Chiang A.C. Fundamental Methods of Mathematical Economics

McGraw-Hill, 1984. — 788 p.Elegant Yet Lucid Writing Style: Chiang's strength is the eloquence of the writing and the manner in which it is developed. While the content of the text can be difficult, it is understandable.
Meshes Sophisticated with the Accessible: Sophisticated material is presented in the text, but not a lot of prior knowledge is assumed. The background needed for the course is there. The combination of depth of material and ease of exposition is the reason that graduate students and faculty alike have kept their copies of Chiang from their undergraduate days.
Many new, innovative examples based on current economics.
Expanded applications, especially in chapters 8,11, and 12
New chapter covering envelope theorem, maximum value function, and duality. In part five add a new chapter on optimal control theory and modernize the models. Delete part 6 (Mathematical Programming) and move nonlinear programming (21) to follow Optimization with equality constraints (12).
A Classic Text: Chiang literally wrote the book on the subject matter and is one of the most widely-respected Economics texts in the world.The Nature of Mathematical Economics
Economic ModelsStatic (or Equilibrium) Analysis
Equilibrium Analysis in Economics
Linear Models and Matrix Algebra
Linear Models and Matrix Algebra (continued)Comparative-Static Analysis
Comparative Statics and the Concept of the Derivative
Rules of Differentiation and their use in Comparative Statics
Comparative-Static Analysis of General-Function ModelsOptimization Problems
Optimization: A Special Variety of Equilibrium Analysis
Exponential and Logarithmic Functions
The Case of More Than One Choice Variable
Optimization with Equality Constraints
Further Topics in Optimization (includes Envelope Theorem and DualityDynamic Analysis
Economic Analysis and Integral Calculus
Continuous Time: First Order Differential Equations
Higher-Order Differential Equations
DiscreteTime: First Order Difference Equations
Higher Order Difference Equations
Simultaneous Differential Equations and Difference Equations
Introduction to Optimal Control Theory