# Using Mathematics in Economics, 2nd edition

• Leighton Thomas

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## Overview

This text explains the basics of mathematics and how it can be used in economics. The book is an ideal introduction to mathematics for students of economics, whatever their mathematical background. The first part of the book deals with equation systems and their solutions. It draws the distinction between the structural and reduced forms of equation systems and this provides a recurring theme throughout the book. The middle section deals with differential and integral calculus with particular stress on constrained optimisation problems. There are separate chapters on the mathematical economics of the firm and the consumer, and the book concludes with introductions to dynamic analysis and matrix algebra.

A new section on basic algebra will be included at the beginning of the text, which will provide the mathematical prerequisites for a proper understanding of the rest of the book and would aim to remedy any mathematical deficiencies of students entering university.

More exercises will be added throughout the book, particularly examples involving comparative statics.

The chapter on matrix algebra will be expanded to involve determinants and more material on inverse matrices.

Preface.
1.Functions and Equations.
2.Simultaneous Linear Equations.
3.Stocks, Flows and Equilibrium in Economics.
4.The Reduced and Structural Forms of Equation Systems.
5.Stock-flow Markets.
6.Geometric Progressions and Discounted Cash Flows.
7.The Differentiation of Functions of One Variable.
8.Higher-order Derivatives.
9.Integration.
10.Differentiation of Functions of More than One Variable.
11.Total Differentials and Total Derivatives.
12.Unconstrained and Constrained Optimisation.
13.Calculus in Economics I: the Firm.
14.Calculus in Economics II: the Consumer.
15.Exponential and Logarithmic Functions.
16.Introduction to Dynamics.
17.Introduction to Matrix Algebra.

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