Mathematical Formulas for Economists
The present collection of formulas has been composed for students of economics or management science at universities, colleges and trade schools. It contains basic knowledge in mathematics, financial mathematics and statistics in a compact and clearly arr
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Bernd Luderer · Volker Nollau Klaus Vetters
Mathematical Formulas for Economists Third Edition
With 62 Figures and 6 Tables
123
Professor Dr. Bernd Luderer Chemnitz University of Technology Department of Mathematics Reichenhainer Straße 41 09126 Chemnitz Germany [email protected] Professor Dr. Volker Nollau Dr. Klaus Vetters Dresden University of Technology Department of Mathematics and Science Zellescher Weg 12-14 01069 Dresden Germany [email protected] [email protected]
Library of Congress Control Number: 2006934208
ISBN-10 3-540-46901-X Springer Berlin Heidelberg New York ISBN-13 978-3-540-46901-8 Springer Berlin Heidelberg New York ISBN 3-540-27916-4 2nd Edition Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. Springer is part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 2002, 2005, 2007 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Production: LE-TEX Jelonek, Schmidt & V¨ ockler GbR, Leipzig Cover-design: Erich Kirchner, Heidelberg SPIN 11898412
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Preface
This collection of formulas constitutes a compendium of mathematics for economics and business. It contains the most important formulas, statements and algorithms in this significant subfield of modern mathematics and addresses primarily students of economics or business at universities, colleges and trade schools. But people dealing with practical or applied problems will also find this collection to be an efficient and easy-to-use work of reference. First the book treats mathematical symbols and constants, sets and statements, number systems and their arithmetic as well as fundamentals of combinatorics. The chapter on sequences and series is followed by mathematics of finance, the representation of functions of one and several independent variables, their differential and integral calculus and by differential and difference equations. In each case special emphasis is placed on applications and models in economics. The chapter on linear algebra deals with matrices, vectors, determinants and systems of linear equations. This is followed by the representation of structures and algorithms of linear programming. Finally, the reader finds formulas on descrip
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