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  • Textbook
  • © 2011

Analysis for Computer Scientists

Foundations, Methods, and Algorithms

  • 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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (25 chapters)

  1. Front Matter

    Pages I-X
  2. Numbers

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 1-11
  3. Real-Valued Functions

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 13-24
  4. Trigonometry

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 25-35
  5. Complex Numbers

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 37-44
  6. Sequences and Series

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 45-62
  7. Limits and Continuity of Functions

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 63-72
  8. The Derivative of a Function

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 73-93
  9. Applications of the Derivative

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 95-110
  10. Fractals and L-Systems

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 111-125
  11. Antiderivatives

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 127-133
  12. Definite Integrals

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 135-147
  13. Taylor Series

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 149-157
  14. Numerical Integration

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 159-167
  15. Curves

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 169-189
  16. Scalar-Valued Functions of Two Variables

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 191-210
  17. Vector-Valued Functions of Two Variables

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 211-218
  18. Integration of Functions of Two Variables

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 219-231
  19. Linear Regression

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 233-250
  20. Differential Equations

    • Michael Oberguggenberger, Alexander Ostermann
    Pages 251-266

About this book

This textbook 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. 

Features: thoroughly describes the essential concepts of analysis; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text; supplementary software can be downloaded from the book’s webpage.

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 tobe 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)

Authors and Affiliations

  • Institute of Basic Sciences in Civil Eng, University of Innsbruck, Innsbruck, Austria

    Michael Oberguggenberger

  • Department of Mathematics, University of Innsbruck, Innsbruck, Austria

    Alexander Ostermann

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.

Bibliographic Information