Sean Dineen Livres

Focusing on a rigorous approach to calculus, this book is designed for students pursuing careers in fields like statistics, economics, and engineering. It emphasizes understanding mathematics alongside technical skills, covering both differential and integral calculus within a solid foundation of mathematical analysis. The concise introduction of concepts aims to provide a comprehensive yet efficient learning experience, ensuring that students develop a deep comprehension that benefits their long-term academic and professional endeavors.

Aimed primarily at higher level undergraduates, this book provides a deeper understanding of the subject which will pay dividends in enabling readers to appreciate the uses and limitations of the techniques of multivariate calculus when applying them to new problems. Sean Dineen has provided a solid description of the basic concepts, via simple familiar explanations, which are then tested in technically demanding examples. By recognising the varied background that students can bring to the subject at this level, the author has assumed the minimal amount of prerequisite knowledge necessary to understand the comprehensive view given in this book.

The study of infinite dimensional holomorphy explores holomorphic functions in complex topological vector spaces, intertwining various mathematical disciplines such as topology, complex variables, and functional analysis. It emphasizes the interconnectedness of these fields and the evolution of mathematical thought over decades. The author reflects on the challenges of selecting topics for a course, highlighting two distinct approaches: the geometric-algebraic theory linked to bounded symmetric domains and the topological theory, which is the focus of this work.

Originally published: Oxford: Clarendon Press, 1989.