Calculus Capers

A Careful Exposition of Limits

• 1.01 The Limit Concept and Its Definition
• 1.02 Variations on the Limit Definition
• 1.03 How to Construct a Delta-Epsilon Proof
• 1.04 Proofs of the Generic Limit Laws
• 1.05 Proofs of the Limit Inequalities
• 1.06 Continuity and Discontinuity
• 1.07 Proofs of the Continuity of Basic Algebraic Functions
• 1.08 Proofs of the Continuity of Basic Transcendental Functions
• 1.09 Some Special Limits
• 1.10 The Limit Definition of e
• 1.11 Strategies for Evaluating Limits
• 1.12 Finding Asymptotes
• 1.13 The Intermediate Value Theorem
• 1.14 Tangent Lines

Other Calculus Topics

• Taylor Polynomials (GIF animation):  see the Taylor polynomials converge to three different functions
• Slope Fields (webMathematica):  input the functional form of a derivative and see the slope field

Drillmasters

• Delta Epsilon Proofs Drillmaster, ordering the statements in a delta epsilon proof
• Derivatives Drillmaster (Basic), basic derivative rules (no products, quotients, or compositions) on algebraic functions
• Derivatives Drillmaster (Basic Plus), basic derivative rules (no products, quotients, or compositions) on algebraic, exponential, sine, and cosine functions
• Derivatives Drillmaster (Algebraic), derivatives of algebraic functions
• Derivatives Drillmaster (Exp/Log), derivatives of exponential and logarithmic functions
• Derivatives Drillmaster (Intermediate), derivatives of algebraic, exponential and logarithmic functions
• Derivatives Drillmaster (Trig), derivatives of trigonometric functions
• Derivatives Drillmaster (Advanced), derivatives of algebraic, exponential, logarithmic, and trigonometric functions
• Derivatives Drillmaster (Comprehensive), derivatives of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions