Analysis for Computer Scientists

Foundations, Methods, and Algorithms

  • Michael Oberguggenberger
  • Alexander Ostermann

Part of the Undergraduate Topics in Computer Science book series (UTICS)

Table of contents

  1. Front Matter
    Pages I-X
  2. Michael Oberguggenberger, Alexander Ostermann
    Pages 1-11
  3. Michael Oberguggenberger, Alexander Ostermann
    Pages 13-24
  4. Michael Oberguggenberger, Alexander Ostermann
    Pages 25-35
  5. Michael Oberguggenberger, Alexander Ostermann
    Pages 37-44
  6. Michael Oberguggenberger, Alexander Ostermann
    Pages 45-62
  7. Michael Oberguggenberger, Alexander Ostermann
    Pages 63-72
  8. Michael Oberguggenberger, Alexander Ostermann
    Pages 73-93
  9. Michael Oberguggenberger, Alexander Ostermann
    Pages 95-110
  10. Michael Oberguggenberger, Alexander Ostermann
    Pages 111-125
  11. Michael Oberguggenberger, Alexander Ostermann
    Pages 127-133
  12. Michael Oberguggenberger, Alexander Ostermann
    Pages 135-147
  13. Michael Oberguggenberger, Alexander Ostermann
    Pages 149-157
  14. Michael Oberguggenberger, Alexander Ostermann
    Pages 159-167
  15. Michael Oberguggenberger, Alexander Ostermann
    Pages 169-189
  16. Michael Oberguggenberger, Alexander Ostermann
    Pages 191-210
  17. Michael Oberguggenberger, Alexander Ostermann
    Pages 211-218
  18. Michael Oberguggenberger, Alexander Ostermann
    Pages 219-231
  19. Michael Oberguggenberger, Alexander Ostermann
    Pages 233-250
  20. Michael Oberguggenberger, Alexander Ostermann
    Pages 251-266

About this book

Introduction

Mathematics and mathematical modelling are of central importance in computer science, and therefore it is vital that computer scientists are aware of the latest concepts and techniques.

This concise and easy-to-read textbook/reference presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations.

Topics and features:

  • Thoroughly describes the essential concepts of analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives and antiderivatives, definite integrals and double integrals, and curves
  • Provides summaries and exercises in each chapter, as well as computer experiments
  • Discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations
  • Presents tools from vector and matrix algebra in the appendices, together with further information on continuity
  • Includes definitions, propositions and examples throughout the text, together with a list of relevant textbooks and references for further reading
  • Supplementary software can be downloaded from the book’s webpage at www.springer.com

This textbook is essential for undergraduate students in Computer Science. Written to specifically address the needs of computer scientists and researchers, it will also serve professionals looking to bolster their knowledge in such fundamentals extremely well.

Dr. Michael Oberguggenberger is a professor in the Department of Civil Engineering Sciences at the University of Innsbruck, Austria. Dr. Alexander Ostermann is a professor in the Department of Mathematics at the University of Innsbruck, Austria.

Keywords

Algorithms Analysis Computer Science MATLAB Maple Numerical Mathematics

Authors and affiliations

  • Michael Oberguggenberger
    • 1
  • Alexander Ostermann
    • 2
  1. 1.Institute of Basic Sciences in Civil EngUniversity of InnsbruckInnsbruckAustria
  2. 2.Department of MathematicsUniversity of InnsbruckInnsbruckAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-446-3
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Computer Science
  • Print ISBN 978-0-85729-445-6
  • Online ISBN 978-0-85729-446-3
  • Series Print ISSN 1863-7310
  • About this book