Vector Spaces

  Vector Spaces, with S&B page numbers

  Convexity; Concave and Convex Functions

  Norms and Metrics, Normed Vector Spaces, and Metric Spaces

  Sequences and Convergence in Metric Spaces

  Limits of Functions in Euclidean Spaces

  Continuous Functions in Metric Spaces

  The Bolzano-Weierstrass Property and Compactness

  Approximation and Taylor Polynomials

  Quadratic Forms

  Second-Order Conditions and Quadratic Forms with Constraints

  Unconstrained Optimization

  Derivatives and Maximization of Concave Functions

  Maximization vs. Minimization

  Differentiable Quasiconcave Functions

  The Solution Function and Value Function for a Maximization Problem

  Example: The Pareto Maximization Problem

  The Implicit Function Theorem

  The Envelope Theorem

  Nonlinear Programming and the Kuhn-Tucker Conditions

  Example: Linear Programming and the Kuhn-Tucker Conditions

  The Basic Model of Demand Theory (introduction to Econ 501A)