In their efforts to minimize special assumptions, early practitioners eschewed familiar tools like differential calculus. More recently, these familiar tools have found renewed favour. They argue that mathematization is not a secondary feature of the theory but rather one of the basic reasons for its creation and development. More recently, sophisticated mathematical analysis has become widespread in the field of macroeconomics, where dynamic models incorporating uncertainty are prevalent. These require somewhat different mathematical tools to the static constrained optimization predominant in microeconomics.
Finance is a field in which the application of mathematical analysis has proved especially potent.
Formal models stimulated the innovation of new financial instruments, such as derivative securities, which have transformed financial markets. Aimed primarily at doctoral students, it is not for the mathematically fainthearted. However, specialized mathematical tools are reviewed in appendices, making the book accessible to those with a general mathematical background. He covers the basic topics of linear algebra, calculus, optimization and differential equations and their applications in economics. Careful study of this text would provide most of the mathematical knowledge required to beginning graduate level.