Visual Calculus I

1. The Limit

  The Limit Concept, slope of tangent line

Limit Concept: example
Slope of Tangent Line: example

One Sided Limit

Matched: example
Unmatched example

Infinite Limits, Limit at Infinity

Infinite: example
Finite: example
Infinite Limit: example

2. The Derivative

Basic Differentiation Rules, derivative formulas

Derivative of a sum: example

3. Applications of the Derivative

Linear Approximation

Linear Approximation: example

Newton's Iteration Method

Newton's Method: example

Increasing/Decreasing Functions

Increasing/Decreasing Functions: example

Other Applications of Derivatives

Mean Value Theorem: example1, example2
Roll's Theorem: example1, example2

4. The Integral

Area Computation, Riemann Sum

Riemann Sum: Midpoint Method: example
Riemann Sum: Endpoint Method: example