Business Mathematics

    Preface

    About the author

    Introduction

    Module 1 Relationships/Functions

        1.1  Introduction

            1.1.1  Module 1 overview

        1.2  Relationships/Functions

            1.2.1  Introduction to functions

            1.2.2  What is a function?

            1.2.3  Why do we care about functions?

            1.2.4  Examples of functions

            1.2.5  Ways of expressing a function

            1.2.6  Scratches on paper

            1.2.7  Non-linear functions

        1.3  Graphing functions

            1.3.1  Graphing functions

        1.4  Functions working on functions

            1.4.1  Functions working on functions

        1.5  Functions with more than one input

            1.5.1  Introduction

            1.5.2  Example: compounding investments

            1.5.3  Turning the question around, what's in the box?

            1.5.4  Visual presentation of functions of more than one variable

        1.6  Summary

    Module 2 Linear functions

        2.1  Introduction to module 2

            2.1.1  Module 2 overview

            2.1.2  Recap module 1

        2.2  Ways of measuring change

            2.2.1  Absolute change

            2.2.2  Relative changes and percentages

            2.2.3  A comparison of the two ways of measuring change

        2.3  Linearity

            2.3.1  Introduction and examples

            2.3.2  Interpretation of the coefficients in the linear cost function

            2.3.3  Why lines are so ubiquitous and important as models

            2.3.4  Questions about lines

            2.3.5  What makes a line a line?

            2.3.6  How viable is the constant change assumption? - a reality check.

        2.4  Realistic problems - practical constraints

            2.4.1  Identifying the constraints

            2.4.2  Satisfying all the labor constraints

            2.4.3  The profit function

            2.4.4  Identifying the optimal network combination

            2.4.5  Recap

        2.5  Planes

        2.6  Module summary

    Module 3 A library of useful functions

        3.1  Introduction

            3.1.1  Module 3 overview

            3.1.2  Last time

        3.2  The power function

            3.2.1  Examples

            3.2.2  Definitions and rules

            3.2.3  The cost function revisited

        3.3  The exponential function

            3.3.1  Introduction

            3.3.2  Rules for manipulating the exponential function

        3.4  The log function

            3.4.1  Introduction and definition

            3.4.2  Different bases

            3.4.3  Log manipulations

        3.5  Summary

    Module 4 Growth in discrete time

        4.1  Introduction to Module 4

            4.1.1  Module 4 overview

            4.1.2  Recap Module 3

        4.2  Examples of growth in discrete time

            4.2.1  The telephone survey

            4.2.2  Explicit calculation of the number of phases required

        4.3  Defining the geometric series

            4.3.1  Notation for geometric series

            4.3.2  Summing a geometric series

        4.4  Interest, present and future value

            4.4.1  Simple interest

            4.4.2  Compound interest

            4.4.3  Present and future value

            4.4.4  Annuities

        4.5  More examples of geometric series

            4.5.1  Monthly mortgage repayments

            4.5.2  Exponential smoothing

            4.5.3  Using the formula to solve problems

            4.5.4  ** Derivation of the sum of the geometric series

        4.6  Non-constant multipliers

            4.6.1  Returns on an asset

        4.7  Summary

    Module 5 Growth in continuous time & introduction to the derivative

        5.1  Introduction to Module 5

            5.1.1  Module 5 overview

            5.1.2  Recap module 4

        5.2  Compound growth

            5.2.1  Definitions

            5.2.2  Continuous compounding

            5.2.3  Examples

            5.2.4  ** The continuous compounding formula derivation

        5.3  The derivative

            5.3.1  Secant lines

            5.3.2  Motivation for the calculus

            5.3.3  Rules for taking derivatives

            5.3.4  Example cost function

        5.4  Summary

    Module 6 Derivatives

        6.1  Introduction to module 6

            6.1.1  Module 6 overview

            6.1.2  Recap module 5

        6.2  Warm up examples

        6.3  Increasing functions, decreasing functions and turning points

        6.4  Liquor store example

        6.5  Cost function example

        6.6  Elasticity

        6.7  More rules for derivatives

            6.7.1  The product rule for derivatives

            6.7.2  The chain rule - the rule for a composition of functions

        6.8  Summary

    Module 7 Optimization

        7.1  Introduction to module 7

            7.1.1  Module 7 overview

            7.1.2  Recap module 6

        7.2  Practice up examples

        7.3  Optimization

            7.3.1  Where you find these ideas used

            7.3.2  Characterizing an optimal value

            7.3.3  Example using the retail space problem

            7.3.4  A classic example from economics, (revenue, costs and profit maximization)

        7.4  Summary

    Module 8 Working with functions of more than one variable.

        8.1  Introduction to module 8

            8.1.1  Module 8 overview

            8.1.2  Recap module 7

        8.2  Functions of more than one variable

        8.3  Partial derivatives

        8.4  Common sense in modeling

        8.5  Summary

    Module 9 Probability

        9.1  Introduction to module 9

            9.1.1  Module 9 overview

            9.1.2  Recap module 8

        9.2  Introduction to probability

        9.3  Probability statements

        9.4  Probability trees

        9.5  Expected values, means, variances and standard deviations

            9.5.1  Means

            9.5.2  Variance and standard deviation

        9.6  Probabilities on joint events

        9.7  Conditional probability

        9.8  Covariance and portfolios

            9.8.1  Covariance

            9.8.2  Portfolio math

        9.9  Summary

    Module 10 Statistics

        10.1  Introduction to module 10

            10.1.1  Module 10 overview

            10.1.2  Recap Class 9

        10.2  Introduction to statistics

            10.2.1  Introduction

            10.2.2  Graphical techniques for summarizing and presenting data

            10.2.3  The population/sample paradigm

            10.2.4  Numerical summaries of data

            10.2.5  The normal distribution

            10.2.6  The Empirical Rule

            10.2.7  Ideas required for a confidence interval

            10.2.8  Sampling distributions/Central Limit Theorem

            10.2.9  Confidence intervals

        10.3  Correlation and simple regression

            10.3.1  Correlation

            10.3.2  Introduction to regression

            10.3.3  Interpretation of the regression coefficients

        10.4  Summary

    Module 11 Practice questions

        11.1  Module 1 questions

        11.2  Module 2 questions

        11.3  Module 3 questions

        11.4  Module 4 questions

        11.5  Module 5 questions

        11.6  Module 6 questions

        11.7  Module 7 questions

        11.8  Module 8 questions

        11.9  Module 9 questions

        11.10  Module 10 questions

    Module 12 Solutions to practice questions

        12.1  Module 1 answers

        12.2  Module 2 answers

        12.3  Module 3 answers

        12.4  Module 4 answers

        12.5  Module 5 answers

        12.6  Module 6 answers

        12.7  Module 7 answers

        12.8  Module 8 answers

        12.9  Module 9 answers

        12.10  Module 10 answers