Advertisement

Mathematical Analysis and the Mathematics of Computation

  • Werner Römisch
  • Thomas Zeugmann

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Werner Römisch, Thomas Zeugmann
    Pages 1-46
  3. Werner Römisch, Thomas Zeugmann
    Pages 47-118
  4. Werner Römisch, Thomas Zeugmann
    Pages 119-156
  5. Werner Römisch, Thomas Zeugmann
    Pages 157-200
  6. Werner Römisch, Thomas Zeugmann
    Pages 201-268
  7. Werner Römisch, Thomas Zeugmann
    Pages 269-336
  8. Werner Römisch, Thomas Zeugmann
    Pages 337-420
  9. Werner Römisch, Thomas Zeugmann
    Pages 421-428
  10. Werner Römisch, Thomas Zeugmann
    Pages 429-446
  11. Werner Römisch, Thomas Zeugmann
    Pages 447-524
  12. Werner Römisch, Thomas Zeugmann
    Pages 525-594
  13. Werner Römisch, Thomas Zeugmann
    Pages 595-614
  14. Werner Römisch, Thomas Zeugmann
    Pages 615-674
  15. Back Matter
    Pages 675-703

About this book

Introduction

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.

Keywords

Approximation Differential Calculus Integral Calculus Integral Equations Interpolation Mathematical Analysis Mathematics of Computing Numerical Analysis Ordinary Differential Equations (ODEs)

Authors and affiliations

  • Werner Römisch
    • 1
  • Thomas Zeugmann
    • 2
  1. 1.Institut für MathematikHumboldt-Universität zu BerlinBerlinGermany
  2. 2.Division of Computer ScienceHokkaido UniversitySapporoJapan

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-42755-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Computer Science
  • Print ISBN 978-3-319-42753-9
  • Online ISBN 978-3-319-42755-3
  • Buy this book on publisher's site