Now established as one of the leading introductory texts for students studying these subjects, this new edition combines a non-rigorous approach to the subject with applications in economics and business. Fundamental mathematical concepts are explained as simply and briefly as possible, using a wide selection of worked examples, graphs and real-world applications.
Introduction.Chapter 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.
Chapter 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 (on the website).
2.6 Elasticity of Demand, Supply and Income.
2.7 Budget and Cost Constraints (on the website).
2.8 Excel for Linear Functions.
2.9 Summary.
Chapter 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.
Appendix.
Chapter 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 Functions of the Form a/(bx + c).
4.5 Excel for Non-linear Functions.
4.6 Summary.
Chapter 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.
Appendix.
Chapter 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.
Chapter 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.
Chapter 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 Summary.
Chapter 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.
Chapter 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.
Bibliography.
List of Worked Examples.
Index.