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تصویر Mathematics in Economics: Models and Methods

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Mathematics in Economics: Models and Methods

توضیحات

Mathematics in Economics is a valuable guide to the mathematical apparatus that underlies so much of modern economics. The approach to mathematics is rigorous and the mathematical techniques are always presented in the context of the economics problem they are used to solve. Students can therefore gain insight into, and familiarity with, the mathematical models and methods involved in the transition from "phenomenon" to quantitative statement.

Topics covered include:

  • Sets and Numbers
  • Matrices and Vectors
  • Modelling Consumer Choice
  • Discrete Variables
  • Functions
  • Equilibrium
  • Eigenvalues and Eigenvectors
  • Limits and their Uses
  • Continuity and Its Uses
  • Partial Differentiation
  • The Gradient
  • Taylor's Theorem - An Approximation Tool
  • Economic Dynamics: Differential Equations.
Each chapter ends with exercises designed to help students understand and practice the techniques they have learnt. The author has provided solutions to selected problems so that the book will function as an effective teaching tool on introductory courses in mathematics for economics, quantitative methods and for mathematicians taking a first course in economics. Mathematics in Economics has been developed from a course taught jointly by Ken Binmore (Professor of Economics) and Adam Ostaszewski (Senior Lecturer in Mathematics).

Adam Ostaszewski is currently Senior Lecturer in Mathematics at the London School of Economics. He teaches matematical methods appropriate to economic theory (including game thoery and control theory) and special topic courses to graduates and undergraduates. His main research interets include set-theoretic topology and theoretical economics, concentrating on mathematical problems ansd spanning a wide field of applications.
Part I:.

1. Sets and Numbers.

2. Matrices and Vectors.

3. Modelling Consumer Choice.

4. Discrete Variables.

5. Functions.

6. Equilibrium.

7. Eigenvalues and Eigenvectors.

Part II:.

1. Limits and Their Uses.

2. Continuity and Its Uses.

3. Uses of the Derivative.

4. Continuous Compounding and Exponential Growth.

5. Partial Differentiation.

6. The Gradient.

7. Taylor's Theorem - An Approximation Tool.

8. Optimisation in Two Variables.

9. Economic Dynamics: Differential Equations.