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Mathematics for the Physical Sciences (2015) by Leslie Copley [Dr Soc] epub

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  Mathematics for the Physical Sciences by
Leslie Copley
  De Gruyter | Physics | March 2015 | ISBN-10: 3110409453 | 446 pages | ePub | 53.06 MB
 

  A text on advanced mathematical methods with numerous applications, detailed derivations and solutions, and a
unique range of practical topics.
  
  Aims and Scope
  
  The book begins with a thorough
introduction to complex analysis, which is then used to understand the properties of ordinary differential equations and
their solutions. The latter are obtained in both series and integral representations. Integral transforms are
introduced, providing an opportunity to complement complex analysis with techniques that flow from an algebraic
approach. This moves naturally into a discussion of eigenvalue and boundary vale problems. A thorough discussion of
multi-dimensional boundary value problems then introduces the reader to the fundamental partial differential equations
and “special functions” of mathematical physics. Moving to non-homogeneous boundary value problems the
reader is presented with an analysis of Green’s functions from both analytical and algebraic points of view. This
leads to a concluding chapter on integral equations.
  
  TABLE OF CONTENTS
  
  Frontmatter
 
Contents
  Foreword
  1 Functions of a Complex Variable
  2 Cauchy’s Theorem
  3 The Calculus
of Residues
  4 Dispersion Representations
  5 Analytic Continuation
  6 Asymptotic Expansions
  7
Padé Approximants
  8 Fourier Series and Transforms
  9 Ordinary Linear Differential Equations
  10
Partial Differential Equations and Boundary Value Problems
  11 Special Functions
  12 Non-Homogeneous
Boundary Value Problems: Green’s Functions
  13 Integral Equations
  Bibliography
  
 
Topics
  Applied Mathematics
  Theoretical and Mathematical Physics
  
  
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