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Calculus I


A photograph of Matthew Leingang

 Professor Matthew Leingang

  • Clinical Associate Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University
  • Ph.D. 2000 (Mathematics), Harvard University
  • Bio & Publications

About the Course

In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject.

The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way.


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Course Readings

  • Stewart, James. Essential Calculus, Early Transcendentals. (2007) Thomson Books/Cole.


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