Great Calculus Reference Texts for Students Who Want to Learn More

The standard college calculus textbooks (popular examples are Anton, Larson, and Stewart, although Simmons seems to be a superior text to me) are supposed to provide thorough calculus training for large bodies of students with diverse background and intentions. They also form an indispensible resource for the instructor by supplying a large collection of problems for practice. Mathematics cannot be learned properly without doing a large number of problems.

Yet, for the student who wants to go deeper, or who wants to see the “big picture”, these books are generally not sufficient. In the usual college calculus course sequence, there is simply not enough time to spend on the main mathematical concepts at the heart of calculus, such as linear approximation, differentiability, orders of contact, or rectifiability of curves. The deeper facts about limits and continuity and the properties of real numbers, sequences, and functions which follow from order-completeness (such as the maximum value theorem) are normally skipped. In multivariable calculus, the routine texts do not usually have an adequate coverage of certain fundamental concepts related to geometry and physics, such as differential forms, or a more in-depth look at fields and potentials, or a unified treatment of the higher dimensional versions of the fundamental theorem of calculus.

Here is a list of some great calculus reference texts for students who want to dig deeper.

Single Variable Calculus

The books listed below are timeless masterpieces which go much deeper into calculus than ordinary popular textbooks. They are meant for the student who cannot be content with remaining just a user of calculus, but who intends to become a master of the subject.

What if I do not want to go deep?

Everyone can benefit from the short, enjoyable, and easy to read book below.

Other Related Web Pages

Multivariable and Vector Calculus

Some good books on Calculus of Several Variables

  • Calculus of Several Variables, by Serge Lang (Springer).
  • Second Year Calculus, by David M. Bressoud (Springer)
  • Introduction to Calculus and Analysis, Volume II, by Richard Courant and Fritz John (Springer).
  • Advanced Calculus: A Differential Forms Approach, by Harold M. Edwards (Birkhauser).
  • Calculus, Volume 2, by Tom Apostol (Wiley).
  • Advanced Calculus, by R. Creighton Buck (Waveland).
  • Calculus on Manifolds, by Michael Spivak (HarperCollins)