Euclidean Space
Some Notation: Set of All Functions, Set of All Subsets
Vector Spaces, with S&B page numbers
Convexity; Concave and Convex Functions
Norms and Metrics, Normed Vector Spaces, and Metric Spaces
Limits of Functions in Euclidean Spaces
The Bolzano-Weierstrass Property and Compactness
Approximation and Taylor Polynomials
Second-Order Conditions and Quadratic Forms with Constraints
Derivatives and Maximization of Concave Functions
Differentiable Quasiconcave Functions
The Solution Function and Value Function for a Maximization Problem
Nonlinear Programming and the Kuhn-Tucker Conditions
Example: Linear Programming and the Kuhn-Tucker Conditions
Example: The Pareto Maximization Problem
Constrained Maximization vs. Constrained Minimization
The Basic Model of Demand Theory (introduction to Econ 501A)