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Introduction to Scientific Computing and Data Analysis

  • Textbook
  • © 2023

Overview

Authors:
  1. Mark H. Holmes

    1. Department of Mathematical Sciences, Rensselaer Polytechnic University, Troy, USA

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  • Codes used for all of the computational examples are available on GitHub
  • Covers optimization methods, regression principal & independent component analysis & variational calculus
  • Problem solving & the constructive use of the mathematical foundations of the subject

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 13)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction to Scientific Computing

    • Mark H. Holmes
    Pages 1-30

  3. Solving A Nonlinear Equation

    • Mark H. Holmes
    Pages 31-71

  4. Matrix Equations

    • Mark H. Holmes
    Pages 73-127

  5. Eigenvalue Problems

    • Mark H. Holmes
    Pages 129-204

  6. Interpolation

    • Mark H. Holmes
    Pages 205-254

  7. Numerical Integration

    • Mark H. Holmes
    Pages 255-302

  8. Initial Value Problems

    • Mark H. Holmes
    Pages 303-358

  9. Optimization: Regression

    • Mark H. Holmes
    Pages 359-409

  10. Optimization: Descent Methods

    • Mark H. Holmes
    Pages 411-474

  11. Data Analysis

    • Mark H. Holmes
    Pages 475-527

  12. Back Matter

    Pages 529-554
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Keywords

About this book

This textbook provides an introduction to numerical computing and its applications in science and engineering. The topics covered include those usually found in an introductory course, as well as those that arise in data analysis. This includes optimization and regression-based methods using a singular value decomposition. The emphasis is on problem solving, and there are numerous exercises throughout the text concerning applications in engineering and science. The essential role of the mathematical theory underlying the methods is also considered, both for understanding how the method works, as well as how the error in the computation depends on the method being used. The codes used for most of the computational examples in the text are available on GitHub.  This new edition includes material necessary for an upper division course in computational linear algebra.

Authors and Affiliations

  • Department of Mathematical Sciences, Rensselaer Polytechnic University, Troy, USA

    Mark H. Holmes

About the author

Mark Holmes is a Professor at Rensselaer Polytechnic Institute.  His current research interests include mechanoreception and sleep-wake cycles. Professor Holmes has three published books in Springer's Texts in Applied Mathematics series: Introduction to Perturbation Methods, Introduction to the Foundations of Applied Mathematics, and Introduction to Numerical Methods in Differential Equations.

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