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Conceptual Calculus

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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 concepts[edit | edit source]

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

2. Infinite Questions with Finite Answers[edit | edit source]

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

3. Geometry of Functions[edit | edit source]

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

4. The derivative[edit | edit source]

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

5. How to use the derivative[edit | edit source]

  • Approximating a function by a polynomial

6. Infinite Series[edit | edit source]

7. Integration[edit | edit source]

8. How to use the integral[edit | edit source]