Skip to main content

Calculus 1A: Differentiation

Access on edX

This course is currently archived on edX. Certificate enrollment is closed.

About this course

How does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.

But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.

This course, in combination with Part 1, covers the AP* Calculus AB curriculum.

This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.

Learn more about our High School and AP* Exam Preparation Courses

This course was funded in part by the Wertheimer Fund.

*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

What you'll learn

  • How to evaluate limits graphically and numerically
  • The physical meaning, and geometric interpretation of the derivative
  • To calculate the derivative of any function
  • To sketch many functions by hand
  • To make linear and quadratic approximations of functions
  • To apply derivatives to maximize and minimize functions and find related rates


Abridged Syllabus


  1. Limit Laws
  2. Continuity
  3. Intermediate Value Theorem


  1. Introducing the Derivative
  2. Rules for differentiation of all known functions
  3. Approximations

Applications of Differentiation

  1. Curve Sketchingv
  2. Optimization
  3. Related Rates

Course staff

David Jerison

Professor of Mathematics Massachusetts Institute of Technology

Gigliola Staffilani

Abby Rockefeller Mauzé Professor of Mathematics Massachusetts Institute of Technology

Jennifer French

Lecturer & Digital Learning Scientist Massachusetts Institute of Technology

Stephen Wang

Associate Teaching Professor Rice University

  1. Course Number:

  2. Classes Start:

  3. Classes End:

  4. Estimated Effort:

    6–10 hours per week
  5. Length:

    13 weeks
  6. Year Created: