Calculus 1A: Differentiation
Discover the derivative—what it is, how to compute it, and when to apply it in solving real world problems. Part 1 of 3.
Course Information
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About this Course
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 is a series of the following three modules:
What you'll learn
- 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
Prerequisites
Algebra and Trigonometry (Precalculus)
Meet your instructors
David Jerison
Professor of Mathematics
David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis.
Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each.
