Related Resources

Tips for Success in Undergraduate Math Courses by Jessica Purcell. Some very good advice for college calculus students. Read this carefully and do as it suggests.

Common Errors in Undergraduate Mathematics by Eric Schechter

The calculus page problems list problems by D. A. Kouba at UC Davis

Assorted Applets

The Web page contains a plethora of interesting resources to help you visualize important mathematical concepts. Most of these are Java applets, which run interactively as plug-ins in your web browser. To use them you must have Java enabled in your browser preferences - by default, it probably is already.

• Some Java applets from MIT's OpenCourseWare page for 18.013A:
  • Operations on functions
  • Trigonometric functions
  • Slope of a line
  • Derivative and tangent line
  • Constant, linear, quadratic and cubic approximations
  • Numerical integration
  • Polar plotter
  • Curves in two dimensions
• Function and Derivative Animations, by Przemyslaw Bogacki and Gordon Melrose (.avi files, can play e.g. with Windows Media® Player)
• Java applets of secant lines and tangent lines (from IES, Manipula Math):
  • A smooth function
  • One-sided derivatives at a point of non-differentiability
• Secant lines for a function with two non-differentiable points (applet by Daniel J. Heath)
• Animations of secant lines approaching (or not approaching) tangent lines (by Douglas N. Arnold):
  • At a point of differentiability
  • At a point of non-differentiability (the one-sided derivatives don't match)
  • At another point of non-differentiability (vertical tangent; the derivative is infinite)
• Constructing functions that are continuous but nowhere differentiable (!), applet from Maths Online
• Chain rule applet (from a multimedia calculus course by Scott Sarra)
• First and second derivatives applet (by Scott Sarra)
• More first and second derivatives, with parameters you can tweak (applet from Maths Online)
• Derivatives of a^x, sin x, cos x (applets by Daniel J. Heath)
• Converging to the number e (applet from IES, Manipula Math); note that the simulation doesn't let you go far enough to approach that close to e
• Zooming in on a tangent line (animation by Douglas N. Arnold)
• Linear approximation of sin x at 0 (applet from UBC Calculus Online)
• Finding a function's extremum, applet from Maths Online
• Rolle's theorem and the mean value theorem (applet from IES, Manipula Math)
• Some nice integral applets (by Daniel J. Heath):
  • Riemann sums
  • Definite integrals and the integral function 1
  • Definite integrals and the integral function 2
• Numerical Integration Simulation (by Joseph L. Zachary)
• Some applets on volumes of solids (from IES, Manipula Math):
  • Solid 1
  • Solid 2
  • Solid of revolution 1
• Direction field applet (by Scott Sarra)
• More direction field applets (from UBC Calculus Online)
• Yet another direction field applet (from IES, Manipula Math)
• Parametric equation applet (by Scott Sarra)
• Another parametric equation applet (from IES, Manipula Math)
• Cycloid animation (AVI) (by Przemyslaw Bogacki and Gordon Melrose)
• Cycloid applet (from Maths Online)
• Computing arc length (AVI) (animation by Przemyslaw Bogacki and Gordon Melrose)
• Approximating arc length (applet by Daniel J. Heath)
• Polar curve applet (from IES, Manipula Math)
• Several polar curve animations (by Przemyslaw Bogacki and Gordon Melrose):
  • limacons:
    • r = 1 + sin t (AVI)
    • r = 3 - 2 cos t (AVI)
    • r = 1 + 2 cos t (AVI)
    • r = 3 - sin t (AVI)
  • rose curves:
    • r = 3 cos(3t) (AVI)
    • r = 5 sin(2t) (AVI)
  • spiral: r = t (AVI)
  • circle: r = cos t (AVI)
• Converging and diverging series animations (by Przemyslaw Bogacki and Gordon Melrose):
  • 1 / N^(1/2) (AVI)
  • 1 / N (AVI)
  • 1 / N² (AVI)
  • 1 / N¹⁵ (AVI)
• Numerical tools for computing sequences / series (from Maths Online)
• Taylor approximations (applet by Daniel J. Heath)
• Power series grapher

And just for the fun of it, there's the Quadratic Formula Song (WMA - 1.1 MB).