on any topic to view that particular lesson. Videos are organized to enhance understanding. The first video provides a big-picture view of the topic, and each subsequent video provides the user with more difficult examples. For the best experience, It is suggested that you press pause when you need to think about a concept. Rewatch videos if necessary, and you will be amazed at your level of understanding by the end.

Why Is This E-Book Free?

Information should be free and available to all. Not only should information be free, but it should be available anywhere at any time. This e-book can be viewed on all devices, including desktops, iPads and other mid-size devices, and phones with internet access. After creating online videos to supplement and enhance my classroom instruction, I decided to compile my work into an online textbook. Rather than charge for these services, I am providing my work to the world free of charge, as it should be.



Graphing and Writing Linear Equations

Solving Polynomial Equations

Functions and Domain

Graphing and Writing Piece-Wise Functions

Topic in Trigonometry

Exponentials and Logarithms

Limits and Continuity


Limits: Tier One: Plug It in

Limits: Tier Two: Algebra Gymnastics

Limits: Tier Three: Vertical Asymptote

Properties of Limits


The Intermediate Value Theorem

Limits to Infinity and End Behavior

Analyzing the Global Behavior of Functions Using Limits



The Definition of the Derivative

Tangent Lines and Normal Lines


Properties of Derivatives

Power Rule

Derivatives of Different Types of Functions

Product Rule

Quotient Rule

Chain Rule

Implicit Differentiation

Derivatives of Inverse Functions

Derivatives and Physics

Applications of Derivatives


The Derivative as a Rate of Change

Increasing and Decreasing

Relative and Absolute Maximum and Minima

First Derivative Analysis

Concavity and Inflection Points

First and Second Derivative Analysis

The Graphical Interpretations of f, f ', and f ''

The Mean Value Theorem


Related Rates


L'Hospital's Rule



Approximating Integrals Using the Riemann Approximation Method (LRAM, RRAM, and MRAM)

Approximating Integrals Using Trapezoidal Rule

The Definition of the Integral with Notation

Integration Using Known Geometric Areas


The Definite Integral

The Fundamental Theorem of Calculus Part I

Integration by Substitution

Slope Fields

Initial Value Problems

Solving First Order Separable Differential Equations

Applications of Integrals


Modeling Exponential Growth and Decay

Using the Integral to Find Net Change

Net Change and Physics

Finding Areas Between Curves

Finding Volumes: Constructing Cross Sections on a Base

Finding Volumes: Solids of Revolutions Using Disc Method

Finding Volumes: Solids of Revolutions Using Washer Method

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