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