Essential Mathematics for Economics and Business

Description

Many students who embark on the study of economics and/or business are surprised and apprehensive to find that mathematics is a core subject on their course. Yet, to progress beyond a descriptive level in most subjects, an understanding and a certain fluency in basic mathematics is essential. In this text a minimal background in mathematics is assumed: the text starts in Chapter 1 with a review of basic mathematical operations such as multiplying brackets, manipulating fractions, percentages, use of the calculator, evaluating and transposing formulae, the concept of an equation and the solution of simple equations. Throughout the text worked examples demonstrate concepts and mathematical methods with a simple numerical example followed by further worked examples applied to real-world situations. The worked examples are also useful for practice. Start by reading the worked example to make sure you understand the method; then test yourself by attempting the example with a blank sheet of paper! You can always refer back to the detailed worked example if you get stuck. You should then be in a position to attempt the progress exercises. In this new edition, the worked examples in the text are complemented by an extensive question bank in WileyPLUS and MapleTA. Essential Mathematics for Economics and Business1 Cover Essential Mathematics for Economics and Business Copyright Contents Introduction 1 Mathematical Preliminaries 1.1 Some Mathematical Preliminaries 1.2 Arithmetic Operations 1.3 Fractions 1.4 Solving Equations 1.5 Currency Conversions 1.6 Simple Inequalities 1.7 Calculating Percentages 1.8 The Calculator. Evaluation and Transposition of Formulae 1.9 Introducing Excel 2 The Straight Line and Applications 2.1 The Straight Line 2.2 Mathematical Modelling 2.3 Applications: Demand, Supply, Cost, Revenue 2.4 More Mathematics on the Straight Line 2.5 Translations of Linear Functions 2.6 Elasticity of Demand, Supply and Income 2.7 Budget and Cost Constraints 2.8 Excel for Linear Functions 2.9 Summary 3 Simultaneous Equations 3.1 Solving Simultaneous Linear Equations 3.2 Equilibrium and Break-even 3.3 Consumer and Producer Surplus 3.4 The National Income Model and the IS-LM Model 3.5 Excel for Simultaneous Linear Equations 3.6 Summary 4 Non-linear Functions and Applications 4.1 Quadratic, Cubic and Other Polynomial Functions 4.2 Exponential Functions 4.3 Logarithmic Functions 4.4 Hyperbolic (Rational) Functions of the Form a/(bx + c) 4.5 Excel for Non-linear Functions 4.6 Summary 5 Financial Mathematics 5.1 Arithmetic and Geometric Sequences and Series 5.2 Simple Interest, Compound Interest and Annual Percentage Rates 5.3 Depreciation 5.4 Net Present Value and Internal Rate of Return 5.5 Annuities, Debt Repayments, Sinking Funds 5.6 The Relationship between Interest Rates and the Price of Bonds 5.7 Excel for Financial Mathematics 5.8 Summary 6 Differentiation and Applications 6.1 Slope of a Curve and Differentiation 6.2 Applications of Differentiation, Marginal Functions, Average Functions 6.3 Optimisation for Functions of One Variable 6.4 Economic Applications of Maximum and Minimum Points 6.5 Curvature and Other Applications 6.6 Further Differentiation and Applications 6.7 Elasticity and the Derivative 6.8 Summary 7 Functions of Several Variables 7.1 Partial Differentiation 7.2 Applications of Partial Differentiation 7.3 Unconstrained Optimisation 7.4 Constrained Optimisation and Lagrange Multipliers 7.5 Summary 8 Integration and Applications 8.1 Integration as the Reverse of Differentiation 8.2 The Power Rule for Integration 8.3 Integration of the Natural Exponential Function 8.4 Integration by Algebraic Substitution 8.5 The Definite Integral and the Area under a Curve 8.6 Consumer and Producer Surplus 8.7 First-order Differential Equations and Applications 8.8 Differential Equations for Limited and Unlimited Growth 8.9 Integration by Substitution and Integration by Parts 8.10 Summary 9 Linear Algebra and Applications 9.1 Linear Programming 9.2 Matrices 9.3 Solution of Equations: Elimination Methods 9.4 Determinants 9.5 The Inverse Matrix and Input/Output Analysis 9.6 Excel for Linear Algebra 9.7 Summary 10 Difference Equations 10.1 Introduction to Difference Equations 10.2 Solution of Difference Equations (First-order) 10.3 Applications of Difference Equations (First-order) 10.4 Summary Solutions to Progress Exercises Worked Examples Index