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# Calculus 1A: Differentiation

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## 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.

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.

## 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

David Jerison

## Reviews for edX's Calculus 1A: Differentiation 5.0 Based on 4 reviews

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Did you take this course? Share your experience with other students.

• 1
Prashant S
5.0 11 months ago
by completed this course, spending 35 hours a week on it and found the course difficulty to be medium.
-Must for everyone!!!

Good:

-Short videos

-Concept explaination

-Short quizz really tests your knowledge AWESOME :)

-Limits are explained in a great way.

-Why this course is not self paced?
Dna47a D
5.0 7 months ago
completed this course.
An excellent course from MIT. Can't describe it but you have to take it to experience how good the course materials are.
Marat M
5.0 3 years ago
by completed this course.
0 person found
Max F
5.0 3 years ago
completed this course.
0 person found