Calculus 1A: Differentiation - Massachusetts Institute of Technology

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.

• 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