Resources For The Calculus Student:

  • Online course website with hundreds of calculus and related courses.
  • Calculus problems with step-by-step solutions – Calculus problems with detailed, solutions. It’s calculus done the old-fashioned way – one problem at a time, one easy-to-follow step at a time, with problems ranging in difficulty from easy to challenging. Also available are scanned solutions to problems in differential, integral and multi-variable calculus and series.
  • Excerpts from “How To Ace Calculus” – Excerpts from “How to Ace Calculus: The Streetwise Guide” a recently published book with an unorthodox humorous approach to learning calculus. For those with a sense of humor only.
  • Calculus animations in Maple and Calculus animations in Mathematica – A series of Quicktime movies, contributed by Deej Heath of Pacific Lutheran University. These illustrate many ideas of calculus, and also include instructions on how to make similar animations yourself using Maple or Mathematica.
  • Calculus Applets – A collection of Java applets illustrating calculus concepts by Deej Heath at Pacific Lutheran University.
  • Tips on preparing for exams – How to study and do well on exams
  • Sample Exams – See if you are ready for your exam by taking our collection of sample exams.
  • Mathematics and the job market – A list of professions which use mathematics Resources For The Calculus Instructor:

  • Sample exam problems – Here are sample exams problems from first year calculus, in tex format, sorted by problem area. Feel free to modify these and use them for your own exams.
  • Calculus classroom demonstrations – Calculus demonstrations that you can use in the classroom to spice up your lectures and prevent those nodding heads.


Sites with Calculus Exams.

  • Exams With Solutions – has a wide collection of exams with solutions in mathematics and other subjects. See Calculus Exams With Solutions for calculus exams sorted by level.
  • Calc I – sample exams from the University of Illinois at Chicago.
  • Sample exams – from the SUNY Stony Brook.
  • Sample exams – and more Sample exams from MIT.
  • Actuarial Review Problems: – Multiple choice problems with solutions, from precalc to Multivariable caclulus. From Ronald Miech at UCLA.
  • Sample exams – from Rutgers.
  • Sample Exams – from Northern Illinois University.
  • The AP Calculus AB Exam site: – Has past exams and sample problems for AP calculus exam.
  • Some more University websites with old calculus exams.
    U. Mass , Wabash , Toronto , Columbia , Bradley , Washington University , Bates .

Tutorials and courses in calculus:

  • Online math courses from MIT. The OpenCourseWare project at MIT puts many valuable resources online. Calculus and many other math courses are represented.

Animated demonstrations of calculus:

  • Gallery of animated and graphical demonstrations of calculus and related topics, from the University of Vienna.
  • Tutorials for the Calculus Phobe: A collection of animated calculus tutorials in Flash format.

Sites with Calculus problems.

Aid for Calculus: About 300 sample problems from John A. Taylor, with solutions. Nicely indexed. This wiki site has lots of user generated sample problems with solutions in calculus and other areas.
Dr. Math: Great list of problems. Also has something to say on calculus and other topics.
S.O.S. Math – Calculus: Good list of problems with solutions. Through Fourier Series.
The Math Shop: Some solved problems, java applets for calculus, and review material.
Hotmath: Follow the students button to get a list of solutions to the odd problems in the calculus texts of Stewart; Larson, Hostetler, Edwards; and Tan
Find The Error: Douglas Shaw challenges you to find the error in some calculus proofs.
WYKAmath: Integral and derivative problems with nicely explained answers. Also some videos that may appeal to youtube fans.

Sites with Sage, Mathematica, Maple, etc. based calculus notebooks and problems:

Sage Calculus Tutorial: A calculus tutorial based on the free and open-source Sage Computer Algebra System.
Mathematica notebooks: A large collection of Mathematica notebooks, from the Mathematics Department at Wright State University. In both Windows and Mac formats.
Interactive Learning in Calculus and Differential Equations with Applications: A collection of Mathematica notebooks explaining topics in these areas, from the Mathematics Department at Indiana University of Pennsylvania.
WebCalc: A completely on-line calculus course at Texas A&M. Needs Scientific Notebook, but a free viewer version is available.
Calculus & Mathematica: An online introductory calculus course at the University of Illinois at Urbana-Champaign and Ohio State University.

Online texts:

Calculus Made Easy A classic calculus supplement by Sylvanius P. Thompson. Published in 1914, it was very popular. The treatment is intuitive. Available via a digital library.
Free Online Textbooks Links to free online texts in a variety of mathematical areas, including calculus.
Online math textbooks from a list maintained by George Cain, at the Georgia Institute of Technology.
Calculus textbook by Gilbert Strang. Full textbook available in pdf format.

Tutorials and explanations of calculus topics:

Online calculus notes: From the University of British Columbia. Has some nice explanations and some interactive features.
Calculating the Volume of a Vase: A very nicely presented project in which the volume of a real vase is computed. From the Duke University Mathematics Department.
Karl’s Calculus Tutor: Lots of nice explanations of calculus concepts.
Mudd Math Fun Facts: Nice explanations of many calculus (and other mathematical) concepts. Also has geometry, algebra, probability etc. sections. Organized by level of difficulty.
Common Errors: Common errors in undergraduate mathematics, compiled by Eric Schechter at Vanderbilt University.
Graphics for the calculus classroom: A collection of graphics and animations that illustrate calculus concepts.
Survival Guide: One person’s calculus survival guide.
AP Calculus: College Board’s guide to AP Calculus.
Dave’s math Tables: Tables of integrals, derivatives, and series expansions.
Learning Calculus: Some calculus motivational propaganda.
Animated examples by Louis A. Talman of the Metropolitan State College of Denver. A nice collection of very informative animations.
Dr. Vogel’s Gallery of Calculus Pathologies A collection of strange functions that illustrate points about continuity and differentiablility.
World Web Math Linked collection of calculus explanations from MIT.
Wikipedia Entry on calculus in the online encyclopedia. Many links to specialized topics.
Calculus Tutorials and Problems Free interactive tutorials on clauclus topics, including Mean Value Theorem, Runge Kutta, Fourier Series. Many links to specialized topics.
Wyzant has a collection of calculus explanations on selected topics from precalc through vectors.

Collections of calculus site links:

Yahoo directory: Yahoo’s directory of calculus sites.
Mozilla directory: Mozilla’s directory of calculus sites. A general math site with lots of nicely done mathematical content, including some calculus concepts and calculus links.
Math Forum Internet Mathematics Library: Hosted by Drexel University. Comprehensive, up-to-date resources on multiple math topics. See
Single Variable Calculus
Multivariable Calculus Offers a directory to calculus and other mathematics resources.
Calculus Resources Online: Lots of good links from the The University of Tennessee at Knoxville.
Calculus site rankings: Ranked and reviewed list of calculus sites from Montclair State University. (We’re number 2, so we try harder.)

Vector calculus and multivariable calculus sites:

Georgia Tech Vector calculus home page: Lecture notes, plus extensive collection of Maple and Mathematica notebooks.
Multivariate Calculus With Maple:: Mulitvariable calculus explanations, with many problems implemented and solved using Maple. Nice explanations of some topics.
The Calc 4 Home Page: A vector calculus site at Northeastern University.
Exploring Multivariable Calculus: Paul Seeburger’s website for exploring calculus visually. Has nice collection of applets, including some 3D effects.

Calculators for derivatives, integrals etc.: As well as integrals and derivatives, it does limits, series expansions, vector analysis, integral transforms etc. A powerful tool. An online integrator. Be careful or you will be replaced by a $12 calculator. Based on Mathematica. An online cacluator for derivatives, integrals. Also does plots and formula simplification.
Encalc: A free online cacluator that includes numerical integration and numerous physical formulas
Graphing calculator: Graphs several equations at once.

Calculus applets and software:

Math Applets for Calculus at SLU: Mike May at St. Louis University has a selection of applets to illustrate important concepts of single and multivariable calculus. An extensive collection of applets to illustrate interactively the ideas of single variable calculus.
MathServ Calculus Toolkit: An online toolkit for graphing, limits, derivatives, inverses etc.
FADBAD: A C++ program for automatic differentiation. You can download it if you like.
Some Java applets: A collection of Java applets illustrating concepts of calculus. A scientific calculator.

Calculus videos:

Center of Math: has video lectures on differential and integral calculus topics.
Just Math Tutorials: has a large collection of youtube videos on calculus and other math topics.
Midnight Tutor: This site has a large collection of videos that both explain concepts and work through problems.
Calculus videos: The Khan academy has many free videos with calculus explanations.
Brightstorm: has a variety of free videos offering calculus explanations.

Applications of Calculus:

Calculus and Probability: Calculus Applied to Probability and Statistics for Liberal Arts and Business Majors
Calculus and Society, History etc:

A history of calculus: Part of a math history project at St. Andrews College.
Why calculus?: Why calculus is important. From Helmer Aslaken at the National University of Singapore.
History of mathematics: An outstanding history website.
Earliest Uses of Symbols of Calculus: Origins of notations of caculus.
Commercial Calculus Products:

Help With Math: Offers MathXpert software to help learn precalculus and calculus.
Related Topics: Precalculus, Differential Equations, Linear Algebra etc.:

Precalculus Notes : Extensive collection of nice explanations of precalculus topics by Ken Kuniyuki of San Diego Mesa College.

Fun math links:

Birthdays: Mathematicians who have birthdays today.
pi: The history of PI.
Prizes and competitions:

Results of the National High School Student Calculus Competitions` can be found at: Calculus Competition Awards. There are currently no plans for future competitions.