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Student Solutions Manual for Mathematical Methods for Physics and Engineering

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Preface page ix 1 Preliminary algebra 1 2 Preliminary calculus 17 3 Complex numbers and hyperbolic functions 39 4 Series and limits 55 5 Partial differentiation 71 6 Multiple integrals 90 7 Vector algebra 104 8 Matrices and vector spaces 119 9 Normal modes 145 10 Vector calculus 156 11 Line, surface and volume integrals 176 v CONTENTS 12 Fourier series 193 13 Integral transforms 211 14 First-order ODEs 228 15 Higher-order ODEs 246 16 Series solutions of ODEs 269 17 Eigenfunction methods for ODEs 283 18 Special functions 296 19 Quantum operators 313 20 PDEs: general and particular solutions 319 21 PDEs: separation of variables and other methods 335 22 Calculus of variations 353 23 Integral equations 374 24 Complex variables 386 25 Applications of complex variables 400 26 Tensors 420 27 Numerical methods 440 28 Group theory 461 29 Representation theory 480 vi CONTENTS 30 Probability 494 31 Statistics 519

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, Student Solutions Manual for Mathematical Methods for Physics
and Engineering, third edition

Mathematical Methods for Physics and Engineering, third edition, is a highly ac-
claimed undergraduate textbook that teaches all the mathematics needed for
an undergraduate course in any of the physical sciences. As well as lucid
descriptions of the topics and many worked examples, it contains over 800
exercises. New stand-alone chapters give a systematic account of the ‘special
functions’ of physical science, cover an extended range of practical applica-
tions of complex variables, and give an introduction to quantum operators.
This solutions manual accompanies the third edition of Mathematical Meth-
ods for Physics and Engineering. It contains complete worked solutions to over
400 exercises in the main textbook, the odd-numbered exercises that are pro-
vided with hints and answers. The even-numbered exercises have no hints,
answers or worked solutions and are intended for unaided homework prob-
lems; full solutions are available to instructors on a password-protected website,
www.cambridge.org/9780521679718.

K e n R i l e y 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 over 40 years, he has served on many committees concerned
with the 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.

M i c h a e l H o b s o n read natural sciences at the University of Cambridge, spe-
cialising 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 Reader at the Cavendish Laboratory,
his research interests include both theoretical and observational aspects of cos-
mology, and he is the principal author of General Relativity: An Introduction for
Physicists. 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.

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