Scientific Computing

Vol. III - Approximation and Integration

  • John A.┬áTrangenstein

Part of the Texts in Computational Science and Engineering book series (TCSE, volume 20)

Table of contents

  1. Front Matter
    Pages i-xxv
  2. John A. Trangenstein
    Pages 1-222
  3. John A. Trangenstein
    Pages 223-332
  4. John A. Trangenstein
    Pages 333-491
  5. John A. Trangenstein
    Pages 493-559
  6. Back Matter
    Pages 561-592

About this book


This is the third of three volumes providing a comprehensive presentation of the fundamentals of scientific computing. This volume discusses topics that depend more on calculus than linear algebra, in order to prepare the reader for solving differential equations. This book and its companions show how to determine the quality of computational results, and how to measure the relative efficiency of competing methods. Readers learn how to determine the maximum attainable accuracy of algorithms, and how to select the best method for computing problems. This book also discusses programming in several languages, including C++, Fortran and MATLAB. There are 90 examples, 200 exercises, 36 algorithms, 40 interactive JavaScript programs, 91 references to software programs and 1 case study.

Topics are introduced with goals, literature references and links to public software. There are descriptions of the current algorithms in GSLIB and MATLAB.

This book could be used for a second course in numerical methods, for either upper level undergraduates or first year graduate students. Parts of the text could be used for specialized courses, such as nonlinear optimization or iterative linear algebra.


algorithm approximation convergence differentiation efficiency error extrapolation integration interpolation

Authors and affiliations

  • John A.┬áTrangenstein
    • 1
  1. 1.Professor Emeritus of Mathematics, Department of MathematicsDuke UniversityDurhamUSA

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG, a part of Springer Nature 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-69109-1
  • Online ISBN 978-3-319-69110-7
  • Series Print ISSN 1611-0994
  • Series Online ISSN 2197-179X
  • Buy this book on publisher's site