This book and its companion (part I) present the elements of analysis and linear algebra used in financial models and in microeconomics. Functions of one and several variables and matrices are developed in part I and vector spaces, linear mappings and optimization methods are developed in part II. Instead of formal proofs as in mathematical books, we develop examples and economic illustrations of the use of the concepts presented in the book. The books complement “Probability in Finance” and “Stochastic Processes in Finance” providing a broad overview of the mathematics of financial models.

• Introduction

1. Vector spaces and linear mappings
   1. Vector spaces: definitions and general properties
   2. Linear mappings
   3. Finite-dimensional spaces and matrices
   4. Norms and inner products
   5. Hilbert spaces
   6. Separation theorems and Farkas lemma
2. Functions of several variables
   1. Metric spaces
   2. Continuity and differentiability
   3. Implicit and homogeneous functions
3. Optimization without constraints
   1. Preliminaries
   2. Optimizing a single-variable function
   3. Optimizing a function of two variables
   4. Functions of n variables
4. Constrained optimization
   1. Functions of two variables and equality constraint
   2. Functions of p variables with m equality constraints
   3. Functions of p variables with mixed constraints

• Index