link Source: www.edx.org
date_range Starts on February 15, 2023
event_note Ends on May 17, 2023
list 13 sequences
assignment Level : Intermediate
chat_bubble_outline Language : English
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Key Information

credit_card Free access
verified_user Fee-based Certificate
timer 78 hours in total

About the content

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

The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.

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

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.

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Syllabus

  • 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
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Instructors

David Jerison
Professor of Mathematics
Massachusetts Institute of Technology

Gigliola Staffilani
Abby Rockefeller Mauzé Professor of Mathematics
Massachusetts Institute of Technology

Jennifer French
Digital Learning Scientist and Lecturer
Massachusetts Institute of Technology

Karene Chu
Digital Learning Scientist and Research Scientist
Massachusetts Institute of Technology

Duncan Levear
Postdoctoral Associate/DLL
Massachusetts Institute of Technology

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Content Designer

MIT

MIT is a world-class educational institution where teaching and research — with relevance to the practical world as a guiding principle — continue to be its primary purpose.

MIT is independent, coeducational, and privately endowed. Its five schools and one college encompass numerous academic departments, divisions and degree-granting programs, as well as interdisciplinary centers, laboratories and programs whose work cuts across traditional departmental boundaries.

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