Quantitative Methods: An Introduction for Business Management

Contents

Preface

Part I Motivations and Foundations

1 Quantitative Methods: Should We Bother?

1.1 A decision problem without uncertainty: product mix

1.1.1 The case of similar products

1.1.2 The case of heterogeneous products

1.2 The role of uncertainty

1.2.1 A problem in supply chain management

1.2.2 Squeezing information out of known facts

1.2.3 Variations on coin flipping

1.3 Endogenous vs. exogenous uncertainty: Are we alone?

1.3.1 The effect of organized markets: pricing a forward contract

1.4 Quantitative models and methods

1.4.1 Descriptive vs. prescriptive models

1.5 Quantitative analysis and problem solving

Problems

For further reading

References

2 Calculus

2.1 A motivating example: economic order quantity

2.1.1 Task 1: representing the total cost function

2.1.2 Task 2: plotting the total cost function

2.1.3 Task 3: finding the best decision

2.2 A little background

2.2.1 Real vs. integer numbers

2.2.2 Intervals on the real line

2.2.3 The sum notation

2.2.4 Permutations and combinations

2.3 Functions

2.3.1 Linear functions

2.3.2 Polynomial functions

2.3.3 Rational functions

2.3.4 Exponential functions

2.4 Continuous functions

2.5 Composite functions

2.6 Inverse functions

2.6.1 The logarithm

2.7 Derivatives

2.7.1 Definition of the derivative

2.7.2 Continuity and differentiability

2.8 Rules for calculating derivatives

2.8.1 Derivative of functions obtained by sum, multiplication, and division

2.8.2 Derivative of composite functions

2.8.3 Derivative of inverse functions