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Calculus Home

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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!

Calculus 1 Chapters

Zoom in around point (9,3) on graph of sqrt(x) to show linear approximation

Introductory Ideas

Show/Hide Partial Chapter Contents
  • First Calculus Calculations: Simple Motion
  • Generalizing to Other Rates of Change
  • Introducing Linear Approximations and Differentials
  • Average Rate of Change
  • Estimating df/dx at x = a

Static image of graph used in Limits Lab

Limits & Continuity

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  • Introduction to Limits
  • “Tolerance;” Epsilon, Delta & Formal Limit Definition
  • Approximations to Find a Limit (Lab)
  • Limits that Do and Do Not Exist
  • One-sided Limits
  • Vertical Asymptotes
  • Calculating Limits: limit laws, substitution, factor, use conjugates, …
  • The Squeeze Theorem; Special Limits
  • Limits at Infinity: the meaning, some that do/do not exist, limits of polynomials, rational functions, exponentials and logarithms, computing limits at infinity with square roots
  • Continuity & The Intermediate Value Theorem

All of course with problems for you to practice, each with a complete solution one click away.


Calculating Derivates Chapter cover, featuring the Product Rule

Calculating Derivatives

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  • Derivatives of Polynomials, Exponentials, Trig Functions, …
  • Product and Quotient Rules
  • Chain Rule
  • Implicit Differentiation
  • Derivatives of Inverse Functions

More Chapters are coming very soon — please see below.

Legacy Material: Summaries & Practice Problems (with solutions)

The material below does not have the depth or interactivity of the material above. Instead each single screen contains a summary of the key ideas, along with practice problems (each of course with a complete solution one click away). Previous students have found these pages quite helpful; they’re not just not nearly as developed as the full Chapters above.

We will be releasing the remaining fully-developed chapters for Calculus 1 in the coming weeks. Please check back — or, better, join the Forum for upcoming announcements!

Calculus 1 (Legacy)