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 Please open this box if you are new to the site.
First, welcome! We hope we’ll be able to help you learn Calculus as well as you’d like.

If you can, begin your Calculus studies with Chapter 1: “Introductory Ideas,” where we lay the groundwork for what’s to come. You’ll immediately be doing easy Calculus calculations, and we’ll just keep building from there!

And if you need to jump into a later topic because that’s where you are in your course, by all means please do.

Either way, we and the rest of our learning community are eager to help you learn well. Please join us on the Forum and let us know what questions and thoughts you have. We hope to see you there!

Due to the evolution of our site, our material exists in two forms:

  • “Chapter > Section > Topic”: Our new material goes screen-by-screen, so you can build your solid understanding step-by-step. We’ve crafted focused, interactive Desmos calculators so you can explore key ideas for yourself, and hence apply those new ideas to each new problem type you encounter. The accompanying Check Questions and Practice Problems (all of course with complete solutions a click away) are then focused on that screen’s material.
  • “Legacy Material”: By contrast, our Legacy Material treats each Topic on a single screen, with a brief summary at the top and then Practice Problems with complete solutions. Previous students have found these pages quite helpful; they’re just not nearly as developed as the new material.

The tables below show all of the content currently on the site (except for Blog posts). They also show how the Legacy Material aligns with the new material. Please dive in wherever would be most helpful to you!

CHAPTER 1: Introductory Ideas

(single screen)
A. First Calculations; Linear Approximations; DifferentialsA.1 First Calculus Calculations: Simple Motion
A.2 Generalizing to Other Rates of Change
A.3 Introducing Linear Approximations;
A.4 Linear Approximations: Practice Problems Approximations
A.5 Differentials;
     Begin to Determine $\dfrac{df}{dx}$ at $x=a$
B. Average Rate of Change; Better estimate for $\dfrac{df}{dx}$ at $x = a$ B.1 Average Velocity for a Trip;
Over Any Interval
B.2 Generalizing Average Rate of Change
B.3 Lab 1: Approximate and Bound Error of $\dfrac{df}{dx}$

CHAPTER 2: Limits & Continuity

(single screen)
A. The Concept of Limits A.1 Limits Introduction
A.2 Tolerance and Pancake Story
A.3 Epsilon, Delta, and Formal Limit Definition
A.4 Lab 2: Find a Limit Using Approximations
A.5 Some Limits That Exist; Some That Do Not
A.6 One-Sided Limits
A.7 Vertical Asymptotes
B. Calculating Limits B.1 Limit LawsB.2 Evaluating Limits: Problems & Solutions
B.3 Substitution to Find a Limit
B.4 Factor to Find a Limit
B.5 Use Conjugates to Find a Limit
B.6 Use Algebra to Find a Limit
B.7 The Squeeze Theorem
B.8 Special Trig Limits
C. Limits at Infinity C.1 Introduction to Limits at Infinity Limits at Infinity: Problems & Solutions
C.2 The Epsilon Strip
C.3 Some Limits at Infinity that Exist; Some That Do Not
C.4 Some Limits at Negative Infinity
C.5 Limits of Polynomials
C.6 Limits of Rational Functions
C.7 Limits of Exponential and Logarithmic Functions
C.8 Limits at Infinity with Square Roots Limit at Infinity Problems with Square Roots
D. Continuity and Intermediate Value TheoremD.1 Continuity at a Point and Over an IntervalContinuity & Intermediate Value Theorem (IVT)
D.2 Discontinuity Types; Removable Discontinuities
D.3 Continuous Functions; Continuity Theorems
D.4 Intermediate Value Theorem

CHAPTER 3: The Derivative

This foundational Chapter is in progress!

CHAPTER 4: Calculating Derivatives

(single screen)
A. Derivatives of Polynomials, Exponential, & Trig Functions A.1 Derivatives of Constant, Linear, & Power FunctionsCalculate Derivatives
A.2 Derivatives of Exponential Functions
A.3 Derivatives of $\sin x$ and $\cos x$
B. The Product and Quotient Rules B.1 The Product Rule Calculate Derivatives
B.2 The Quotient Rule
C. The Chain Rule C.1 Chain Rule – Introduction Chain Rule
C.2 Chain Rule – Basic Practice
C.3 Chain Rule – Deeper Work
C.4 Chain Rule – Used to Find Yet More Derivatives
D. Implicit DifferentiationD.1 Explicitly and Implicitly Defined Functions
D.2 Implicit Differentiation Implicit Differentiation
Derivative of ln x
E. Inverse FunctionsE.2 Derivative of Inverse Functions

CHAPTER 5: Applications of Derivatives

We currently only have legacy material for this Chapter, but are working to get new material up soon.
(single screen)
Tangent & Normal Lines
Maxima & Minima
Curve Sketching
Mean Value Theorem
L’HΓ΄pital’s Rule
Related Rates

CHAPTER 6: The Integral and Integration

We currently only have legacy material for this Chapter, but are working to get new material up soon.
(single screen)
Definite Integration
Indefinite Integration

If you need help with something we don’t have materials for yet,
please feel free to ask on our Forum and we’ll do our best to assist!