RES.18-001 | Fall 2023 | Undergraduate

# Calculus Online Textbook

The calculus courses at MIT are 18.01 Single Variable Calculus and 18.02 Multivariable Calculus. Videos of those courses are on OpenCourseWare (OCW) along with lots of other useful materials. This site is about a completely separate calculus textbook by Gilbert Strang, and it will be helpful to viewers of OCW who would like to have online access to a textbook.

Professor Strang’s many contributions to OCW are mostly about linear algebra:

Each of those courses has a full set of video lectures recorded on the MIT campus. Those videos have been watched by millions of viewers around the world (especially 18.06 Linear Algebra). Calculus and linear algebra are the two principal lead-ins to pure and applied mathematics.

Professor Strang’s Highlights of Calculus course on OCW is a series of short videos. They focus on the main idea of the subject, involving two functions: function 2 is the “derivative” of function 1, and function 1 is the “integral” of function 2. If you are given one of those functions, then this calculus textbook and the Highlights of Calculus videos show how to derive the other function. The heart of calculus is to use those functions to solve real problems, as described in Lecture 1: Big Picture of Calculus.

Below, Professor Strang shares some thoughts on the history of the calculus textbook:

For the textbook itself, its first printing was in 1991. That was a time of active “rethinking” of the course. I remember being in the audience at a discussion organized by the US National Science Foundation, about needed changes in typical calculus courses (to make them more relevant and interesting to students). Sitting at the back, I thought one necessary step would be a new textbook. That is the book you see here on OpenCourseWare, published by Wellesley-Cambridge Press.

Chapter 0 of the book came in a later edition. Its purposes were to add more figures to illustrate the key ideas of calculus, and also to develop in a new way the most important function in this subject. That function is the exponential $$e^x$$. It has a very special feature, because it is both function 1 and function 2! In other words, the derivative of $$e^x$$is $$e^x$$, and the integral of $$e^x$$is $$e^x$$ (plus any constant C). This becomes the most important function in many applications, including the enormous field of “differential equations” (because it solves the most fundamental differential equation dy/dx = y).

I hope the book and the exercises and the videos and even Chapter 0 will be useful to you! Best wishes in all your work.

Gilbert Strang

Fall 2023
Online Textbook