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 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 Chemnitz,
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 third English edition of this book was very popular both with students
and with practitioners. So we are very pleased to present this fourth, carefully
checked and extended edition. New topics are: rank statistics, analysis of
variance (ANOVA), analysis of covariance.
Finally we would like to emphasize that remarks and criticism are always
Mathematical Symbols and Constants . . . . . . . . . . . . . . . . . . . . . . . . 1
Notations and symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Mathematical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Sets and Propositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Notion of a set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Relations between sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Operations with sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Rules for operations with sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Product sets and mappings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Propositional calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Number Systems and Their Arithmetic . . . . . . . . . . . . . . . . . . . . . . . 9
Natural, integer, rational, and real numbers . . . . . . . . . . . . . . . . . . . . 9
Calculation with real numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Absolute values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Factorial and binomial coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Finite sums . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Powers and roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Logarithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Complex numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Combinatorial Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Permutations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Arrangements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Combinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Sequences and Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Sequences of numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Sequences of functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Infinite series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Function and power series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25