Wave Propagation: An Invariant Imbedding Approach: Mathematics and Its Applications, cartea 17
Autor N.D. Bellman, J. Vasudevanen Limba Engleză Hardback – 31 mar 1986
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Specificații
ISBN-13: 9789027717665
ISBN-10: 9027717664
Pagini: 388
Ilustrații: XIV, 367 p.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.74 kg
Ediția:1986
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
ISBN-10: 9027717664
Pagini: 388
Ilustrații: XIV, 367 p.
Dimensiuni: 155 x 235 x 26 mm
Greutate: 0.74 kg
Ediția:1986
Editura: SPRINGER NETHERLANDS
Colecția Springer
Seria Mathematics and Its Applications
Locul publicării:Dordrecht, Netherlands
Public țintă
ResearchCuprins
1 / Introduction.- 1. Introduction.- 2. Propagation of a Plane Electromagnetic Wave in a Stratified Medium.- 3. Basic Differential Equations of the Electromagnetic Field.- 4. Propagation of E.M. Waves through Multilayers.- 5. The Schrödinger Equation.- 6. The Rectangular Potential Barrier.- 7. The JWKB Solutions.- References.- II / Eikonal Equation and the WKB Approximation.- 1. Introduction.- 2. The Eikonal Expansion.- 3. Derivation of the Solution of the Schrödinger Equation using Matrix Methods.- 4. Asymptotic Behavior of the Solutions.- References.- III / Invariant Imbedding.- 1. Introduction.- 2. Invariant Imbedding Method.- 3. The Classical Approach.- 4. The Invariant Imbedding Approach for Particle Transport.- 5. Riccati Transformations.- 6. Linearization and Solution of the Riccati Equations.- 7. Conservation Relations.- 8. Scattering Matrix Formalism.- 9. Homogeneous Anisotropic Media Forming an Obstacle.- References.- IV / Application to the Wave Equation.- 1. Introduction.- 2. A Continuous Medium Problem.- 3. Bremmer Solutions.- 4. Coupled Differential and Integral Equations for the Two Beams.- 5. Convergence Properties of the Series Solutions.- 6. Bremmer Series Using Finite Order Scattering Reflection and Transmission Functions.- 7. Wave Equations with a Source Term.- References.- V / The Bremmer Series.- 1. Introduction.- 2. A New Type of Refractive Index Profile in Each Layer and the Reflection and Transmission Coefficients.- 3. Splitting of the Wave Function.- 4. Extensions to Other Types of Series.- References.- VI / Generalizations.- 1. Introduction.- 2. Method of Successive Diagonalization.- 3. Approximation to the Eikonal Solution Using Quasilinearization.- References.- VII / Time Dependent Processes.- 1. Introduction.- 2. Time Dependent TransportProblems.- 3. Transport Equation in the Limit of Large Velocities and Large ?.- 4. The Eigenvalue Problems.- 5. Eigenvalue Problems of Sturm-Liouville Systems.- 6. Time Dependent Wave Equation.- 7. Wiener Integrals.- References.- VIII / Asymptotic Properties.- 1. Introduction.- 2. Asymptotic Behavior of the Solutions of the Schrödinger Equation.- 3. The Phase Approach.- 4. Integral Equation Representation.- References.- IX / Operator Techniques.- 1. Introduction.- 2. The Baker-Campbell-Hausdorff Series.- 3. The Magnus Expansion.- 4. Higher Dimensional Wave Equations.- 5. Multidimensional Imbedding.- 6. Higher Order Equations.- References.- X / Variational Principles.- 1. Introduction.- 2. Bubnov-Galerkin Method.- 3. The Rayleigh-Ritz Method.- 4. Sturm-Liouville Theory.- 5. Rayleigh-Ritz Method and Physical Processes.- 6. The Maximum Functional.- 7. Dynamic Programming Method.- References.- XI / Dynamic Programming and Solution of Wave Equations.- 1. Introduction.- 2. Properties of the Green’s Function.- 3. The Sturm Oscillation Theorem and Unimodal Properties.- 4. Characteristic Values and Characteristic Functions.- 5. Determination of Characteristic Values of the Sturm-Liouville Equation.- 6. Another Type of Cauchy System for the Green’s Function and the Solution of Two Point Boundary Value Problem.- 7. Fredholm Resolvent.- 8. The Riccati Equation.- 9. Quasilinearization.- 10. The Cross-Ratio Relations.- 11. Matrix Riccati Equation and Auxiliary Functions.- References.- XII / Approximations.- 1. Introduction.- 2. Quadrature.- 3. Differential Quadrature.- 4. Determination of Weighting Coefficients.- 5. Higher Order Problems.- 6. Spline Approximation.- 7. Approximate Solutions.- 8. Segmental Curve Fitting.- 9. Dynamic Programming Approach.- 10. Splines Via DynamicProgramming.- 11. Derivation of Spline by Dynamic Programming.- 12. Equivalence of the Recursion Relations Obtained by Dynamic Programming and the Usual Results.- References.- Exercises and Notes.- Index of Names.- Index of Subjects.