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This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.
List of contents
Sets, Numbers and Vectors.- Production Systems.- Mappings, Functions.- Affine and Linear Functions.- Linear Optimisation, Duality. Zero-Sum Games.- Functions, Their Limits, and Their Derivatives.- Nonlinear Functions.- Nonlinear Optimisation.- Set Valued Functions. Equilibria. Games.- Integrals.- Differential Equations.- Difference Equations.- Models and Theories in Economics.
About the author
Prof. Dr.rer.nat. Dres.rer.pol.h.c. Wolfgang Eichhorn ist Leiter des Instituts für Wirtschaftstheorie und Operations Research an der Universität Karlsruhe. Autor zahlreicher Veröffentlichungen in internationalen Fachzeitschriften der Wirtschaftswissenschaft, Mathematik, des Operations Research sowie der Versicherungswissenschaft.
Summary
This book about mathematics and methodology for economics is the result of the lifelong experience of the authors. It is written for university students as well as for students of applied sciences. This self-contained book does not assume any previous knowledge of high school mathematics and helps understanding the basics of economic theory-building. Starting from set theory it thoroughly discusses linear and non-linear functions, differential equations, difference equations, and all necessary theoretical constructs for building sound economic models. The authors also present a solid introduction to linear optimisation and game theory using production systems. A detailed discussion on market equilibrium, in particular on Nash Equilibrium, and on non-linear optimisation is also provided. Throughout the book the student is well supplied with numerous examples, some 2000 problems and their solutions to apply the knowledge to economic theories and models.
