Calculus 1A: Differentiation

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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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