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About this book

This textbook contains and explains essential mathematical formulas within an economic context. A broad range of aids and supportive examples will help readers to understand the formulas and their practical applications. This mathematical formulary is presented in a practice-oriented, clear, and understandable manner, as it is needed for meaningful and relevant application in global business, as well as in the academic setting and economic practice.

The topics presented include, but are not limited to: mathematical signs and symbols, logic, arithmetic, algebra, linear algebra, combinatorics, financial mathematics, optimisation of linear models, functions, differential calculus, integral calculus, elasticities, economic functions, and the Peren theorem.

Given its scope, the book offers an indispensable reference guide and is a must-read for undergraduate and graduate students, as well as managers, scholars, and lecturers in business, politics, and economics.

Table of Contents

Frontmatter

Chapter 1. Mathematical Signs and Symbols

Abstract
The signs and symbols are partly shown in applications. For definitions see dedicated passage.
Franz W. Peren

Chapter 2. Logic

Abstract
a, b, ... are letters or other symbols which can be used as placeholders for statements or truths.
Franz W. Peren

Chapter 3. Arithmetic

Abstract
A universal set, \(\mathbb{S}\)U, is bounded upwards (or downwards) if it has at least one upper (or lower) bound B.
Franz W. Peren

Chapter 4. Algebra

Abstract
Variables are placeholders (e.g. a,b, x, y, ...) that can be replaced by numbers from a given universal set \(\mathbb{S}\)U.
A term within a universal set \(\mathbb{S}\)U is an expression composed of variables, numbers and/or arithmetic symbols. Division by zero is not possible.
Franz W. Peren

Chapter 5. Linear Algebra

Abstract
Linear algebra is used, among other things, in the analysis of complex business and economic systems.
Franz W. Peren

Chapter 6. Combinatorics

Abstract
A basic task of combinatorics is to determine the number of possible arrangements (permutations) for a (basic) population of N different elements e1, e2, ..., eN.
Franz W. Peren

Chapter 7. Financial Mathematics

Abstract
Interest claims that arise during the period are added to the interestbearing capital at the end of the year. In the following interest periods, the interest of the previous interest periods is also included.
Franz W. Peren

Chapter 8. Optimisation of Linear Models

Abstract
By means of the Lagrange method or linear optimisation, the relative extremes (minima or maxima) of a linear (target) function can be determined under restrictive linear constraints.
Franz W. Peren

Chapter 9. Functions

Abstract
In the graphical representation of the function y = f (x) in the rectangular coordinate system, each pair of values (x, y) is uniquely assigned to a point P(x, y) on the x-y-plane. This results in the so-called function graph or function graph.
Franz W. Peren

Chapter 10. Differential Calculus

Abstract
If the function f = f (x) is differentiable in the entire domain, the derivative function exists (1st derivative of f ).
Franz W. Peren

Chapter 11. Integral Calculus

Abstract
While differential calculus deals with the determination of the derivative (absolute gradient) f ‘(x) of a given function f (x), integral calculus - starting from a given derivative function f ‘(x) - is interested in the underlying original function f (x).
Franz W. Peren

Chapter 12. Elasticities

Abstract
The subject of this chapter is the analysis of the relative rate of change of economic variables when there is a functional relationship between them, for example y = y(x).
Franz W. Peren

Chapter 13. Economic Functions

Abstract
The supply function represents the relationship between the market price of a good (independent variable) and the quantity supplied (dependent variable) in the form of a unique graph (function).
Franz W. Peren

Chapter 14. The Peren Theorem The Mathematical Frame in Which We Live

Abstract
Humans consume the natural resources of the Earth faster than the Earth is able to regenerate them. Mankind on the whole lives above its means and often at the expense of future generations. Current economic activity, with the aim of maximising monetary profits and generating quantitative growth and prosperity, cannot be continued.
Franz W. Peren

Backmatter

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