Mathematics for Economists: An Integrated Approach

ISBN-13: 9780521287692 / Angielski / Miękka / 1983 / 196 str.

E. Roy Weintraub

Opis

The responses to questions such as 'What is the explanation for changes in the unemployment rate?' frequently involve the presentation of a mathematical relationship, a function that relates one set of variables to another set of variables. It should become apparent that as one's understanding of functions, relationships, and variables becomes richer and more detailed, one's ability to provide explanations for economic phenomena becomes stronger and more sophisticated. The author believes that a student's intuition should be involved in the study of mathematical techniques in economics and that this intuition develops not so much from solving problems as from visualizing them. Thus the author avoids the definition-theorem-proof style in favor of a structure that encourages the student's geometric intuition of the mathematical results. The presentation of real numbers and functions emphasizes the notion of linearity. Consequently, linear algebra and matrix analysis are integrated into the presentation of the calculus of functions of several variables. The book concludes with a chapter on classical programming, and one on nonlinear and linear programming. This textbook will be of particular interest and value to graduate and senior undergraduate students of economics, because each major mathematical idea is related to an example of its use in economics.

Spis treści

Preface; 1. Real numbers; 2. Functions from R to R; 3. R2 and Rn; 4. Functions from Rn to R; 5. Functions from Rm to Rn: the linear case; 6. Differentiable functions from Rm to Rn; 7. Square matrices; 8. Stability of linear dynamic systems; 9. Quadratic forms; 10. Concave, convex, and homogeneous functions from Rn to R; 11. Optimization (I); 12. Optimization (II); Additional exercises; Bibliography; Index.