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edX Calculus 1A: Differentiation

Massachusetts Institute of Technology via edX

  • Overview
  1. edX
    Platform:
    edX
    Provider:
    Massachusetts Institute of Technology
    Length:
    12 weeks
    Effort:
    6-10 hours a week
    Language:
    English
    Credentials:
    Paid Certificate Available
    Overview
    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.

    Learn more about our High School and AP* Exam Preparation Courses
    Calculus 1B: Integration
    Calculus 1C: Coordinate Systems & Infinite Series

    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
    Syllabus
    Abridged Syllabus


    Limits
    1. Limit Laws
    2. Continuity
    3. Intermediate Value Theorem
    Differentiation
    1. Introducing the Derivative
    2. Rules for differentiation of all known functions
    3. Approximations
    Applications of Differentiation
    1. Curve Sketching
    2. Optimization
    3. Related Rates

    Taught by
    David Jerison

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