Free Calculus Textbooks

One common definition I found of calculus is, “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.”

In many ways, calculus is one of those courses that students planning on majoring in Computer Science, Mathematics, Economics, Engineering and many of the science fields will utilize during their career. It is something of a building block to advanced mathematics and science courses. With students at my college, it was the course that separated the CIS majors from the CS majors.

Sounds ominous but I don’t mean to. I liked Calculus. Calculus IV was one of my few electives. I can tell you from experience that the first semester course is the most difficult for most students. It drove me to thrift and used book stores in search of textbooks, study guides and anything else I could put my hands on. My small collection often helped me figure out concepts that I was having trouble with. It was like having 7 professors instead of one. I ended up relying upon those books throughout all four semesters of my study of calculus.

While I found help in the racks of discarded textbooks, today’s students have a virtual library-full of online calculus materials to turn to. From 1st semester students to those studying Advanced Calculus, Quantum Physics or some other high-level material, there’s something here that will hopefully be able to help.

List of Free Calculus Textbooks

A Treatise on the Theory of Invariants

Written by: Oliver E. Glenn (University of Pennsylvania)

Vintage calculus textbook. Theory of Invariants may offer students alternative explanations of the material that may click better than modern texts.

Active Calculus

Written by: Matthew Boelkins, David Austin and Steven Schlicker (Grand Valley State University)

Active Calculus; open source calculus textbook by three professors at Grand Valley State University. Utilizes an approach that may be difficult for self-study.

Advanced Calculus

Written by: Lynn H. Loomis (Harvard) & Shlomo Sternberg (Harvard)

Advanced Calculus is a substantial free online textbook written by two Harvard professors. We’ll show you where to find it and outline the chapter headings.


Written by: Gilbert Strang (MIT)

Great for calculus students. MIT professor Gilbert Strang’s 1991 edition of his multivariable calculus textbook, with answer key and instructor’s manual.

Difference Equations to Differential Equations

Written by: Dan Sloughter (Furman University)

Free online calculus textbook written by Dan Sloughter of Furman University that is freely available to all mathematics students.

Elementary Calculus

Written by: Michael Corral (Schoolcraft College)

Learn where to find Michael Carrol’s Elementary Calculus free online textbook and explore the topics it covers.

Infinitesimal Calculus

Written by: Keith Duncan Stroyan (University of Iowa)

University of Iowa professor, Keith Duncan Stroyan, has shared his textbook, Mathematical Background: Foundations of Infinitesimal Calculus.

Introduction to Methods of Applied Mathematics

Written by: Sean Mauch (Caltech)

Huge mathematics textbook. Sean Mauch of Caltech began writing Introduction to Methods of Applied Mathematics as a student. It’s now used around the world.

Introduction to Tensor Calculus and Continuum Mechanics

Written by: John H. Heinbockel (Old Dominion University)

Introductory 2-semester text on tensor calculus, differential geometry and continuum mechanics for applied mathematics, engineering and physics students.

Multivariable Calculus

Written by: George Cain and James Herod (GA Tech)

This calculus textbook has been used for several years by the students and faculty at Georgia Tech for a course on multivariable calculus.

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