This book is based on lecture notes I wrote for a first-year compulsory quantitative methods course in the Australian National University (ANU) over a period of seven years. Before I started teaching the course in 2002, an encyclopaedic textbook on introductory quantitative methods that had limited focus on economics was used. However, teaching mathematics out of such a textbook to my students seemed ineffective because many of them disliked studying mathematics unless they saw practical applications. Accordingly, as an economist, I looked for other textbooks in mathematical economics. Many good textbooks were available, but they were too advanced for an introductory course, in terms of both mathematics and economics. Although they contained many applications to economics, they usually assumed that students have learnt some introductory economics. These applications are not straightforward for first-year students with little, if any, background in economics. I decided to write my own lecture notes given this unsatisfactory situation.

Scope

The material in the main text ranges from a revision of high-school mathematics to applications of calculus (single-variate, multivariate and integral) to economics and finance. For example: linear and quadratic functions are introduced in the context of demand and supply analysis; geometric sequences, exponential and logarithmic functions are introduced in the context of finance; single-variate calculus is explained in the course of solving a firm's profit maximisation problem; a consumer's utility maximisation is used to motivate introducing multivariate calculus; and integral calculus is explained in the context of calculating the deadweight loss of taxation.