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