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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: The Manchester Physics Series
- Sprache: Englisch
Mathematics for Physicists is a relatively short volume covering all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Early chapters deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. There are worked examples throughout the text, and chapter-end problem sets.
Mathematics for Physicists features:
- Interfaces with modern school mathematics syllabuses
- All topics usually taught in the first two years of a physics degree
- Worked examples throughout
- Problems in every chapter, with answers to selected questions at the end of the book and full solutions on a website
This text will be an excellent resource for undergraduate students in physics and a quick reference guide for more advanced students, as well as being appropriate for students in other physical sciences, such as astronomy, chemistry and earth sciences.
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Seitenzahl: 710
Veröffentlichungsjahr: 2015
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The Manchester Physics Series
General Editors
J.R. FORSHAW, H.F. GLEESON, F.K. LOEBINGER
School of Physics and Astronomy, University of Manchester
Properties of Matter
B.H. Flowers and E. Mendoza
Statistical Physics
Second Edition
F. Mandl
Electromagnetism
Second Edition
l.S. Grant and W.R. Phillips
Statistics
R.J. Barlow
Solid State Physics
Second Edition
J.R. Hook and H.E. Hall
Quantum Mechanics
F. Mandl
Computing for Scientists
R.J. Barlow and A.R. Barnett
The Physics of Stars
Second Edition
A.C. Phillips
Nuclear Physics
J.S. Lilley
Introduction to Quantum Mechanics
A.C. Phillips
Particle Physics
Third Edition
B.R. Martin and G. Shaw
Dynamics and Relativity
J.R. Forshaw and A.G. Smith
Vibrations and Waves
G.C. King
Mathematics for Physicists
B.R. Martin and G. Shaw
Mathematics for Physicists
B.R. MARTIN
Department of Physics and Astronomy University College London
G. SHAW
Department of Physics and Astronomy Manchester University
This edition first published 2015 © 2015 John Wiley & Sons, Ltd
Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
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Library of Congress Cataloging-in-Publication Data.
Martin, B. R. (Brian Robert), author. Mathematics for physicists / B.R. Martin, G. Shaw. pages cm Includes bibliographical references and index. ISBN 978-0-470-66023-2 (cloth) – ISBN 978-0-470-66022-5 (pbk.) 1. Mathematics. 2. Mathematical physics. I. Shaw, G. (Graham), 1942– author. II. Title. QC20.M35 2015 510–dc23
2015008518
CONTENTS
Editors' preface to the Manchester Physics Series
Authors' preface
Notes and website information
‘Starred’ material
Website
Examples, problems and solutions
1 Real numbers, variables and functions
1.1 Real numbers
1.2 Real variables
1.3 Functions, graphs and co-ordinates
Problems 1
Notes
2 Some basic functions and equations
2.1 Algebraic functions
2.2 Trigonometric functions
2.3 Logarithms and exponentials
2.4 Conic sections
Problems 2
Notes
3 Differential calculus
3.1 Limits and continuity
3.2 Differentiation
3.3 General methods
3.4 Higher derivatives and stationary points
3.5 Curve sketching
Problems 3
Notes
4 Integral calculus
4.1 Indefinite integrals
4.2 Definite integrals
4.3 Change of variables and substitutions
4.4 Integration by parts
4.5 Numerical integration
4.6 Improper integrals
4.7 Applications of integration
Problems 4
Notes
5 Series and expansions
5.1 Series
5.2 Convergence of infinite series
5.3 Taylor's theorem and its applications
5.4 Series expansions
*5.5 Proof of d'Alembert's ratio test
*5.6 Alternating and other series
Problems 5
Notes
6 Complex numbers and variables
6.1 Complex numbers
6.2 Complex plane: Argand diagrams
6.3 Complex variables and series
6.4 Euler's formula
Problems 6
Notes
7 Partial differentiation
7.1 Partial derivatives
7.2 Differentials
7.3 Change of variables
7.4 Taylor series
7.5 Stationary points
*7.6 Lagrange multipliers
*7.7 Differentiation of integrals
Problems 7
Notes
8 Vectors
8.1 Scalars and vectors
8.2 Products of vectors
8.3 Applications to geometry
8.4 Differentiation and integration
Problems 8
Notes
9 Determinants, Vectors and Matrices
9.1 Determinants
9.2 Vectors in
n
Dimensions
9.3 Matrices and linear transformations
9.4 Square Matrices
Problems 9
Notes
10 Eigenvalues and eigenvectors
10.1 The eigenvalue equation
*10.2 Diagonalisation of matrices
Problems 10
Notes
11 Line and multiple integrals
11.1 Line integrals
11.2 Double integrals
11.3 Curvilinear co-ordinates in three dimensions
11.4 Triple or volume integrals
Problems 11
12 Vector calculus
12.1 Scalar and vector fields
12.2 Line, surface, and volume integrals
12.3 The divergence theorem
12.4 Stokes' theorem
Problems 12
Notes
13 Fourier analysis
13.1 Fourier series
13.2 Complex Fourier series
13.3 Fourier transforms
Problems 13
Notes
14 Ordinary differential equations
14.1 First-order equations
14.2 Linear ODEs with constant coefficients
*14.3 Euler's equation
Problems 14
Notes
15 Series solutions of ordinary differential equations
15.1 Series solutions
15.2 Eigenvalue equations
15.3 Legendre's equation
15.4 Bessel's equation
Problems 15
Notes
16 Partial differential equations
16.1 Some important PDEs in physics
16.2 Separation of variables: Cartesian co-ordinates
16.3 Separation of variables: polar co-ordinates
*16.4 The wave equation: d'Alembert's solution
*16.5 Euler Equations
*16.6 Boundary conditions and uniqueness
Problems 16
Notes
Answers to selected problems
Problems 1
Problems 2
Problems 3
Problems 4
Problems 5
Problems 6
Problems 7
Problems 8
Problems 9
Problems 10
Problems 11
Problems 12
Problems 13
Problems 14
Problems 15
Problems 16
Index
EULA
List of Tables
Chapter 3
Table 3.1
Chapter 4
Table 4.1
Table 4.2
Chapter 5
Table 5.1
Chapter 12
Table 12.1
Table 12.2
Chapter 14
Table 14.1
Chapter 15
Table 15.1
Guide
Cover
Table of Contents
Preface
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Editors' preface to the Manchester Physics Series
The Manchester Physics Series is a set of textbooks at first degree level. It grew out of the experience at the University of Manchester, widely shared elsewhere, that many textbooks contain much more material than can be accommodated in a typical undergraduate course; and that this material is only rarely so arranged as to allow the definition of a short self-contained course. The plan for this series was to produce short books so that lecturers would find them attractive for undergraduate courses, and so that students would not be frightened off by their encyclopaedic size or price. To achieve this, we have been very selective in the choice of topics, with the emphasis on the basic physics together with some instructive, stimulating and useful applications.
Although these books were conceived as a series, each of them is self-contained and can be used independently of the others. Several of them are suitable for wider use in other sciences. Each Author's Preface gives details about the level, prerequisites, etc., of that volume.
The Manchester Physics Series has been very successful since its inception over 40 years ago, with total sales of more than a quarter of a million copies. We are extremely grateful to the many students and colleagues, at Manchester and elsewhere, for helpful criticisms and stimulating comments. Our particular thanks go to the authors for all the work they have done, for the many new ideas they have contributed, and for discussing patiently, and often accepting, the suggestions of the editors.
Finally, we would like to thank our publisher, John Wiley & Sons, Ltd., for their enthusiastic and continued commitment to the Manchester Physics Series.
J. R. Forshaw
H. F. Gleeson
F. K. Loebinger
August 2014
Authors' preface
Our aim in writing this book is to produce a relatively short volume that covers all the essential mathematics needed for a typical first degree in physics, from a starting point that is compatible with modern school mathematics syllabuses. Thus, it differs from most books, which include many advanced topics, such as tensor analysis, group theory, etc., that are not required in a typical physics degree course, except as specialised options. These books are frequently well over a thousand pages long and contain much more material than most undergraduate students need. In addition, they are often not well interfaced with school mathematics and start at a level that is no longer appropriate. Mathematics teaching at schools has changed over the years and students now enter university with a wide variety of mathematical backgrounds.
The early chapters of the book deliberately overlap with senior school mathematics, to a degree that will depend on the background of the individual reader, who may quickly skip over those topics with which he or she is already familiar. The rest of the book covers the mathematics that is usually compulsory for all students in their first two years of a typical university physics degree, plus a little more. Although written primarily for the needs of physics students, it would also be appropriate for students in other physical sciences, such as astronomy, chemistry, earth science, etc.
We do not try to cover all the more advanced, optional courses taken by some physics students, since these are already well treated in more advanced texts, which, with some degree of overlap, take up where our book leaves off. The exception is statistics. Although this is required by undergraduate physics students, we have not included it because it is usually taught as a separate topic, using one of the excellent specialised texts already available.
The book has been read in its entirety by one of the editors of the Manchester Physics Series, Jeff Forshaw of Manchester University, and we are grateful to him for many helpful suggestions that have improved the presentation.
B.R. Martin
G. Shaw
April 2015
Notes and website information
‘Starred’ material
Some sections of the book are marked with a star. These contain more specialised or advanced material that is not required elsewhere in the book and may be omitted at a first reading.
Website
Any misprints or other necessary corrections brought to our attention will be listed on www.wiley.com/go/martin/mathsforphysicists. We would also be grateful for any other comments about the book.
Examples, problems and solutions
Worked examples are given in all chapters. They are an integral part of the text and are designed to illustrate applications of material discussed in the preceding section. There is also a set of problems at the end of each chapter. Some equations which are particularly useful in problem solving are highlighted in the text for ease of access and brief ‘one-line’ answers to most problems are given at the end of the book, so that readers may quickly check whether their own answer is correct. Readers may access the full solutions to all the odd-numbered problems at www.wiley.com/go/martin/mathsforphysicists. Full solutions to all problems are available to instructors at the same website, which also contains electronic versions of the figures.
