Conceptual Calculus

Welcome to calculus, a branch of mathematics rooted in the study of "infinity". Many books about calculus have already been written, with some more approachable than others. The purpose of this text is to provide an accessible and well-motivated introduction to the subject, without sweeping the formalities under the rug.

1. Core conceptsEdit

  • Everything you'll ever need to know about calculus (the rest is details)

2. Infinite Questions with Finite AnswersEdit

  • Infinite sequences of numbers
  • The real numbers
  • Functions of real numbers
  • The limit of a function

3. Geometry of FunctionsEdit

  • Familiar Functions, Familiar shapes
  • Slope
  • Area
  • Length
  • Volume

4. The derivativeEdit

  • Secant lines and rates of change
  • Defining the derivative
  • Computing derivatives
  • Linear approximation

5. How to use the derivativeEdit

  • Approximating a function by a polynomial

6. Infinite SeriesEdit

7. IntegrationEdit

8. How to use the integralEdit