Dan Stanescu - A Gentle Introduction to Scientific Computing (Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series)

Series Editors:

Frederic Magoules, Choi-Hong Lai

About the Series

This series, comprising of a diverse collection of textbooks, references, and handbooks, brings together a wide range of topics across numerical analysis and scientific computing. The books contained in this series will appeal to an academic audience, both in mathematics and computer science, and naturally find applications in engineering and the physical sciences.

Handbook of Sinc Numerical Methods

Frank Stenger

Computational Methods for Numerical Analysis with R

James P Howard, II

Numerical Techniques for Direct and Large-Eddy Simulations

Xi Jiang, Choi-Hong Lai

Decomposition Methods for Differential Equations

Theory and Applications

Juergen Geiser

Mathematical Objects in C++

Computational Tools in A Unified Object-Oriented Approach

Yair Shapira

Computational Fluid Dynamics

Frederic Magoules

Mathematics at the Meridian

The History of Mathematics at Greenwich

Raymond Gerard Flood, Tony Mann, Mary Croarken

Modelling with Ordinary Differential Equations: A Comprehensive Approach

Alfio Borz

Numerical Methods for Unsteady Compressible Flow Problems

Philipp Birken

A Gentle Introduction to Scientific Computing

Dan Stanescu, Long Lee

For more information about this series please visit: https://www.crcpress.com/Chapman-HallCRC-Numerical-Analysis-and-Scientific-Computing-Series/book-series/CHNUANSCCOM

MATLAB is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This book's use or discussion of MATLAB software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB software.

First edition published 2022

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Library of Congress Cataloging-in-Publication Data

Names: Stanescu, Dan, 1982- author.

Title: A gentle introduction to scientific computing / Dan Stanescu, University of Wyoming, USA, Long Lee, University of Wyoming, USA.

Description: First edition. | Boca Raton : Chapman & Hall, CRC Press, 2022. | Series: Chapman & Hall/CRC numerical analysis and scientific computing series | Includes bibliographical references and index.

Identifiers: LCCN 2021056202 (print) | LCCN 2021056203 (ebook) | ISBN 9780367206840 (hardback) | ISBN 9781032261317 (paperback) | ISBN 9780429262876 (ebook)

Subjects: LCSH: Numerical analysisData processing. | Computer science. | ScienceData processing.

Classification: LCC QA297 .S695 2022 (print) | LCC QA297 (ebook) | DDC 518.0285dc23/eng20220301

LC record available at https://lccn.loc.gov/2021056202

LC ebook record available at https://lccn.loc.gov/2021056203

ISBN: 9780367206840 (hbk)

ISBN: 9781032261317 (pbk)

ISBN: 9780429262876 (ebk)

DOI: 10.1201/9780429262876

Typeset in Latin Modern font

by KnowledgeWorks Global Ltd.

Publisher's note: This book has been prepared from camera-ready copy provided by the authors.

There exists a large variety of books dealing with computational methods and the material included here is therefore by no means new or original. The natural question that arises is then: why a new book? The simple answer is that the presentation here is driven by personal experience; the material is looked at in a way that has been found the most useful when teaching it to a large body of students over more than fifteen years. Together, the authors work in the field spans around five decades, with more than thirty years of experience in teaching numerical methods. In terms of mathematical complexity, the approach is somewhat of a middle ground between the more involved and very systematic, while more heavily theoretic, presentation found in texts like M.H. Holmes []. One of the other points where this presentation differs from others might also be the choice to place an emphasis on computational efficiency. Many computational scientists, mathematicians in particular, eventually devote themselves to the more academic task of developing proof-of-concept programs that use low-dimensional toy models to show how the computation may proceed. While this is a very important endeavor, the truth is that eventually we need computer models that track real-world phenomena, like for weather prediction, component design and optimization or turbulent flow simulation. For such real applications, which can easily still keep even the largest computers available today busy for days, weeks or even years in a row, computational efficiency is crucial. For this reason, this material emphasizes, to the largest extent possible, some simple techniques that can make a large difference in computer time. They are definitely worth being learned from the very beginning so that thinking about efficiency becomes second nature.

A class at the junior level has been taught at the University of Wyoming based on some initial notes, out of which this book has slowly grown out over the years. Other, sometimes more advanced, courses in numerical methods were a staple in the mathematics department as well as other departments across the University of Wyoming campus. They all took for granted a previous exposure to a computer science course, such as Introduction to Coding. By contrast, when initially designed, this junior-level class had as a particular objective to introduce mathematics majors, without any prior computer science exposure whatsoever, to numerical methods. Initially taught to sections of about ten students every other semester, the class now runs every semester, with two full sections totaling around seventy students in the Fall semester and one in Spring. About half of the students are mathematics (pure or education) majors, with the large majority of the rest coming from engineering. The students are expected to have a knowledge of multivariable calculus; no initial knowledge of linear algebra or differential equations is required. To compensate, one of the initial chapters covers the most important linear algebra concepts. These are dealt with completely during the first week of classes, although some reinforcement is sought throughout the semester via homework assignments. On the other hand, the basics of ordinary differential equations are presented before pertinent numerical methods are introduced in , which is dedicated to this topic. This latter chapter is usually the last one addressed; the better part of two weeks is spent on the topic, with at least one lecture focusing on solving boundary value problems. This choice is motivated by the fact that the shooting method is a good final project choice: it brings together a couple of topics visited throughout the semester (i.e. solving nonlinear equations and differential equations) while also inviting students to exercise their capacity for generalization and abstraction.