MATHEMATICAL METHODS FOR PHYSICS AND …

1 Cambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressMATHEMATICAL METHODS FOR PHYSICSAND ENGINEERINGThe third edition of this highly acclaimed undergraduate textbook is suitablefor teaching all the mathematics ever likely to be needed for an undergraduatecourse in any of the physical sciences. As well as lucid descriptions of all thetopics covered and many worked examples, it contains more than 800 number of additional topics have been included and the text has undergonesignificant reorganisation in some areas. New stand-alone chapters: give a systematic account of the special functions of physical science cover an extended range of practical applications of complex variables includ-ing WKB METHODS and saddle-point integration techniques provide an introduction to quantum tabulations, of relevance in statistics and numerical integration, havebeen added.

2 In this edition, all 400 odd-numbered exercises are provided withcomplete worked solutions in a separate manual, available to both students andtheir teachers; these are in addition to the hints and outline answers given inthe main text. The even-numbered exercises have no hints, answers or workedsolutions and can be used for unaided homework; full solutions to them areavailable to instructors on a password-protected rileyread mathematics at the University of Cambridge and proceededto a there in theoretical and experimental nuclear PHYSICS . He became aresearch associate in elementary particle PHYSICS at Brookhaven, and then, havingtaken up a lectureship at the Cavendish Laboratory, Cambridge, continued thisresearch at the Rutherford Laboratory and Stanford; in particular he was involvedin the experimental discovery of a number of the early baryonic resonances. Aswell as having been Senior Tutor at Clare College, where he has taught physicsand mathematics for over 40 years, he has served on many committees concernedwith the teaching and examining of these subjects at all levels of tertiary andundergraduate education.

3 He is also one of the authors of200 Puzzling hobsonread natural sciences at the University of Cambridge,specialising in theoretical PHYSICS , and remained at the Cavendish Laboratory tocomplete a in the PHYSICS of star-formation. As a research fellow at TrinityCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressHall, Cambridge and subsequently an advanced fellow of the Particle Physicsand Astronomy Research Council, he developed an interest in cosmology, andin particular in the study of fluctuations in the cosmic microwave was involved in the first detection of these fluctuations using a ground-based interferometer. He is currently a University Reader at the CavendishLaboratory, his research interests include both theoretical and observationalaspects of cosmology, and he is the principal author ofGeneral Relativity: AnIntroduction for Physicists.

4 He is also a Director of Studies in Natural Sciencesat Trinity Hall and enjoys an active role in the teaching of undergraduate physicsand benceobtained both his undergraduate degree in Natural Sciencesand his in Astrophysics from the University of Cambridge. He then becamea Research Associate with a special interest in star-formation processes and thestructure of star-forming regions. In particular, his research concentrated on thephysics of jets and outflows from young stars. He has had considerable experi-ence of teaching mathematics and PHYSICS to undergraduate and University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressMATHEMATICAL METHODS FORPHYSICS AND ENGINEERING third editionK. F. RILEY, M. P. HOBSON and S. J. BENCEC ambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressUniversity Printing House, Cambridge CB2 8BS, United KingdomCambridge University Press is a part of the University of furthers the University s mission by disseminating knowledge in the pursuit ofeducation, learning and research at the highest international levels of on this title: K.

5 F. Riley, M. P. Hobson and S. J. Bence 2006 This publication is in copyright. Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place without the writtenpermission of Cambridge University edition Cambridge University Press 1998 Reprinted 1998 (with minor corrections), 2000 (twice), 2001 Second edition Ken Riley, Mike Hobson, Stephen Bence 2002 Reprinted (with corrections) 2003, 2004 Reprinted 2005 Third edition 200616th printing 201817th printing (with minor corrections) 2018 Printed in the United Kingdom by TJ International Ltd, Padstow CornwallA catalogue record for this publication is available from the British LibraryISBN 978-0-521-86153-3 HardbackISBN 978-0-521-67971-8 PaperbackCambridge University Press has no responsibility for the persistence or accuracy ofURLs for external or third-party internet websites referred to in this publication,and does not guarantee that any content on such websites is, or will remain,accurate or University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressContentsPreface to the third editionxxPreface to the second editionxxiiiPreface to the first editionxxv1 Preliminary Simple functions and equations1 Polynomial equations; factorisation.

6 Properties of Trigonometric identities10 Single angle; compound angles; double- and half-angle Coordinate Partial fractions18 Complications and special Binomial Properties of binomial Some particular METHODS of proof30 Proof by induction; proof by contradiction; necessary and sufficient Hints and answers392 Preliminary Differentiation41 Differentiation from first principles; products; the chain rule; quotients;implicit differentiation; logarithmic differentiation; Leibnitz theorem; specialpoints of a function; curvature; theorems of differentiationvCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University Integration59 Integration from first principles; the inverse of differentiation; by inspec-tion; sinusoidal functions; logarithmic integration; using partial fractions;substitution method; integration by parts; reduction formulae; infinite andimproper integrals; plane polar coordinates; integral inequalities; applicationsof Hints and answers813 Complex numbers and hyperbolic The need for complex Manipulation of complex numbers85 Addition and subtraction; modulus and argument; multiplication; complexconjugate; Polar representation of complex numbers92 Multiplication and division in polar de Moivre s theorem95trigonometric identities; finding thenth roots of unity; solving Complex logarithms and complex Applications to differentiation and Hyperbolic functions102 Definitions; hyperbolic trigonometric analogies; identities of hyperbolicfunctions; solving hyperbolic equations.

7 Inverses of hyperbolic functions;calculus of hyperbolic Hints and answers1134 Series and Summation of series116 Arithmetic series; geometric series; arithmetico-geometric series; the differencemethod; series involving natural numbers; transformation of Convergence of infinite series124 Absolute and conditional convergence; series containing only real positiveterms; alternating series Operations with Power series131 Convergence of power series; operations with power Taylor series136 Taylor s theorem; approximation errors; standard Maclaurin Evaluation of Hints and answers149viCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University PressCONTENTS5 Partial Definition of the partial The total differential and total Exact and inexact Useful theorems of partial The chain Change of Taylor s theorem for many-variable Stationary values of many-variable Stationary values under Thermodynamic Differentiation of Hints and answers1856 Multiple Double Triple Applications of multiple integrals191 Areas and volumes; masses, centres of mass and centroids; Pappus theorems;moments of inertia; mean values of Change of variables in multiple integrals199 Change of variables in double integrals.

8 Evaluation of the integralI= e x2dx; change of variables in triple integrals; general properties Hints and answers2117 Vector Scalars and Addition and subtraction of Multiplication by a Basis vectors and Magnitude of a Multiplication of vectors219 Scalar product; vector product; scalar triple product; vector triple productviiCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University Equations of lines, planes and Using vectors to find distances229 Point to line; point to plane; line to line; line to Reciprocal Hints and answers2408 Matrices and vector Vector spaces242 Basis vectors; inner product; some useful Linear Basic matrix algebra250 Matrix addition; multiplication by a scalar; matrix Functions of The transpose of a The complex and Hermitian conjugates of a The trace of a The determinant of a matrix259 Properties of The inverse of a The rank of a Special types of square matrix268 Diagonal; triangular; symmetric and antisymmetric; orthogonal; Hermitianand anti-Hermitian; unitary; Eigenvectors and eigenvalues272Of a normal matrix; of Hermitian and anti-Hermitian matrices; of a unitarymatrix; of a general square Determination of eigenvalues and eigenvectors280 Degenerate Change of basis and similarity Diagonalisation of Quadratic and Hermitian forms288 Stationary properties of the eigenvectors; quadratic Simultaneous linear equations292 Range; null space;Nsimultaneous linear equations inNunknowns.

9 Singularvalue Hints and answers3149 Normal Typical oscillatory Symmetry and normal modes322viiiCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University Rayleigh Ritz Hints and answers33210 Vector Differentiation of vectors334 Composite vector expressions; differential of a Integration of Space Vector functions of several Scalar and vector Vector operators347 Gradient of a scalar field; divergence of a vector field; curl of a vector Vector operator formulae354 Vector operators acting on sums and products; combinations of grad, div and Cylindrical and spherical polar General curvilinear Hints and answers37511 Line, surface and volume Line integrals377 Evaluating line integrals; physical examples; line integrals with respect to Connectivity of Green s theorem in a Conservative fields and Surface integrals389 Evaluating surface integrals; vector areas of surfaces; physical Volume integrals396 Volumes of three-dimensional Integral forms for grad, div and Divergence theorem and related theorems401 Green s theorems; other related integral theorems; physical Stokes theorem and related theorems406 Related integral theorems.

10 Physical Hints and answers41412 Fourier The Dirichlet The Fourier coefficients417ixCambridge University Press978-0-521-67971-8 MATHEMATICAL METHODS for PHYSICS and Engineering3rd EditionFrontmatterMore in this web service Cambridge University Symmetry Discontinuous Non-periodic Integration and Complex Fourier Parseval s Hints and answers43113 Integral Fourier transforms433 The uncertainty principle; Fraunhofer diffraction; the Dirac -function;relation of the -function to Fourier transforms; properties of Fouriertransforms; odd and even functions; convolution and deconvolution; correlationfunctions and energy spectra; Parseval s theorem; Fourier transforms in Laplace transforms453 Laplace transforms of derivatives and integrals; other properties of Concluding Hints and answers46614 First-order ordinary differential General form of First-degree first-order equations470 Separable-variable equations; exact equations; inexact equations, integrat-ing factors; linear equations; homogeneous equations; isobaric equations;Bernoulli s equation; miscellaneous Higher-degree first-order equations480 Equations soluble forp;forx;fory