(Ebook) Math for Business and Economics Compendium of Essential Formulas 3rd Edition by Franz W Peren ISBN 3662688603 9783662688601

(Ebook) Math for Business and Economics Compendium of Essential Formulas 3rd Edition by Franz W Peren ISBN 3662688603 9783662688601

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ISBN 10: 3662688603 
ISBN 13: 9783662688601
Author: Franz W Peren

This 3rd edition revised and extended compendium contains and explains essential mathematical formulas within an economic context. Newly added content introduces the mathematical practical application of optimization by using the Lagrange function, presenting the issue of linear optimization cases where the relative extremes (minima or maxima) of a linear (target) function can be determined under restrictive linear constraint and its relevance for business management practice.  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, and financial mathematics, including an international comparison between different national methods used in the calculation of interest, optimization of linear models, functions, differential calculus, integral calculus, elasticities, annuity calculation, 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.

(Ebook) Math for Business and Economics Compendium of Essential Formulas 3rd Table of contents:

Chapter 1 Mathematical Signs and Symbols
1.1 Pragmatic Signs
1.2 General Arithmetic Relations and Links
1.3 Sets of Numbers
1.4 Special Numbers and Links
1.5 Limit
1.6 Exponential Functions, Logarithm
1.7 Trigonometric Functions, Hyperbolic Functions
1.8 Vectors, Matrices
1.9 Sets
1.10 Relations
1.11 Functions
1.12 Order Structures
1.13 SI Multiplying and Dividing Prefixes
1.14 Greek Alphabet
Chapter 2 Logic
2.1 Mathematical Logic
2.2 Propositional Logic
2.2.1 Propositional Variable
2.2.2 Truth Tables
Chapter 3 Arithmetic
3.1 Sets
3.1.1 General
3.1.2 Set Relations
3.1.3 Set Operations
3.1.4 Relations, Laws, Rules of Calculation for Sets
3.1.5 Intervals
3.1.6 Numeral Systems
3.1.6.1 Decimal System (Decadic System)
3.1.6.2 Dual System (Binary System)
3.1.6.3 Roman Numeral System
3.2 Elementary Calculus
3.2.1 Elementary Foundations
3.2.1.1 Axioms
3.2.1.2 Factorisation
3.2.1.3 Relations
3.2.1.4 Absolute Value, Signum
3.2.1.5 Fractions
3.2.1.6 Polynomial Division
3.2.1.7 Horner’s Scheme (Horner’s Method)
3.2.2 Conversions of Terms
3.2.2.1 Binomial Formulas (a, b ∈ R)
3.2.2.2 Binomial Theorem (a+b)n with a, b ∈ R, n ∈ N.
3.2.2.3 General Binomial Theorem for Natural Exponents (n ∈ N)
3.2.2.4 General Binomial Theorem for Real Exponents (α ∈ R)
3.2.2.5 Polynomial Terms with a,b, c,d ∈ R
3.2.3 Summation and Product Notation
3.2.3.1 Summation Notation
3.2.3.2 Product Notation
3.2.4 Powers, Roots
3.2.5 Logarithms
Logarithmic Systems: Common Logarithm
Natural Logarithm
Logarithm to an Arbitrary Base
3.2.6 Factorial
3.2.7 Binomial Coefficient (read “n choose k”)
Pascal’s Triangle for Determining the Binomial Coefficients
3.3 Sequences
3.3.1 Definition
Supremum, Infimum, Limits
3.3.2 Limit of a Sequence
Null Sequence
Improper Limit
Examples of Limits of Selected Numerical Sequences (k ∈ N*)
3.3.3 Arithmetic and Geometric Sequences
Arithmetic Sequences
Geometric Sequence
3.4 Series
3.4.1 Definition
3.4.2 Arithmetic and Geometric Series
Arithmetic Series
Arithmetic Series of Higher Order
Geometric Series
Infinite Geometric Series
Chapter 4 Algebra
4.1 Fundamental Terms
4.2 Linear Equations
4.2.1 Linear Equations with One Variable
4.2.2 Linear Inequations with One Variable
4.2.3 Linear Equations with Multiple Variables
4.2.4 Systems of Linear Equations
4.2.5 Linear Inequations with Multiple Variables
4.3 Non-linear Equations
4.3.1 Quadratic Equations with One Variable
4.3.2 Cubic Equations with One Variable
4.3.3 Biquadratic Equations
4.3.4 Equations of the nth Degree
4.3.5 Radical Equations
4.4 Transcendental Equations
4.4.1 Exponential Equations
4.4.2 Logarithmic Equations
4.5 Approximation Methods
4.5.1 Regula falsi (Secant Method)
4.5.2 Newton’s Method (Tangent Method)
4.5.3 General Approximation Method (Fixed-point Iteration)
Chapter 5 Linear Algebra
5.1 Fundamental Terms
5.1.1 Matrix
5.1.2 Equality/Inequality of Matrices
5.1.3 Transposed Matrix
5.1.4 Vector
5.1.5 Special Matrices and Vectors
5.2 Operations with Matrices
5.2.1 Addition of Matrices
5.2.2 Multiplication of Matrices
5.2.2.1 Multiplication of a Matrix with a Scalar
5.2.2.2 The Scalar Product of Two Vectors
5.2.2.3 Multiplication of a Matrix by a Column Vector
5.2.2.4 Multiplication of a Row Vector by a Matrix
5.2.2.5 Multiplication of Two Matrices
5.3 The Inverse of a Matrix
5.3.1 Introduction
5.3.2 Determination of the Inverse with the Usage of the Gaussian Elimination Method
5.4 The Rank of a Matrix
5.4.1 Definition
5.4.2 Determination of the Rank of a Matrix
5.5 The Determinant of a Matrix
5.5.1 Definition
5.5.2 Calculation of Determinants
5.5.3 Characteristics of Determinants
5.6 The Adjoint of a Matrix
5.6.1 Definition
5.6.2 Determination of the Inverse with the Usage of the Adjoint
Chapter 6 Combinatorics
6.1 Introduction
6.2 Permutations
6.3 Variations
6.4 Combinations
Chapter 7 Financial Mathematics
7.1 Calculation of Interest
7.1.1 Fundamental Terms
7.1.2 Annual Interest
7.1.2.1 Simple Interest Calculation I
7.1.2.2 Compound Computation of Interest
7.1.2.3 Composite Interest
7.1.3 Interest During the Period
7.1.3.1 Simple Interest Calculation (linear)
7.1.3.2 Simple Interest Using the Nominal Annual Interest Rate
7.1.3.3 Compound Interest (exponential)
7.1.3.4 Interest with Compound Interest Using a Conforming Annual Interest Rate
7.1.3.5 Mixed Interest
7.1.3.6 Steady Interest Rate
7.2 Annual Percentage Rate
7.3 Depreciation
7.3.1 Time Depreciation
7.3.1.1 Linear Depreciation
7.3.1.2 Arithmetic-Degressive Depreciation
7.3.1.3 Geometric-Degressive Depreciation
7.3.2 Units of Production Depreciation
7.3.3 Extraordinary Depreciation
7.4 Annuity Calculation
7.4.1 Fundamental Terms
7.4.2 Finite, Regular Annuity
7.4.2.1 Annual Annuity with Annual Interest
7.4.2.2 Annual Annuity with Sub-Annual Interest
7.4.2.3 Sub-Annual Annuity with Annual Interest
7.4.2.4 Sub-Annual Annuity with Sub-Annual Interest
Alternative Calculation Using the ICMA Method
Alternative Calculation Using the ICMA Method
Alternative Calculation Using the ICMA Method
Alternative Calculation Using the ICMA Method
7.4.3 Finite, Variable Annuity
7.4.3.1 Irregular Annuity
7.4.3.2 Arithmetic Progressive Annuity
7.4.3.3 Geometric Progressive Annuity
7.4.4 Perpetuity
7.5 Sinking Fund Calculation
7.5.1 Fundamental Terms
7.5.2 Annuity Repayment
7.5.3 Repayment by Instalments
7.5.4 Repayment with Premium
7.5.4.1 Annuity Repayment with Premium premium
7.5.4.2 Repayment of an Instalment Debt with Premium
7.5.5 Repayment with Discount (Disagio)
7.5.5.1 Annuity Repayment with Discount when Immediately Booked as Interest Expense
7.5.5.2 Annuity Repayment with Discount when a Disagio is Included in Prepaid Expenses
7.5.5.3 Instalment Repayment with Discount when Immediately Booked as Interest Expense
7.5.5.4 Instalment Repayment with Discount when a Disagio is Included in Prepaid Expenses
7.5.6 Grace Periods
7.5.7 Rounded Annuities
7.5.7.1 Percentage Annuity
7.5.7.2 Repayment of Bonds
7.5.8 Repayment During the Year
7.5.8.1 Annuity Repayment During the Year
7.5.8.2 Repayment by Instalments During the Year
7.6 Investment Calculation
7.6.1 Fundamental Terms
7.6.2 Fundamentals of Financial Mathematics
7.6.3 Methods of Static Investment Calculation
7.6.4 Methods of Dynamic Investment Calculation
7.6.4.1 Net Present Value Method (Net Present Value, Amount of Capital, Final Asset Value)
7.6.4.2 Annuity Method
7.6.4.3 Internal Rate of Return Method

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