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Mathematical Methods for Physics and Engineering: A Comprehensive Guide / Edition 2

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Overview

The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganised and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F-tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.

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Editorial Reviews

From The Critics
A textbook for undergraduate students of science or engineering with a background in science and mathematics at the junior level in the US and A-level in Britain. It begins by showing how familiar mathematical methods can be applied to science problems, then moves into problems that require learning new methods. The second edition takes account of comments on the 1998 first. Annotation c. Book News, Inc., Portland, OR
From the Publisher
From reviews of previous editions: '…a great scientific textbook. It is a tour de force … to write mathematical sections that are both complete and at an appropriate academic level. The authors have clearly succeeded in this challenge, making this a remarkable pedagogical book … The choice of exercises is excellent and possibly the best feature of the book. In summary, this textbook is a great reference at undergraduate levels, particularly for those who like to teach or learn using lots of examples and exercises.' R. Botet, European Journal of Physics

'… the book provides scientists who need to use the tool of mathematics for practical purposes with a single, comprehensive book. I recommend this book not only to students in physics and engineering sciences, but also to students in other fields of natural sciences.' P. Steward, Optik

'… suitable as a textbook for undergraduate use … this is a book that in view of its content and its modest softcover price, will find its way on to many bookshelves.' Nigel Steele, The Times Higher Education Supplement

'Riley et al. has clear, thorough and straightforward explanations of the subjects treated. It rigorously adopts a three-stage approach throughout the book: first a heuristic, intuitive introduction, then a formal treatment, and finally one or two examples. This consistent presentation, the layout, and the print quality make the book most attractive … and value for money. It contains a thousand pages, there are plenty of exercises with each chapter.' J. M. Thijssen, European Journal of Physics

This is a valuable book with great potential use in present-day university physics courses. Furthermore, the book will be useful for graduate too, and researchers will find it useful for looking up material which they have forgotten since their undergraduate days.' J. M. Thijssen, European Journal of Physics

'This textbook is a well-written, modern, comprehensive, and complete collection of topics in mathematical methods ranging from a review of differential and integral calculus to group and representation theory, probability, the calculus of variations, and tensors.' Science Books and Films

'This is a very comprehensive textbook suitable for most students enrolling on undergraduate degree courses in engineering. It contains 31 stand-alone chapters of mathematical methods which enable the students to understand the principles of the basic mathematical techniques and the authors have produced a clear, thorough and straightforward explanation of each subject. … finding a single textbook which covers the engineering student's need throughout their entire course is by no means an easy task. I believe the authors have achieved it … complete fully worked solutions … which I think is a useful asset for both students and lecturers.' Civil Engineering

' ... this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics ever likely to be needed for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics covered and many worked examples, it contains more than 800 exercises.' L'enseignement mathematique

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Product Details

  • ISBN-13: 9780521890670
  • Publisher: Cambridge University Press
  • Publication date: 8/28/2002
  • Edition description: Older Edition
  • Edition number: 2
  • Pages: 1256
  • Product dimensions: 6.85 (w) x 9.72 (h) x 2.20 (d)

Meet the Author

Ken Riley read Mathematics at the University of Cambridge and proceeded to a Ph.D. there in theoretical and experimental nuclear physics. He became a Research Associate in elementary particle physics at Brookhaven, and then, having taken up a lectureship at the Cavendish Laboratory, Cambridge, continued this research at the Rutherford Laboratory and Stanford; in particular he was involved in the experimental discovery of a number of the early baryonic resonances. As well as having been Senior Tutor at Clare College, where he has taught physics and mathematics for nearly forty years, he has served on many committees concerned with teaching and examining of these subjects at all levels of tertiary and undergraduate education. He is also one of the authors of 200 Puzzling Physics Problems.

Michael Hobson read Natural Sciences at the University of Cambridge, specialising in theoretical physics, and remained at the Cavendish Laboratory to complete a Ph.D. in the physics of star-formation. As a Research Fellow at Trinity Hall, Cambridge, and subsequently an Advanced Fellow of the Particle Physics and Astronomy Research Council, he developed an interest in cosmology, and in particular in the study of fluctuations in the cosmic microwave background. He was involved in the first detection of these fluctuations using a ground-based interferometer. He is currently a University Lecturer at the Cavendish Laboratory and his research interests include both theoretical and observational aspects of cosmology. He is also a Director of Studies in Natural Sciences at Trinity Hall and enjoys an active role in the teaching of undergraduate physics and mathematics.

Stephen Bence obtained both his undergraduate degree in Natural Sciences and his Ph.D. in Astrophysics from the University of Cambridge. He then became a Research Associate with a special interest in star-formation processes and the structure of star-forming regions. In particular his research has concentrated on the physics of jets and outflows from young stars. He has had considerable experience of teaching mathematics and physics to undergraduate and pre-university students.

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Table of Contents

1 Preliminary algebra 1
2 Preliminary calculus 41
3 Complex numbers and hyperbolic functions 83
4 Series and limits 115
5 Partial differentiation 151
6 Multiple integrals 187
7 Vector algebra 212
8 Matrices and vector spaces 241
9 Normal modes 316
10 Vector calculus 334
11 Line, surface and volume integrals 377
12 Fourier series 415
13 Integral transforms 433
14 First-order ordinary differential equations 468
15 Higher-order ordinary differential equations 490
16 Series solutions of ordinary differential equations 531
17 Eigenfunction methods for differential equations 554
18 Special functions 577
19 Quantum operators 648
20 Partial differential equations : general and particular solutions 675
21 Partial differential equations : separation of variables and other methods 713
22 Calculus of variations 775
23 Integral equations 803
24 Complex variables 824
25 Applications of complex variables 871
26 Tensors 927
27 Numerical methods 984
28 Group theory 1041
29 Representation theory 1076
30 Probability 1119
31 Statistics 1221
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