Analysis and Linear Algebra: An Introduction for Economists

290 Pages·2023·9.928 MB·English

by  Thomas Holey, Armin Wiedemann

Thomas Holey · Armin Wiedemann
Analysis
and Linear
Algebra
An Introduction for Economists
Analysis and Linear Algebra
Thomas Holey · Armin Wiedemann
Analysis and Linear Algebra
An Introduction for Economists
Thomas Holey Armin Wiedemann
Duale Hochschule Baden-Württemberg Duale Hochschule Baden-Württemberg
Mannheim Mannheim
Mannheim, Germany Mannheim, Germany
ISBN 978-3-662-66246-5 ISBN 978-3-662-66247-2 (eBook)
https://doi.org/10.1007/978-3-662-66247-2
© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part
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Preface to the Fifth Edition
In the fifth edition, we have considered the treatment of sequences and series at some
points. With this we take into account the content-related structure of many lectures
and want to express this with the new title Analysis and Linear Algebra. The subtitle
An Introduction for Economists refers to the applications and examples that are to be
assigned to economics or economic informatics.
The chapter Applications of Differential Calculus has been extended by a section on
Taylor series, in examples it is shown how these tools can be used. In the chapter Finan-
cial Mathematics, we have taken into account the trend of the times and the interest rates
have been approximated to the current values. Some more exercise problems have been
added and literature references have been added.
The slide set as a lecture basis and the detailed solutions to the exercises for the 5th
edition are available on Springerlink.
Mannheim, Germany Thomas Holey
May 2021 Armin Wiedemann
V
Preface to the Fourth Edition
In the fourth edition, errors that affected the figures in Chap. 6 were corrected.
The interest in exercise problems is still great. Accordingly, we have taken on addi-
tional exercise problems. The note on the URL of the publisher’s website, where detailed
solutions to the tasks are available, is now directly in the exercise part of the individual
chapters. The literature references have been updated again.
Mannheim, Germany Thomas Holey
July 2015 Armin Wiedemann
VII
Preface to the Third Edition
With the third edition we have complied with the request of some readers to include a
chapter with solutions to the exercise problems. In this chapter the solutions to all exer-
cise problems are given, partly the solution path is briefly sketched. Detailed solution
paths to the exercise problems can still be accessed via the website of the publisher for
the book. The literature references have been revised.
Mannheim, Germany Thomas Holey
October 2012 Armin Wiedemann
IX
Preface to the Second Edition
In the second, corrected and revised edition, we have taken up numerous suggestions
from lecturers and students who use the book for lectures and exercises. We have
responded to the request to provide more exercise problems. So after each chapter there
are some basic exercise problems as well as further problems from the field of business
applications. The solutions to the problems can be accessed again via the corresponding
link of the Springer-Verlag.
We would like to thank all those who have given us hints and suggestions for the sec-
ond edition. In particular, we would like to thank Ms. Dipl. Math. Eva Schmitt-Leiß and
Mr. Prof. Dr. Klaus Gläser for helpful discussions.
Mannheim, Germany Thomas Holey
August 2009 Armin Wiedemann
XI
Preface to the First Edition
Quantitative methods form an important basis in almost all economic disciplines.
Accordingly, mathematical introductory lectures can be found in the framework study
plans of these degree programs.
The present book Mathematics for Economists in the series BA-Kompakt is very strongly
oriented towards the framework study plan for the field of economics at vocational acad-
emies in Baden-Württemberg. In the selection of material, we have endeavored to include
the most important topics for students of business administration and business informatics.
A wide range of mathematical basics is presented, which are often also the subject of upper
secondary level: functions of a variable, differential and integral calculus. The book offers
the lecturer the possibility to repeat these basics very quickly and to concentrate more on the
applications, depending on the students’ level of knowledge. If it appears more reasonable
and necessary to spend more time on the basics, one can restrict oneself to the special case
of two variables when dealing with functions of several variables. Then, in linear algebra,
the concepts of determinant and eigenvalue of a matrix are not needed.
In this way, a certain flexibility is created without completely omitting topic areas of
the framework study plan. Some basics are listed in the first chapter, which should be
part of the “toolbox”. The book offers students the opportunity to test their knowledge
with a short self-test.
We would like to thank Mrs. Prof. Dr. Irene Rößler and Mr. Prof. Dr. Frank Hubert
for many helpful discussions and suggestions. We would like to thank the editors, Prof.
Dr. Martin Kornmeier and Prof. Dr. Willy Schneider, for including the book in the series
BA-Kompakt. Our thanks go to Mrs. Katharina Wetzel-Vandai and Mrs. Gabriele Keidel
at Springer-Verlag for their helpful support in editorial matters.
Finally, we would like to point out that a set of slides is available as a lecture basis
and the solutions to the exercises can be downloaded from the publisher at the URL
http://www.springer.com/978-3-7908-1973-1. The solutions to the
test are given in the appendix.
Mannheim, Germany Thomas Holey
Juni 2007 Armin Wiedemann
XIII
Contents
1 Elementary Basics ................................................ 1
1.1 Elementary From Propositional Logic ............................. 1
1.2 Set Theory .................................................. 4
1.3 Basic Arithmetic Operations .................................... 9
1.4 Equations ................................................... 16
1.5 Trigonometry ................................................ 21
1.6 Test ........................................................ 22
References ....................................................... 24
2 Functions ....................................................... 25
2.1 Definition and Representation of Functions ........................ 25
2.2 Some Elementary Functions .................................... 28
2.2.1 Linear Function ....................................... 28
2.2.2 Quadratic Function ..................................... 30
2.2.3 Integer Rational Functions or Polynomials .................. 31
2.2.4 Power Function ....................................... 31
2.2.5 Fractional Rational Functions ............................ 32
2.2.6 Hyperbolic Function ................................... 33
2.2.7 Root Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.8 Exponential Function ................................... 34
2.2.9 Logarithm Function .................................... 36
2.2.10 Trigonometric Functions ................................ 37
2.2.11 Sectionally Defined Functions ............................ 41
2.2.12 Some Economic Functions .............................. 42
2.3 The Inverse Function .......................................... 47
2.4 Chained Functions ............................................ 51
2.5 Properties of Functions ........................................ 52
2.5.1 Limitation ............................................ 52
2.5.2 Monotonicity ......................................... 53
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