2023 | Book

# Math for Business and Economics

## Compendium of Essential Formulas

Author: Franz W. Peren

Publisher: Springer Berlin Heidelberg

2023 | Book

Author: Franz W. Peren

Publisher: Springer Berlin Heidelberg

This 2nd edition, revised and extended compendium contains and explains essential mathematical formulas within an economic context. Newly added content focuses on financial mathematics, now including an international comparison between different national methods used in the calculation of interest. Further, the annuity calculation now contains unique content.

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.

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Abstract

The signs and symbols are partly shown in applications. For definitions see dedicated passage

Abstract

are letters or other symbols which can be used as placeholders
for statements or truths.

Abstract

A universal set, SU, is bounded upwards (or downwards) if it has at least
one upper (or lower) bound B. If both conditions apply, SU is bounded:

Abstract

Variables are placeholders (e.g. a,b,x, y, ...) that can be replaced by
numbers from a given universal set SU.

Abstract

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

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.

Abstract

The interest must always be calculated from the initial capital C0, i.e. the
annual interest due always remains the same.

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.

Abstract

A function f = f (x) is an unique assignment of “x to f of x”: x 7→ f (x).
A function y = f (x)(x 7→ y) has exactly one dependent value y assigned
to each independent value, also called “argument” x.

Abstract

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

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). The original function is called the antiderivative,
inverse derivative or primitive function. The return from the
derivative function to the antiderivative is called integration.

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).

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).

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.
The Peren Theorem demonstrates that the consumption of natural resources
within a closed system, as represented by Earth, is only possible
if their consumption is able to naturally regenerate. If this balance is
disturbed for too long a period, this will then result in the natural death
of the planet. With an increasing global population, the per capita consumption
of natural resources of all humans living on or from the Earth
must be proportionately reduced.