V. Finite Approximation
V. Finite Approximation
V.1.1. Motion and the Idea of Area
V.1.2. Polygons and Polygonal Paths
V.1.3. Triangulation and the Area of Polygons
V.2.1. Analytical Properties of the Real Numbers
V.2.2. Sequential Limits and the Limit Laws
V.3.1. Fractions of a Circle
V.3.2. Length and Area
V.3.3. Limits Involving the Trigonometric Functions
V.4.1. Infinite Series and their Convergence
V.4.2. Some Convergence Tests
V.5.1. Definition and Computation of Limits
V.5.2. One Sided Limits
V.5.3. Infinite Limits
V.5.4. Limits and Paths
V.6.1. Continuity
V.6.2. Properties of Continuous Functions
V.6.3. Approximating Continuous Functions
V.7.1. Asymptotic Notation
V.7.2. Sensitivity to Perturbation
V.7.3. Composite Errors
V.8.1. Average Rate of Change
V.8.2. Instantaneous Rate of Change
V.8.3. The Exponential Function
V.9.1. Rectifiable Curves
V.9.2. Areas Bounded by Closed Curves
V.9.3. Approximating Area under a Function
Worksheet V.1: Rigid Motions and the Area of a Polygon
Worksheet V.2A: The Least Upper Bound Property
Worksheet V.2B: Sequential Compactness of Closed and Bounded Intervals
Worksheet V.2C: Contraction Mappings and their Fixed Points
Worksheet V.3A: Error Bounds in Circumference Estimates
Worksheet V.3B: The Area of an Ellipse
Worksheet V.3C: Motion and the Unit Circle
Worksheet V.4A: Cantor Sets
Worksheet V.4B: Convergence of p-Series
Worksheet V.5: Limits of Rational Powers
Worksheet V.6A: Continuous Functions on Closed and Bounded Intervals
Worksheet V.6B: The Bisection Method
Worksheet V.6C: Indirect Characterizations of Continuity
Worksheet V.7: Uniform Continuity
Worksheet V.8A: Paths and Tangency
Worksheet V.8B: Constructing the Exponential Functions
Worksheet V.9: Specialized Partitions