Today, a firm understanding of mathematics is essential for any serious student of economics. Students of economics need nowadays several important mathematical tools. These include calculus for functions of one or several variables as well as a basic understanding of optimization with and without constraints, e.g. linear programming plays an important role in optimizing production programs. Linear algebra is used in economic theory and econometrics. Students in other areas of economics can benefit for instance from some knowledge about differential and difference equations or mathematical problems arising in finance. The more complex economics becomes, the more deep mathematics is required and used. Today economists consider mathematics as the most important tool of economics and business. This book is not a book on mathematical economics, but a book on higher-level mathematics for economists.
Experience shows that students who enter a university and specialize in economics vary enormously in the range of their mathematical skills and aptitudes. Since mathematics is often a requirement for specialist studies in economics, we felt a need to provide as much elementary material as possible in order to give those students with weaker mathematical backgrounds the chance to get started. Using this book may depend on the skills of readers and their purposes. The book starts with very basic mathematical principles. Therefore, we have included some material that covers several topics of mathematics in school (e.g. fractions, powers, roots and logarithms in Chapter 1 or functions of a real variable in Chapter 3). So the reader can judge whether or not he (she) is sufficiently familiar with mathematics to be able to skip some of the sections or chapters.
Studying mathematics is very difficult for most students of economics and business. However, nowadays it is indeed necessary to know a lot of results of higher mathematics to understand the current economic literature and to use modern economic tools in practical economics and business. With this in mind, we wrote the book as simply as possible. On the other hand, we have presented the mathematical results strongly correct and complete, as is necessary in mathematics. The material is appropriately ordered according to mathematical requirements (while courses, e.g. in macroeconomics, often start with advanced topics such as constrained optimization for functions of several variables). On the one hand, previous results are used by later results in the text. On the other hand, current results in a chapter make it clear why previous results were included in the book.