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From classical mechanics and classical electrodynamics to modern
quantum mechanics many physical phenomena are formulated in terms
of similar partial differential equations while boundary conditions
determine the specifics of the problem. This 45th anniversary
edition of the advanced book classic Mathematical Methods for
Physics demonstrates how many physics problems resolve into similar
inhomogeneous partial differential equations and the mathematical
techniques for solving them. The text has three parts: Part I
establishes solving the homogenous Laplace and Helmholtz equations
in the three main coordinate systems, rectilinear, cylindrical, and
spherical and develops the solution space for series solutions to
the Sturm-Liouville equation, indicial relations, and the expansion
of orthogonal functions including spherical harmonics and Fourier
series, Bessel, and Spherical Bessel functions. Many examples with
figures are provided including electrostatics, wave guides and
resonant cavities, vibrations of membranes, heat flow, potential
flow in fluids, and plane and spherical waves. In Part II the
inhomogeneous equations are addressed where source terms are
included for Poisson's equation, the wave equation, and the
diffusion equation. Coverage includes many examples from averaging
approaches for electrostatics and magnetostatics, from Green
function solutions for time independent and time dependent
problems, and from integral equation methods. In Part III complex
variable techniques are presented for solving integral equations
involving Cauchy Residue theory, contour methods, analytic
continuation, and transforming the contour; for addressing
dispersion relations; for revisiting special functions in the
complex plane; and for transforms in the complex plane including
Green's functions and Laplace transforms. Key Features: *
Mathematical Methods for Physics creates a strong, solid anchor of
learning and is useful for reference. * Lecture note style suitable
for advanced undergraduate and graduate students to learn many
techniques for solving partial differential equations with boundary
conditions * Many examples across various subjects of physics in
classical mechanics, classical electrodynamics, and quantum
mechanics * Updated typesetting and layout for improved clarity
This book, in lecture note style with updated layout and
typesetting, is suitable for advanced undergraduate, graduate
students, and as a reference for researchers. It has been edited
and carefully updated by Gary Powell.
From classical mechanics and classical electrodynamics to modern
quantum mechanics many physical phenomena are formulated in terms
of similar partial differential equations while boundary conditions
determine the specifics of the problem. This 45th anniversary
edition of the advanced book classic Mathematical Methods for
Physics demonstrates how many physics problems resolve into similar
inhomogeneous partial differential equations and the mathematical
techniques for solving them. The text has three parts: Part I
establishes solving the homogenous Laplace and Helmholtz equations
in the three main coordinate systems, rectilinear, cylindrical, and
spherical and develops the solution space for series solutions to
the Sturm-Liouville equation, indicial relations, and the expansion
of orthogonal functions including spherical harmonics and Fourier
series, Bessel, and Spherical Bessel functions. Many examples with
figures are provided including electrostatics, wave guides and
resonant cavities, vibrations of membranes, heat flow, potential
flow in fluids, and plane and spherical waves. In Part II the
inhomogeneous equations are addressed where source terms are
included for Poisson's equation, the wave equation, and the
diffusion equation. Coverage includes many examples from averaging
approaches for electrostatics and magnetostatics, from Green
function solutions for time independent and time dependent
problems, and from integral equation methods. In Part III complex
variable techniques are presented for solving integral equations
involving Cauchy Residue theory, contour methods, analytic
continuation, and transforming the contour; for addressing
dispersion relations; for revisiting special functions in the
complex plane; and for transforms in the complex plane including
Green’s functions and Laplace transforms. Key Features: ·
Mathematical Methods for Physics creates a strong, solid anchor of
learning and is useful for reference. · Lecture note style
suitable for advanced undergraduate and graduate students to learn
many techniques for solving partial differential equations with
boundary conditions · Many examples across various subjects of
physics in classical mechanics, classical electrodynamics, and
quantum mechanics · Updated typesetting and layout for improved
clarity This book, in lecture note style with updated layout and
typesetting, is suitable for advanced undergraduate, graduate
students, and as a reference for researchers. It has been edited
and carefully updated by Gary Powell.
Two elderly shopkeepers bludgeoned to death, the only evidence - a
smudged thumbprint inside a cashbox. A Quaker poisons his mistress
in Slough and, confident he will evade justice, arrives at
Paddington station unaware modern technology had alerted police who
lay in wait. Great Britain has led the world in crime-detection
methods and the forensic sciences; this volume examines real
criminal cases that have tested the legality and admissibility of
these crime-fighting methods as they pass through the British legal
system. Together with many other examples encompassing police
corruption, ballistics, entomology and riot, to name but a few,
this volume demonstrates how crime has influenced present-day
policing methods, Britain's criminal justice system and ultimately
the detection and conviction of some of this country's most
infamous men and women.
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