During the Spring term of 2019 Calculus I will be coordinated by Prof. Corrin Clarkson (clarkson@nyu.edu).

## Welcome to Calculus I!

“The book of the universe is written in the language of mathematics.” Galileo wrote this four hundred years ago, even before Newton and Leibniz discovered calculus. The statement is as valid today as ever: We use functions in all the sciences, and calculus allows us to analyze the functions and draw scientific conclusions.

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.

## Learning Objectives

By the end of the course students will be able to:

- Understand the theoretical concept of a limit; use algebraic means to compute the values of limits and identify when they don’t exist.
- Understand the theoretical concept of the derivative; compute them using the standard rules of differentiation.
- Understand the theoretical concept of the integral; compute both definite and indefinite integrals using the fundamental theorem of calculus.
- See how the mathematical concepts of integration and differentiation are the natural result of an investigation into the nature of the physical world and perform further investigations using the new tools presented in class.
- Communicate mathematically, including understanding, making, and critiquing mathematical arguments.