A Guided Tour of Mathematical Methods: For the Physical Sciences / Edition 2

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Overview

This second edition of A Guided Tour of Mathematical Methods provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students in this area. In contrast to more traditional textbooks, all the material is presented in the form of problems. Within these problems the basic mathematical theory and its physical applications are well integrated. The mathematical insights that the student acquires are therefore driven by their physical insight. Topics that are covered include vector calculus, linear algebra, Fourier analysis, scale analysis, complex integration, Green's functions, normal modes, tensor calculus, and perturbation theory. The second edition contains new chapters on dimensional analysis, variational calculus, and the asymptotic evaluation of integrals. This book can be used by undergraduates and lower-level graduate students in the physical sciences. It can serve as a stand-alone text, or as a source of problems and examples to complement other textbooks.
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Editorial Reviews

From The Critics
Snieder's (geophysics, Colorado School of Mines) textbook is designed for students in physics or geophysics. All the material is presented in the form of problems, to demonstrate for students the application of mathematical techniques and knowledge to physical problems. Coverage includes vector calculus, linear algebra, Fourier analysis, scale analysis, Green's functions, normal modes, tensor calculus, and perturbation theory. Suitable for undergraduates or lower-level graduate students, as either a standalone text or as a source of problems and examples to supplement other textbooks. The text requires a certain basic knowledge of calculus and linear algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)
From the Publisher
"The writing style is clear and concise...Snieder offers an interesting approach to the material, with 127 references." J.D. Fehribach, Worcester Polytechnic Institute, CHOICE
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Product Details

  • ISBN-13: 9780521542616
  • Publisher: Cambridge University Press
  • Publication date: 4/9/2009
  • Edition description: REV
  • Edition number: 2
  • Pages: 524
  • Product dimensions: 6.60 (w) x 9.60 (h) x 1.30 (d)

Meet the Author

Roel Snieder currently holds the Keck Foundation Endowed Chair of Basic Exploration Science at the Colorado School of Mines (USA).
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Table of Contents

1 Introduction 1
2 Dimensional analysis 3
3 Power series 16
4 Spherical and cylindrical coordinates 31
5 Gradient 46
6 Divergence of a vector field 64
7 Curl of a vector field 78
8 Theorem of Gauss 88
9 Theorem of Stokes 97
10 Laplacian 113
11 Conservation laws 133
12 Scale analysis 153
13 Linear algebra 173
14 Dirac delta function 202
15 Fourier analysis 217
16 Analytic functions 245
17 Complex integration 254
18 Green's functions : principles 267
19 Green's functions : examples 288
20 Normal modes 311
21 Potential theory 353
22 Cartesian tensors 379
23 Perturbation theory 412
24 Asymptotic evaluation of integrals 437
25 Variational calculus 461
26 Epilogue, on power and knowledge 492
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