Mathematical Analysis and the Mathematics of Computation - Hardcover

Römisch, Werner; Zeugmann, Thomas

Hardcover

ISBN 10: 3319427539 ISBN 13: 9783319427539

Publisher: Springer, 2016

Synopsis

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications.

The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations.

This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

About this title

About the Author

Prof. Dr. Werner Römisch received his Dr. rer. nat. in 1976 and his habilitation in 1984, both from Humboldt-Universität zu Berlin. He is now an emeritus professor of Humboldt-Universität zu Berlin, Institut für Mathematik. His research interests are stochastic optimization with applications to power systems optimization and airline revenue management, and stochastic equations.

Prof. Dr. Thomas Zeugmann received his Dr. rer. nat. in mathematics in 1983 from Humboldt-Universität zu Berlin, and his habilitation in computer science from the Technische Universität Darmstadt in 1993. He was a professor in Kyushu University and Universität zu Lübeck; since 2004 he has been a professor at Hokkaido University. His research interests include algorithmic learning theory, stochastic algorithms, and parallel algorithms.

From the Back Cover

This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications.

The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, andnumerical solutions of ordinary differential equations.

This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

Edition details

• Publisher: Springer
• Publication date: 2016
• Language: English
• ISBN 10: 3319427539
• ISBN 13: 9783319427539
• Binding: Hardcover
• Edition number: 1
• Number of pages: 726