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. Though selective in its coverage, this book is careful, comprehensive and authoritative. Not an easy read, it is an invaluable reference. A particular feature of this book is its informative footnotes, which highlight the context of some results and and relate them to the literature.
Optimization theory is the basic tool of most economic analysis.
The advent of sophisticated mathematical software on personal computers has added a whole new dimension to mathematical modelling in economics.