Mathematical Formulas for Economists
,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
Professor Dr. Volker Nollau
Dr. Klaus Vetters
Dresden University of Technology
Department of Mathematics and Science
Zellescher Weg 12-14
01069 Dresden
Germany
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, broad-
casting, 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 & Vöckler GbR, Leipzig
Cover-design: Erich Kirchner, Heidelberg
SPIN 11898412 43/3100YL - 5 4 3 2 1 0 Printed on acid-free paper
, Preface
This collection of formulas constitutes a compendium of mathematics for eco-
nomics 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 state-
ments, number systems and their arithmetic as well as fundamentals of com-
binatorics. The chapter on sequences and series is followed by mathematics of
finance, the representation of functions of one and several independent vari-
ables, 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 struc-
tures and algorithms of linear programming. Finally, the reader finds formu-
las on descriptive statistics (data analysis, ratios, inventory and time series
analysis), on probability theory (events, probabilities, random variables and
distributions) and on inductive statistics (point and interval estimates, tests).
Some important tables complete the work.
The present manual arose as a result of many years’ teaching for students
of economic faculties at the Institutes of Technology of Dresden and Chem-
nitz, Germany. Moreover, the authors could take advantage of experience and
suggestions of numerous colleagues. For critical reading of the manuscript we
feel obliged to thank Dr M. Richter and Dr K. Eppler. Our special thank is
due to M. Schoenherr, Dr U. Wuerker and Dr J. Rudl, who contributed to
technical preparation of the book.
After successful use by German readers it is a great pleasure for us to present
this collection of formulas to the English auditorium. The translation is based
on the fifth German edition. We are greatly obliged to Springer-Verlag for
giving us the opportunity to publish this book in English.
The second English edition of this book was very popular both with students
and with practitioners. Thus it was rapidly out of print. So we are very
pleased to present this third, carefully checked edition.
Finally we would like to emphasize that remarks and criticism are always
welcome.
Chemnitz / Dresden, Bernd Luderer
August 2006 Volker Nollau
Klaus Vetters
,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
Professor Dr. Volker Nollau
Dr. Klaus Vetters
Dresden University of Technology
Department of Mathematics and Science
Zellescher Weg 12-14
01069 Dresden
Germany
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, broad-
casting, 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 & Vöckler GbR, Leipzig
Cover-design: Erich Kirchner, Heidelberg
SPIN 11898412 43/3100YL - 5 4 3 2 1 0 Printed on acid-free paper
, Preface
This collection of formulas constitutes a compendium of mathematics for eco-
nomics 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 state-
ments, number systems and their arithmetic as well as fundamentals of com-
binatorics. The chapter on sequences and series is followed by mathematics of
finance, the representation of functions of one and several independent vari-
ables, 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 struc-
tures and algorithms of linear programming. Finally, the reader finds formu-
las on descriptive statistics (data analysis, ratios, inventory and time series
analysis), on probability theory (events, probabilities, random variables and
distributions) and on inductive statistics (point and interval estimates, tests).
Some important tables complete the work.
The present manual arose as a result of many years’ teaching for students
of economic faculties at the Institutes of Technology of Dresden and Chem-
nitz, Germany. Moreover, the authors could take advantage of experience and
suggestions of numerous colleagues. For critical reading of the manuscript we
feel obliged to thank Dr M. Richter and Dr K. Eppler. Our special thank is
due to M. Schoenherr, Dr U. Wuerker and Dr J. Rudl, who contributed to
technical preparation of the book.
After successful use by German readers it is a great pleasure for us to present
this collection of formulas to the English auditorium. The translation is based
on the fifth German edition. We are greatly obliged to Springer-Verlag for
giving us the opportunity to publish this book in English.
The second English edition of this book was very popular both with students
and with practitioners. Thus it was rapidly out of print. So we are very
pleased to present this third, carefully checked edition.
Finally we would like to emphasize that remarks and criticism are always
welcome.
Chemnitz / Dresden, Bernd Luderer
August 2006 Volker Nollau
Klaus Vetters
