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.
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.
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.
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
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Professor of Mathematics -
Abby Rockefeller Mauze Professor
David Jerison
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.
Gigliola Staffilani
Gigliola Staffilani
Abby Rockefeller Mauze Professor
Gigliola Staffilani is the Abby Rockefeller Mauzé Professor of Mathematics since 2007, and was Associate Department Head from July 2013 to 2015. She received the B.S. equivalent from the University of Bologna in 1989, and the M.S. and Ph.D. degrees from the University of Chicago in 1991 and 95. Carlos Kenig was her doctoral advisor. Following a Szegö Assistant Professorship at Stanford, she had faculty appointments at Stanford, Princeton and Brown (tenured at Stanford and Brown), before joining the MIT mathematics faculty in 2002 as tenured associate professor (professor in 2006). Professor Staffilani is an analyst, with a concentration on dispersive nonlinear PDEs. At Stanford, she received the Harold M. Bacon Memorial Teaching Award in 1997, and was given the Frederick E. Terman Award for young faculty in 1998. She was Sloan fellow from 2000-02, a member of the Institute for Advanced Study, in Princeton, NJ in 1996 and 2003 and a member of the Radcliffe Institute for Advanced Study at Harvard University in 2010.
At MIT Professor Staffilani served as co-chair of the Graduate Student Committee in Pure Mathematics from 2009-2013, and is the Faculty Diversity Officer since 2015. In 2013 she was elected member of the Massachusetts Academy of Science and a fellow of the AMS, and in 2014 member of the American Academy of Arts and Sciences. In 2017 she received a Guggenheim fellowship and a Simons Fellowship in Mathematics.