2023 | Book

# Math for Business and Economics

## Compendium of Essential Formulas

Author: Franz W. Peren

Publisher: Springer Berlin Heidelberg

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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.

##### 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
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, SU, is bounded upwards (or downwards) if it has at least one upper (or lower) bound B. If both conditions apply, SU is bounded:
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 SU.
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
The interest must always be calculated from the initial capital C0, i.e. the annual interest due always remains the same.
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
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.
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). The original function is called the antiderivative, inverse derivative or primitive function. The return from the derivative function to the antiderivative is called integration.
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. 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.
Franz W. Peren
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Franz W. Peren