The Classic epsilon-delta definition of a limit

• Sequences
• Cauchy sequences
• Summability
• Functions and Continuity.
• Graphing (Asymptotes). Graphical Introduction to Limits
• Differentiation. (Secant approaches Tangent)

• Weierstrass' Function (continuous everywhere, differentiable nowhere!).
  

• Cantor's Function (continuous, differentiable, increasing, non-constant, derivative = 0 almost everywhere!)
  
• Integration
• Delta Functions

• Riemann Integration Applet

• Why are limits so hard to teach?
• Why are limits so hard for students to understand?
• Teaching epsilon-delta limits as a game

  Choose a function and a number. Let partner A select a y range. Partner B must find an x range so that the graph leaves the box on the sides and not the top and bottom. If Partner B can always win, then the function has a limit at that number. We will play this game first with me as Partner B and the class as Partner A.