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Undergraduate Topics in Computer Science

Analysis for Computer Scientists

Foundations, Methods, and Algorithms

Authors: Oberguggenberger, Michael, Ostermann, Alexander

  • Presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis     
  • Makes thorough use of examples and explanations using MATLAB, Maple, and Java applets     
  • Describes mathematical theory alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises     
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Buy this book

eBook $29.99
price for USA
  • ISBN 978-0-85729-446-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-85729-445-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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.

Reviews

From the reviews:

“This undergraduate work, translated from German, is designed around the concept that mathematical modeling and the underlying mathematics are central to computer science. … place a strong emphasis on algorithmic methods, and include a substantial number of examples of mathematical modeling. … Since the audience is computer science students, there are many examples and exercises … using the software packages MATLAB and Maple. … a useful acquisition for academic institutions where students have access to MATLAB and/or Maple. Summing Up: Recommended. Lower- and upper-division undergraduates.” (D. Z. Spicer, Choice, Vol. 49 (1), September, 2011)

“The book is a translation of the original German version from 2005 … . Each chapter is preceded by a brief introduction for orientation. The text is enriched by computer experiments which should encourage the reader to actively acquire the subject matter. Finally, every chapter has exercises, half of which are to be solved with the help of computer programs. The book can be used from the first semester on as the main textbook for a course, as a complementary text, or for self-study.” (Petr Gurka, Zentralblatt MATH, Vol. 1238, 2012)


Table of contents (25 chapters)

  • Numbers

    Oberguggenberger, Michael (et al.)

    Pages 1-11

  • Real-Valued Functions

    Oberguggenberger, Michael (et al.)

    Pages 13-24

  • Trigonometry

    Oberguggenberger, Michael (et al.)

    Pages 25-35

  • Complex Numbers

    Oberguggenberger, Michael (et al.)

    Pages 37-44

  • Sequences and Series

    Oberguggenberger, Michael (et al.)

    Pages 45-62

Buy this book

eBook $29.99
price for USA
  • ISBN 978-0-85729-446-3
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Download immediately after purchase
Softcover $39.95
price for USA
  • ISBN 978-0-85729-445-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Analysis for Computer Scientists
Book Subtitle
Foundations, Methods, and Algorithms
Authors
Series Title
Undergraduate Topics in Computer Science
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-446-3
DOI
10.1007/978-0-85729-446-3
Softcover ISBN
978-0-85729-445-6
Series ISSN
1863-7310
Edition Number
1
Number of Pages
X, 342
Topics