This volume presents mathematical formulas and theorems commonly used in economics. It offers the first grouping of this material for a specifically economist audience, and it includes formulas like Roy's identity and Leibniz's rule.

The fourth edition is augmented by more than 70 new formulas. In particular, we have included some key concepts and results from trade theory, games of incomplete information and combinatorics. In addition there are scattered additions of new formulas in many chapters. Again we are indebted to a number of people who has suggested corrections, - provements and new formulas. In particular, we would like to thank Jens-Henrik Madsen, Larry Karp, Harald Goldstein, and Geir Asheim. In a reference book, errors are particularly destructive. We hope that readers who ?nd our remaining errors will call them to our attention so that we may purge them from future editions. Oslo and Berkeley, May 2005 Knut Sydsæter, Arne Strøm, Peter Berck From the preface to the third edition Thepracticeofeconomicsrequiresawide-rangingknowledgeofformulasfrommat- matics, statistics, andmathematicaleconomics. Withthisvolumewehopetopresent a formulary tailored to the needs of students and working professionals in economics. In addition to a selection of mathematical and statistical formulas often used by economists, this volume contains many purely economic results and theorems. It containsjusttheformulasandtheminimumcommentaryneededtorelearnthema- ematics involved. We have endeavored to state theorems at the level of generality economists might ?nd useful. In contrast to the economic maxim, everything is twice more continuously di?erentiable than it needs to be , we have usually listed theregularityconditionsfortheoremstobetrue.Wehopethatwehaveachieveda level of explication that is accurate and useful without being pedantic.

Most successful mathematical manual for economists Includes supplementary material: sn.pub/extras

Autorentext
Knut Sydsaeter ist Professor für Mathematik an der Wirtschaftsfakultät der Universität Oslo mit langjähriger Unterrichtserfahrung in Mathematik für Wirtschaftswissenschaftler. Daneben gab er Kurse in Dynamischer Optimierung in Yale, Berkeley und Göteborg. Seine Mathematikbücher wurden bereits in mehrere Sprachen übersetzt.

Inhalt
Set Theory. Relations. Functions.- Equations. Functions of one variable. Complex numbers.- Limits. Continuity. Differentiation (one variable).- Partial derivatives.- Elasticities. Elasticities of substitution.- Systems of equations.- Inequalities.- Series. Taylor's formula.- Integration.- Difference equations.- Differential equations.- Topology in Euclidean space.- Convexity.- Classical optimization.- Linear and nonlinear programming.- Calculus of variations and optimal control theory.- Discrete dynamic optimization.- Vectors in ?n. Abstract spaces.- Matrices.- Determinants.- Eigenvalues. Quadratic forms.- Special matrices. Leontief systems.- Kronecker products and the vec operator. Differentiation of vectors and matrices.- Comparative statics.- Properties of cost and profit functions.- Consumer theory.- Topics from trade theory.- Topics from finance and growth theory.- Risk and risk aversion theory.- Finance and stochastic calculus.- Non-cooperative game theory.- Combinatorics.- Probability and statistics.- Probability distributions.- Method of least squares.