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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.
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This course was funded in part by the Wertheimer Fund.
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- 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
Prerequisite
Algebra and Trigonometry (Precalculus)
Syllabus
Abridged Syllabus
Limits
- Limit Laws
- Continuity
- Intermediate Value Theorem
Differentiation
- Introducing the Derivative
- Rules for differentiation of all known functions
- Approximations
Applications of Differentiation
- Curve Sketching
- Optimization
- Related Rates
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
Content Designer
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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Excelente!
Excelente!
