link Source: www.edx.org
date_range Starts on June 1, 2022
event_note Ends on August 31, 2022
list 13 sequences
assignment Level : Introductory
chat_bubble_outline Language : English
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Key Information

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timer 78 hours in total

About the content

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.

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.

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.

  • 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

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Prerequisite

Algebra and Trigonometry (Precalculus)

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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
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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

Stephen Wang
Associate Teaching Professor
Rice University

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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Platform

Edx

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Excelente!

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Published on August 30, 2021
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Excelente!