Adam, John A.,
Rays, waves, and scattering : topics in classical mathematical physics / John A. Adam. - 1 online resource (xxiv, 588 pages) : illustrations - Princeton series in applied mathematics . - Princeton series in applied mathematics. .
Includes bibliographical references (pages 567-584) and index.
Cover; Title; Copyright; Contents; Preface; Acknowledgments; Chapter 1 Introduction; 1.1 The Rainbow Directory; 1.1.1 The Multifaceted Rainbow; 1.2 A Mathematical Taste of Things to Come; 1.2.1 Rays; 1.2.2 Waves; 1.2.3 Scattering (Classical); 1.2.4 Scattering (Semiclassical); 1.2.5 Caustics and Diffraction Catastrophes; PART I. RAYS; Chapter 2 Introduction to the "Physics" of Rays; 2.1 What Is a Ray?; 2.1.1 Some Mathematical Definitions; 2.1.2 Geometric Wavefronts; 2.1.3 Fermat's Principle; 2.1.4 The Intensity Law; 2.1.5 Heuristic Derivation of Snell's Laws; 2.1.6 Generalization. 2.2 Geometric and Other Proofs of Snell's Laws of Reflection and Refraction2.2.1 The Law of Reflection; 2.2.2 The Law of Refraction; 2.2.3 A Wave-Theoretic Proof; 2.2.4 An Algebraic Proof; Chapter 3 Introduction to the Mathematics of Rays; 3.1 Background; 3.2 The Method of Characteristics; 3.3 Introduction to Hamilton-Jacobi Theory; 3.3.1 Hamilton's Principle; 3.3.2 Rays and Characteristics; 3.3.3 The Optical Path Length Revisited; 3.4 Ray Differential Geometry and the Eikonal Equation Again; 3.4.1 The Mirage Theorem for Horizontally Stratified Media. 3.4.2 A Return to Spherically Symmetric Media: n(r) Continuous3.5 Dispersion Relations: A Wave-Ray Connection; 3.5.1 Fourier Transforms and Dispersion Relations; 3.5.2 The Bottom Line; 3.5.3 Applications to Atmospheric Waves; 3.6 General Solution of the Linear Wave Equation: Some Asymptotics; 3.6.1 Stationary Phase; 3.6.2 Asymptotics for Oscillatory Sources: Wavenumber Surfaces; 3.7 Rays and Waves in a Slowly Varying Environment; 3.7.1 Some Consequences; 3.7.2 Wavepackets and the Group Speed Revisited; Chapter 4 Ray Optics: The Classical Rainbow. 4.1 Physical Features and Historical Details: A Summary4.2 Ray Theory of the Rainbow: Elementary Mathematical Considerations; 4.2.1 Some Numerical Values; 4.2.2 Polarization of the Rainbow; 4.2.3 The Divergence Problem; 4.3 Related Topics in Meteorological Optics; 4.3.1 The Glory; 4.3.2 Coronas (Simplified); 4.3.3 Rayleigh Scattering-a Dimensional Analysis Argument; Chapter 5 An Improvement over Ray Optics: Airy's Rainbow; 5.1 The Airy Approximation; 5.1.1 Some Ray Prerequisites; 5.1.2 The Airy Wavefront; 5.1.3 How Are Colors Distributed in the Airy Rainbow? 5.1.4 The Airy Wavefront: A Derivation for Arbitrary pChapter 6 Diffraction Catastrophes; 6.1 Basic Geometry of the Fold and Cusp Catastrophes; 6.1.1 The Fold; 6.1.2 The Cusp; 6.2 A Better Approximation; 6.2.1 The Fresnel Integrals; 6.3 The Fold Diffraction Catastrophe; 6.3.1 The Rainbow as a Fold Catastrophe; 6.4 Caustics: The Airy Integral in the Complex Plane; 6.4.1 The Nature of Ai(X); Chapter 7 Introduction to the WKB(J) Approximation: All Things Airy; 7.1 Overview; 7.1.1 Elimination of the First Derivative Term; 7.1.2 The Liouville Transformation.
This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable.
In English.
9781400885404 140088540X
10.1515/9781400885404 doi
22573/ctt1vwmnz7 JSTOR 9452669 IEEE
Mathematical physics.
Physique math�ematique.
SCIENCE--Energy.
SCIENCE--Mechanics--General.
SCIENCE--Physics--General.
MATHEMATICS--Applied.
Mathematical physics.
Electronic books.
QC20
530.15
Rays, waves, and scattering : topics in classical mathematical physics / John A. Adam. - 1 online resource (xxiv, 588 pages) : illustrations - Princeton series in applied mathematics . - Princeton series in applied mathematics. .
Includes bibliographical references (pages 567-584) and index.
Cover; Title; Copyright; Contents; Preface; Acknowledgments; Chapter 1 Introduction; 1.1 The Rainbow Directory; 1.1.1 The Multifaceted Rainbow; 1.2 A Mathematical Taste of Things to Come; 1.2.1 Rays; 1.2.2 Waves; 1.2.3 Scattering (Classical); 1.2.4 Scattering (Semiclassical); 1.2.5 Caustics and Diffraction Catastrophes; PART I. RAYS; Chapter 2 Introduction to the "Physics" of Rays; 2.1 What Is a Ray?; 2.1.1 Some Mathematical Definitions; 2.1.2 Geometric Wavefronts; 2.1.3 Fermat's Principle; 2.1.4 The Intensity Law; 2.1.5 Heuristic Derivation of Snell's Laws; 2.1.6 Generalization. 2.2 Geometric and Other Proofs of Snell's Laws of Reflection and Refraction2.2.1 The Law of Reflection; 2.2.2 The Law of Refraction; 2.2.3 A Wave-Theoretic Proof; 2.2.4 An Algebraic Proof; Chapter 3 Introduction to the Mathematics of Rays; 3.1 Background; 3.2 The Method of Characteristics; 3.3 Introduction to Hamilton-Jacobi Theory; 3.3.1 Hamilton's Principle; 3.3.2 Rays and Characteristics; 3.3.3 The Optical Path Length Revisited; 3.4 Ray Differential Geometry and the Eikonal Equation Again; 3.4.1 The Mirage Theorem for Horizontally Stratified Media. 3.4.2 A Return to Spherically Symmetric Media: n(r) Continuous3.5 Dispersion Relations: A Wave-Ray Connection; 3.5.1 Fourier Transforms and Dispersion Relations; 3.5.2 The Bottom Line; 3.5.3 Applications to Atmospheric Waves; 3.6 General Solution of the Linear Wave Equation: Some Asymptotics; 3.6.1 Stationary Phase; 3.6.2 Asymptotics for Oscillatory Sources: Wavenumber Surfaces; 3.7 Rays and Waves in a Slowly Varying Environment; 3.7.1 Some Consequences; 3.7.2 Wavepackets and the Group Speed Revisited; Chapter 4 Ray Optics: The Classical Rainbow. 4.1 Physical Features and Historical Details: A Summary4.2 Ray Theory of the Rainbow: Elementary Mathematical Considerations; 4.2.1 Some Numerical Values; 4.2.2 Polarization of the Rainbow; 4.2.3 The Divergence Problem; 4.3 Related Topics in Meteorological Optics; 4.3.1 The Glory; 4.3.2 Coronas (Simplified); 4.3.3 Rayleigh Scattering-a Dimensional Analysis Argument; Chapter 5 An Improvement over Ray Optics: Airy's Rainbow; 5.1 The Airy Approximation; 5.1.1 Some Ray Prerequisites; 5.1.2 The Airy Wavefront; 5.1.3 How Are Colors Distributed in the Airy Rainbow? 5.1.4 The Airy Wavefront: A Derivation for Arbitrary pChapter 6 Diffraction Catastrophes; 6.1 Basic Geometry of the Fold and Cusp Catastrophes; 6.1.1 The Fold; 6.1.2 The Cusp; 6.2 A Better Approximation; 6.2.1 The Fresnel Integrals; 6.3 The Fold Diffraction Catastrophe; 6.3.1 The Rainbow as a Fold Catastrophe; 6.4 Caustics: The Airy Integral in the Complex Plane; 6.4.1 The Nature of Ai(X); Chapter 7 Introduction to the WKB(J) Approximation: All Things Airy; 7.1 Overview; 7.1.1 Elimination of the First Derivative Term; 7.1.2 The Liouville Transformation.
This one-of-a-kind book presents many of the mathematical concepts, structures, and techniques used in the study of rays, waves, and scattering. Panoramic in scope, it includes discussions of how ocean waves are refracted around islands and underwater ridges, how seismic waves are refracted in the earth's interior, how atmospheric waves are scattered by mountains and ridges, how the scattering of light waves produces the blue sky, and meteorological phenomena such as rainbows and coronas. Rays, Waves, and Scattering is a valuable resource for practitioners, graduate students, and advanced undergraduates in applied mathematics, theoretical physics, and engineering. Bridging the gap between advanced treatments of the subject written for specialists and less mathematical books aimed at beginners, this unique mathematical compendium features problems and exercises throughout that are geared to various levels of sophistication, covering everything from Ptolemy's theorem to Airy integrals (as well as more technical material), and several informative appendixes. Provides a panoramic look at wave motion in many different contextsFeatures problems and exercises throughoutIncludes numerous appendixes, some on topics not often coveredAn ideal reference book for practitionersCan also serve as a supplemental text in classical applied mathematics, particularly wave theory and mathematical methods in physics and engineeringAccessible to anyone with a strong background in ordinary differential equations, partial differential equations, and functions of a complex variable.
In English.
9781400885404 140088540X
10.1515/9781400885404 doi
22573/ctt1vwmnz7 JSTOR 9452669 IEEE
Mathematical physics.
Physique math�ematique.
SCIENCE--Energy.
SCIENCE--Mechanics--General.
SCIENCE--Physics--General.
MATHEMATICS--Applied.
Mathematical physics.
Electronic books.
QC20
530.15