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edX Calculus 1C: Coordinate Systems & Infinite Series

Massachusetts Institute of Technology via edX

  • Overview
  1. edX
    Platform:
    edX
    Provider:
    Massachusetts Institute of Technology
    Length:
    8 weeks
    Effort:
    6-10 hours a week
    Language:
    English
    Credentials:
    Paid Certificate Available
    Overview
    How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.

    How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.
    1. Changing Perspectives
      1. Parametric Equations
      2. Polar Coordinates
    2. Series and Polynomial Approximations
      1. Series and Convergence
      2. Taylor Series and Power Series
    This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.

    Learn more about our High School and AP* Exam Preparation Courses
    Calculus 1A: Differentiation
    Calculus 1B: Integration

    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
    • To compute arc length
    • Methods for parameterizing curves
    • To do calculus in polar coordinates
    • How to approximate functions with Taylor polynomials
    • To determine convergence properties of infinite series
    Taught by
    David Jerison

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