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Introduction to Methods of Approximation in Physics and Astronomy

  • Maurice H. P. M. van Putten

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Preliminaries

    1. Front Matter
      Pages 1-1
    2. Maurice H.P.M. van Putten
      Pages 3-33
    3. Maurice H.P.M. van Putten
      Pages 35-60
    4. Maurice H.P.M. van Putten
      Pages 61-107
    5. Maurice H.P.M. van Putten
      Pages 109-131
  3. Methods of Approximation

    1. Front Matter
      Pages 133-133
    2. Maurice H.P.M. van Putten
      Pages 135-158
    3. Maurice H.P.M. van Putten
      Pages 159-196
    4. Maurice H.P.M. van Putten
      Pages 197-211
    5. Maurice H.P.M. van Putten
      Pages 213-241
    6. Maurice H.P.M. van Putten
      Pages 243-269
  4. Selected Topics

    1. Front Matter
      Pages 271-271
    2. Maurice H.P.M. van Putten
      Pages 273-289
    3. Maurice H.P.M. van Putten
      Pages 291-315
    4. Maurice H.P.M. van Putten
      Pages 317-324
  5. Back Matter
    Pages 325-345

About this book

Introduction

This textbook provides students with a solid introduction to the techniques of approximation commonly used in data analysis across physics and astronomy. The choice of methods included is based on their usefulness and educational value, their applicability to a broad range of problems and their utility in highlighting key mathematical concepts. Modern astronomy reveals an evolving universe rife with transient sources, mostly discovered - few predicted - in multi-wavelength observations. Our window of observations now includes electromagnetic radiation, gravitational waves and neutrinos. For the practicing astronomer, these are highly interdisciplinary developments that pose a novel challenge to be well-versed in astroparticle physics and data-analysis.

The book is organized to be largely self-contained, starting from basic concepts and techniques in the formulation of problems and methods of approximation commonly used in computation and numerical analysis. This includes root finding, integration, signal detection algorithms involving the Fourier transform and examples of numerical integration of ordinary differential equations and some illustrative aspects of modern computational implementation. Some of the topics highlighted introduce the reader to selected problems with comments on numerical methods and implementation on modern platforms including CPU-GPU computing.

Developed from lectures on mathematical physics in astronomy to advanced undergraduate and beginning graduate students, this book will be a valuable guide for students and a useful reference for practicing researchers. To aid understanding, exercises are included at the end of each chapter. Furthermore, some of the exercises are tailored to introduce modern symbolic computation.


Keywords

Introduction to complex function theory QR factorization Methods of approximation Vector fields and finite differencing Approximation by projection Function approximations Root finding and numerical integration Signal detection and signal analysis Fast Fourier Transforms Cachy numbers

Authors and affiliations

  • Maurice H. P. M. van Putten
    • 1
  1. 1.PhysicsSejong University SeoulKorea (Republic of)

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-2932-5
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-981-10-2931-8
  • Online ISBN 978-981-10-2932-5
  • Series Print ISSN 2192-4791
  • Series Online ISSN 2192-4805
  • Buy this book on publisher's site
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