Written by Lynn H. Loomis and Shlomo Sternberg from the Department of Mathematics at Harvard University, this huge online calculus textbook is available in PDF form. (It is 592 pages and over 57 MB.) This revised edition was published in 1990 and is based on an honors course in advanced calculus. The authors suggest using [...]
Free Online Calculus Textbooks
Students studying calculus will be exposed to limits, functions, derivatives, integrals and infinite series. According to Wikipedia, “Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.”
Calculus is in many ways a gateway course – it is a prerequisite for many of the more advanced math courses. Real world applications can be found in science, economics and engineering.
As someone who took four semesters of calculus in college, I can tell you that the first semester was the most difficult. Students finding themselves having trouble understanding the material should definitely seek out supplementary materials to ensure doing well in later semesters of calculus or the advanced courses which rely upon it. Don’t get me wrong, the other three semesters required a great deal of effort too.
I made liberal use of other students’ cast off textbooks. You don’t have to do that to find help. Calculus is fortunately one of those math subjects where there are a nice variety of open textbooks available freely on the Internet. If you have a favorite that I’ve missed, please let me know.
List of Free Online Calculus Textbooks
Advanced Calculus
Calculus
This is a great opportunity for calculus students. MIT professor Gilbert Strang has made the 2005 edition of his textbook, answer key and instructor’s manual available online. Homeschoolers should really check out this complete Calculus course for their kids.
Calculus with Applications
Online calculus textbook that is part of the MIT OpenCourseWare program. It is from an undergraduate course (MIT Course Number: 18.013A) on differential calculus in one and several dimensions. The authors list the text as being appropriate for a course one and a half terms long. It is targeted for students who were introduced to [...]
Difference Equations to Differential Equations
Free online calculus textbook written by Dan Sloughter of Furman University that is freely available to all mathematics students.
Elementary Calculus: An Infinitesimal Approach
Written in 2000 by H. Jerome Keisler and revised in 2010, this calculus textbook is designed for a freshman course on the subject. He builds upon Abraham Robinson’s infinitesimals which “puts the intuitive ideas of the founders of the calculus on a mathematically sound footing, and is easier for beginner to understand than the more [...]
Infinitesimal Calculus
K.D. Stroyan of the University of Iowa has written two books on this subject – A Brief Introduction to Infinitesimal Calculus and Foundations of Infinitesimal Calculus. Both books can be accessed from the same page of his site.
Introduction to Methods of Applied Mathematics
This online textbook being offered of Sean Mauch of Caltech is in PDF format. It covers Algebra, Calculus, Functions of a Complex Variable, Ordinary Differential Equations, Partial Differential Equations, Calculus of Variations and Nonlinear Differential Equations.
Introduction to Tensor Calculus and Continuum Mechanics
John H. Heinbockel, Professor Emeritus, Department of Mathematics and Statistics, Old Dominion University is offering an early version of this textbook online for all students to access. He considers it an introductory 2-semester text on tensor calculus, differential geometry and continuum mechanics suitable for advanced undergraduates or graduate students studying applied mathematics, engineering and physics. [...]
Multivariable Calculus
George Cain and James Herod, 1997. This calculus textbook has been used for several years by the students and faculty at Georgia Tech.
The Calculus
Free online calculus textbook by William V. Smith of BYU. The introduction cautions that it is still a work in progress but it looked fairly complete to me. The selected font, however, is unfortunate as it is somewhat hard to read.