Welcome to Calculus I!
“Calculus is a field of mathematics that analyzes aspects of change in processes or systems that can be modelled by functions. Through its two primary tools – the derivative and the integrals – it allows precise calculation of rates of change and of the total amount of change in such a system. The derivative and the integral grew out of the idea of a limit, [roughly speaking] the logical extension of the concept of a function [considered] over smaller and smaller intervals. The relationship between differential and integral calculus known as the Fundamental Theorem of Calculus was discovered in the late 17th century independently by Isaac Newton and Gottfried Wilhelm Leibniz. Calculus was one of the major scientific breakthrough of the modern era.
Calculus is now the basic entry point for anyone wishing to study physics, chemistry, biology, economics, finance, or actuarial science.” *
Calculus makes it possible to solve a myriad of diverse and challenging problems. In this course, we will study the foundations of calculus. 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.
* Berggren, John L.. “Calculus”. Encyclopedia Britannica, 20 Sep. 2022, https://www.britannica.com/science/calculus-mathematics. Accessed 30 December 2022.
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.
During the Spring 2023 Semester the Calculus I course will be coordinated by Professor Ross Flek. He may be contacted at ross.flek@nyu.edu
Prerequisites
Students who wish to enroll in Calculus I must meet the prerequisites listed on the Mathematics Department CAS Calculus Information page.