Alvaro Meseguer - Fundamentals of Numerical Mathematics for Physicists and Engineers

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Introduces the fundamentals of numerical mathematics and illustrates its applications to a wide variety of disciplines in physics and engineering Applying numerical mathematics to solve scientific problems, this book helps readers understand the mathematical and algorithmic elements that lie beneath numerical and computational methodologies in order to determine the suitability of certain techniques for solving a given problem. It also contains examples related to problems arising in classical mechanics, thermodynamics, electricity, and quantum physics.
Fundamentals of Numerical Mathematics for Physicists and
Engineers
Provides a modern perspective of numerical mathematics by introducing top-notch techniques currently used by numerical analysts Contains two parts, each of which has been designed as a one-semester course Includes computational practicals in Matlab (with solutions) at the end of each section for the instructor to monitor the student's progress through potential exams or short projects Contains problem and exercise sets (also with solutions) at the end of each section  is an excellent book for advanced undergraduate or graduate students in physics, mathematics, or engineering. It will also benefit students in other scientific fields in which numerical methods may be required such as chemistry or biology.

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Fundamentals of Numerical Mathematics for Physicists and Engineers

Alvaro Meseguer

Department of PhysicsUniversitat Polit`ecnica de Catalunya – UPC BarcelonaTech

This edition first published 2020 2020 John Wiley Sons Inc All rights - фото 80

This edition first published 2020

© 2020 John Wiley & Sons, Inc. All rights reserved.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Alvaro Meseguer to be identified as the author of this work has been asserted in accordance with law.

Registered Office

John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

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111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of Warranty

While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: Meseguer, Alvaro (Alvaro Meseguer), author.

Title: Fundamentals of numerical mathematics for physicists and engineers /

Alvaro Meseguer.

Description: Hoboken, NJ : Wiley, 2020. | Includes bibliographical

references and index.

Identifiers: LCCN 2019057703 (print) | LCCN 2019057704 (ebook) | ISBN

9781119425670 (hardback) | ISBN 9781119425717 (adobe pdf) | ISBN

9781119425755 (epub)

Subjects: LCSH: Numerical analysis. | Mathematical physics. | Engineering

mathematics.

Classification: LCC QA297 .M457 2020 (print) | LCC QA297 (ebook) | DDC

518–dc23

LC record available at https://lccn.loc.gov/2019057703

LC ebook record available at https://lccn.loc.gov/2019057704

Cover Design: Wiley

Cover Image: Courtesy of Alvaro Meseguer, (background) © HNK/Shutterstock

About the Author

Alvaro Meseguer, PhD, is Associate Professor at the Department of Physics at Polytechnic University of Catalonia (UPC BarcelonaTech), Barcelona, Spain, where he teaches Numerical Methods, Fluid Dynamics and Mathematical Physics to advanced undergraduates in Engineering Physics and Mathematics. He has published more than 30 articles in peer‐reviewed journals within the fields of computational fluid dynamics, and nonlinear physics.

Preface

Much of the material in this book is derived from lecture notes for two courses on numerical methods taught over many years to undergraduate students in Engineering Physics at the Universitat Politècnica de Catalunya (UPC) BarcelonaTech. Its volume is scaled to a one‐year course, that is, a two‐semester course. Accordingly, the book has two parts. Part Iis addressed to first or second year undergraduate students who have a solid foundation in differential and integral calculus in one real variable (including Taylor series, картинка 81notation, and improper integrals), along with elementary linear algebra (including polynomials and systems of linear equations). Part IIis addressed to slightly more advanced undergraduate or first‐year graduate students with a broader mathematical background, including multivariate calculus, ordinary differential equations, functions of a complex variable, and Fourier series. In both cases, it is assumed that the students are familiar with basic Matlab commands and functions.

The book has been written thinking not only of the student but also of the instructor (or instructors) that is supposed to teach the material following an academic calendar. Each chapter contains mathematical topics to be addressed in the lectures, along with Matlab codes and computer hands‐on practicals. These practicals are problem‐solving tutorials where the students, always supervised and guided by an instructor, use Matlab on a local computer to solve a given exercise that is focused on the topic previously seen in the lectures. From my point of view, teaching numerical methods should encompass not only theoretical lectures, addressing the underlying mathematics on a blackboard, but also practical computations, where the student learns the actual implementation of those mathematical concepts. There are certain aspects of numerical mathematics, such as conditioning or order of convergence , that can only be properly illustrated by experimentation on a computer. These hands‐on practicals may also help the instructor to efficiently assess the performance of a student. This can be easily carried out by using Matlab's publishfunction, for example. The end of each chapter also includes a short list of problems and exercises of theoretical (labeled with an A) and/or computational (labeled with an N) nature. The solutions to many of the exercises (and practicals) can be found at the end of the book. Finally, each chapter includes a Complementary Reading section, where the student may find suitable bibliography to broaden his or her knowledge on different aspects of numerical mathematics. Complementary lists of exercises can also be found in many of these recommended references.

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