III. Rigidity
III. Rigidity
III.1.1. Introductory Comments on Rigidity
III.1.2. Vectors in three Spatial Dimensions
III.1.3. Rigidity and the Determination of Lines and Planes
III.1.4. Intersections of Lines and Planes
III.2.1. Quadratic Functions and Optimization
III.2.2. The Factor Theorem
III.2.3. Sketching Polynomials
III.3.1. Sketching Reciprocals of Polynomials
III.3.2. Asymptotic Behavior
III.3.3. Sketching Rational Functions
III.4.1. Polynomial Inequalities
III.4.2. Inequalities Involving Rational Functions
III.4.3. Inequalities Involving Piecewise Rational Functions
III.5.1. Tangential Intersections
III.5.2. Tangency and Polynomials
III.5.3. Tangency and Rational Functions
III.6.1. Decomposition and Calculation
III.6.2. The Algebraic Derivative
III.6.3. Tangency and Extremal Values
III.6.4. High Degree Intersections
Worksheet III.1A: Rigidity of the Orthogonal Decomposition of Vectors
Worksheet III.1B: Determination of Spatial Planes
Worksheet III.2A: Quadratic Optimization
Worksheet III.2B: Line of Sight and the Horizon
Worksheet III.2C: The Rigidity of Polynomial Functions
Worksheet III.3A: Graphical Representation of Rational Functions
Worksheet III.3B: Decomposition of Rational Functions
Worksheet III.4: Using the Rigidity of Rational Functions to Solve Inequalities
Worksheet III.5: Telescopes and Tangency
Worksheet III.6A: Detecting Wiggles in Polynomial Functions
Worksheet III.6B: Higher Order Intersections