Applied partial differential equations: with Fourier series and boundary value problems
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Pearson Prentice Hall, Pearson Education, Inc.
2004
|
| Ausgabe: | 4. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Rev. ed. of: Elementary applied partial differential equations. 3rd ed. c1998 |
| Beschreibung: | XVIII, 769 S. graph. Darst. 24 cm |
| ISBN: | 0130652431 9780130652430 |
Internformat
MARC
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| 100 | 1 | |a Haberman, Richard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied partial differential equations |b with Fourier series and boundary value problems |c Richard Haberman |
| 250 | |a 4. ed. | ||
| 264 | 1 | |a Upper Saddle River, NJ |b Pearson Prentice Hall, Pearson Education, Inc. |c 2004 | |
| 300 | |a XVIII, 769 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Rev. ed. of: Elementary applied partial differential equations. 3rd ed. c1998 | ||
| 650 | 0 | |a Differential equations, Partial | |
| 650 | 0 | |a Fourier series | |
| 650 | 0 | |a Boundary value problems | |
| 650 | 7 | |a Equações diferenciais parciais |2 larpcal | |
| 650 | 4 | |a Fourier, Séries de | |
| 650 | 4 | |a Problèmes aux limites | |
| 650 | 4 | |a Équations aux dérivées partielles | |
| 650 | 4 | |a Boundary value problems | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Fourier series | |
| 650 | 0 | 7 | |a Fourier-Reihe |0 (DE-588)4155109-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Randwertproblem |0 (DE-588)4048395-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Anwendung |0 (DE-588)4196864-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partielle Differentialgleichung |0 (DE-588)4044779-0 |D s |
| 689 | 0 | 1 | |a Randwertproblem |0 (DE-588)4048395-2 |D s |
| 689 | 0 | 2 | |a Fourier-Reihe |0 (DE-588)4155109-6 |D s |
| 689 | 0 | 3 | |a Anwendung |0 (DE-588)4196864-5 |D s |
| 689 | 0 | |5 DE-604 | |
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Datensatz im Suchindex
| _version_ | 1804140894385864704 |
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| adam_text | APPLIED PARTIM DIFFERENTIAL EQUATIONS WITH FOURIER SERIES AND BOUNDARY
VALUE PROBLEMS FOURTH EDITION RICHARD HABERMAN DEPARTMENT OF MATHEMATICS
SOUTHERN METHODIST UNIVERSITY PEARSON PRENTICE HALL PEARSON EDUCATION,
INC. UPPER SADDLE RIVER, NEW JERSEY 07458 CONTENTS PREFACE XVII 1 HEAT
EQUATION 1 1.1 INTRODUCTION 1 1.2 DERIVATION OF THE CONDUCTION OF HEAT
IN A ONE-DIMENSIONAL ROD 2 1.3 BOUNDARY CONDITIONS 12 1.4 EQUILIBRIUM
TEMPERATURE DISTRIBUTION 14 1.4.1 PRESCRIBED TEMPERATURE 14 1.4.2
INSULATED BOUNDARIES 16 1.5 DERIVATION OF THE HEAT EQUATION IN TWO OR
THREE DIMENSIONS 21 2 METHOD OF SEPARATION OF VARIABLES 35 2.1
INTRODUCTION 35 2.2 LINEARITY 36 2.3 HEAT EQUATION WITH ZERO
TEMPERATURES AT FINITE ENDS 38 2.3.1 INTRODUCTION 38 2.3.2 SEPARATION OF
VARIABLES 39 2.3.3 TIME-DEPENDENT EQUATION 41 2.3.4 BOUNDARY VALUE
PROBLEM 42 2.3.5 PRODUCT SOLUTIONS AND THE PRINCIPLE OF SUPERPOSITION
.... 47 2.3.6 ORTHOGONALITY OF SINES 50 2.3.7 FORMULATION, SOLUTION, AND
INTERPRETATION OF AN EXAMPLE 51 2.3.8 SUMMARY 54 2.4 WORKED EXAMPLES
WITH THE HEAT EQUATION: OTHER BOUNDARY VALUE PROBLEMS 59 2.4.1 HEAT
CONDUCTION IN A ROD WITH INSULATED ENDS 59 2.4.2 HEAT CONDUCTION IN A
THIN CIRCULAR RING 63 2.4.3 SUMMARY OF BOUNDARY VALUE PROBLEMS 68 2.5
LAPLACE S EQUATION: SOLUTIONS AND QUALITATIVE PROPERTIES 71 2.5.1
LAPLACE S EQUATION INSIDE A RECTANGLE 71 VLL VLLL CONTENTS 2.5.2
LAPLACE S EQUATION FOR A CIRCULAR DISK 76 2.5.3 FLUID FLOW PAST A
CIRCULAR CYLINDER (LIFT) 80 2.5.4 QUALITATIVE PROPERTIES OF LAPLACE S
EQUATION 83 3 FOURIER SERIES 89 3.1 INTRODUCTION 89 3.2 STATEMENT OF
CONVERGENCE THEOREM 91 3.3 FOURIER COSINE AND SINE SERIES 96 3.3.1
FOURIER SINE SERIES 96 3.3.2 FOURIER COSINE SERIES 106 3.3.3
REPRESENTING F{X) BY BOTH A SINE AND COSINE SERIES .... 108 3.3.4 EVEN
AND ODD PARTS 109 3.3.5 CONTINUOUS FOURIER SERIES 111 3.4 TERM-BY-TERM
DIFFERENTIATION OF FOURIER SERIES 116 3.5 TERM-BY-TERM INTEGRATION OF
FOURIER SERIES 127 3.6 COMPLEX FORM OF FOURIER SERIES 131 4 WAVE
EQUATION: VIBRATING STRINGS AND MEMBRANES 135 4.1 INTRODUCTION 135 4.2
DERIVATION OF A VERTICALLY VIBRATING STRING 135 4.3 BOUNDARY CONDITIONS
139 4.4 VIBRATING STRING WITH FIXED ENDS 142 4.5 VIBRATING MEMBRANE 149
4.6 REFLECTION AND REFRACTION OF ELECTROMAGNETIC (LIGHT) AND ACOUSTIC
(SOUND) WAVES 151 4.6.1 SNELL S LAW OF REFRACTION 152 4.6.2 INTENSITY
(AMPLITUDE) OF REFLECTED AND REFRACTED WAVES . . 154 4.6.3 TOTAL
INTERNAL REFLECTION 155 5 STURM-LIOUVILLE EIGENVALUE PROBLEMS 157 5.1
INTRODUCTION 157 5.2 EXAMPLES 158 5.2.1 HEAT FLOW IN A NONUNIFORM ROD
158 5.2.2 CIRCULARLY SYMMETRIE HEAT FLOW 159 5.3 STURM-LIOUVILLE
EIGENVALUE PROBLEMS 161 5.3.1 GENERAL CLASSIFICATION 161 5.3.2 REGULAER
STURM-LIOUVILLE EIGENVALUE PROBLEM 162 5.3.3 EXAMPLE AND ILLUSTRATION OF
THEOREMS 164 5.4 WORKED EXAMPLE: HEAT FLOW IN A NONUNIFORM ROD WITHOUT
SOURCES 170 5.5 SELF-ADJOINT OPERATORS AND STURM-LIOUVILLE EIGENVALUE
PROBLEMS . 174 5.6 RAYLEIGH QUOTIENT 189 5.7 WORKED EXAMPLE: VIBRATIONS
OF A NONUNIFORM STRING 195 5.8 BOUNDARY CONDITIONS OF THE THIRD KIND 198
5.9 LARGE EIGENVALUES (ASYMPTOTIC BEHAVIOR) 212 5.10 APPROXIMATION
PROPERTIES 216 CONTENTS IX 6 FINITE DIFFERENCE NUMERICAL METHODS FOR
PARTIAL DIFFERENTIAL EQUATIONS 222 6.1 INTRODUCTION 222 6.2 FINITE
DIFFERENCES AND TRUNCATED TAYLOR SERIES 223 6.3 HEAT EQUATION 229 6.3.1
INTRODUCTION 229 6.3.2 A PARTIAL DIFFERENCE EQUATION 229 6.3.3
COMPUTATIONS 231 6.3.4 FOURIER-VON NEUMANN STABILITY ANALYSIS 235 6.3.5
SEPARATION OF VARIABLES FOR PARTIAL DIFFERENCE EQUATIONS AND ANALYTIC
SOLUTIONS OF ORDINARY DIFFERENCE EQUATIONS 241 6.3.6 MATRIX NOTATION 243
6.3.7 NONHOMOGENEOUS PROBLEMS 247 6.3.8 OTHER NUMERICAL SCHEMES 247
6.3.9 OTHER TYPES OF BOUNDARY CONDITIONS 248 6.4 TWO-DIMENSIONAL HEAT
EQUATION 253 6.5 WAVE EQUATION 256 6.6 LAPLACE S EQUATION 260 6.7 FINITE
ELEMENT METHOD 267 6.7.1 APPROXIMATION WITH NONORTHOGONAL FUNCTIONS
(WEAK FORM OF THE PARTIAL DIFFERENTIAL EQUATION) 267 6.7.2 THE SIMPLEST
TRIANGULAER FINITE ELEMENTS 270 7 HIGHER DIMENSIONAL PARTIAL DIFFERENTIAL
EQUATIONS 275 7.1 INTRODUCTION 275 7.2 SEPARATION OF THE TIME VARIABLE
276 7.2.1 VIBRATING MEMBRANE: ANY SHAPE 276 7.2.2 HEAT CONDUCTION: ANY
REGION 278 7.2.3 SUMMARY 279 7.3 VIBRATING RECTANGULAR MEMBRANE 280 7.4
STATEMENTS AND ILLUSTRATIONS OF THEOREMS FOR THE EIGENVALUE PROBLEM V 2
0 + = 0 289 7.5 GREEN S FORMULA, SELF-ADJOINT OPERATORS AND
MULTIDIMENSIONAL EIGENVALUE PROBLEMS 295 7.6 RAYLEIGH QUOTIENT AND
LAPLACE S EQUATION 300 7.6.1 RAYLEIGH QUOTIENT 300 7.6.2 TIME-DEPENDENT
HEAT EQUATION AND LAPLACE S EQUATION 301 7.7 VIBRATING CIRCULAR MEMBRANE
AND BESSEL FUNCTIONS 303 7.7.1 INTRODUCTION 303 7.7.2 SEPARATION OF
VARIABLES 303 7.7.3 EIGENVALUE PROBLEMS (ONE DIMENSIONAL) 305 7.7.4
BESSEL S DIFFERENTIAL EQUATION 306 7.7.5 SINGULAR POINTS AND BESSEL S
DIFFERENTIAL EQUATION 307 X CONTENTS 7.7.6 BESSEL FUNCTIONS AND THEIR
ASYMPTOTIC PROPERTIES (NEAR Z = 0) 308 7.7.7 EIGENVALUE PROBLEM
INVOLVING BESSEL FUNCTIONS 309 7.7.8 INITIAL VALUE PROBLEM FOR A
VIBRATING CIRCULAR MEMBRANE 311 7.7.9 CIRCULARLY SYMMETRIE CASE 313 7.8
MORE ON BESSEL FUNCTIONS 318 7.8.1 QUALITATIVE PROPERTIES OF BESSEL
FUNCTIONS 318 7.8.2 ASYMPTOTIC FORMULAS FOR THE EIGENVALUES 319 7.8.3
ZEROS OF BESSEL FUNCTIONS AND NODAL CURVES 320 7.8.4 SERIES
REPRESENTATION OF BESSEL FUNCTIONS 322 7.9 LAPLACE S EQUATION IN A
CIRCULAR CYLINDER 326 7.9.1 INTRODUCTION 326 7.9.2 SEPARATION OF
VARIABLES 326 7.9.3 ZERO TEMPERATURE ON THE LATERAL SIDES AND ON THE
BOTTOM OR TOP 328 7.9.4 ZERO TEMPERATURE ON THE TOP AND BOTTOM 330 7.9.5
MODIFIED BESSEL FUNCTIONS 332 7.10 SPHERICAL PROBLEMS AND LEGENDRE
POLYNOMIALS 336 7.10.1 INTRODUCTION 336 7.10.2 SEPARATION OF VARIABLES
AND ONE-DIMENSIONAL EIGENVALUE PROBLEMS 337 7.10.3 ASSOCIATED LEGENDRE
FUNCTIONS AND LEGENDRE POLYNOMIALS 338 7.10.4 RADIAL EIGENVALUE PROBLEMS
341 7.10.5 PRODUCT SOLUTIONS, MODES OF VIBRATION, AND THE INITIAL VALUE
PROBLEM 342 7.10.6 LAPLACE S EQUATION INSIDE A SPHERICAL CAVITY 343 8
NONHOMOGENEOUS PROBLEMS 347 8.1 INTRODUCTION 347 8.2 HEAT FLOW WITH
SOURCES AND NONHOMOGENEOUS BOUNDARY CONDITIONS 347 8.3 METHOD OF
EIGENFUNCTION EXPANSION WITH HOMOGENEOUS BOUNDARY CONDITIONS
(DIFFERENTIATING SERIES OF EIGENFUNCTIONS) 354 8.4 METHOD OF
EIGENFUNCTION EXPANSION USING GREEN S FORMULA (WITH OR WITHOUT
HOMOGENEOUS BOUNDARY CONDITIONS) 359 8.5 FORCED VIBRATING MEMBRANES AND
RESONANCE 364 8.6 POISSON S EQUATION 372 9 GREEN S FUNCTIONS FOR
TIME-INDEPENDENT PROBLEMS 380 9.1 INTRODUCTION 380 9.2 ONE-DIMENSIONAL
HEAT EQUATION 380 9.3 GREEN S FUNCTIONS FOR BOUNDARY VALUE PROBLEMS FOR
ORDINARY DIF- FERENTIAL EQUATIONS 385 XI 9.3.1 ONE-DIMENSIONAL
STEADY-STATE HEAT EQUATION 385 9.3.2 THE METHOD OF VARIATION OF
PARAMETERS 386 9.3.3 THE METHOD OF EIGENFUNCTION EXPANSION FOR GREEN S
FUNCTIONS 389 9.3.4 THE DIRAC DELTA FUNCTION AND ITS RELATIONSHIP TO
GREEN S FUNCTIONS 391 9.3.5 NONHOMOGENEOUS BOUNDARY CONDITIONS 397 9.3.6
SUMMARY 399 9.4 FREDHOLM ALTERNATIVE AND GENERALIZED GREEN S FUNCTIONS
405 9.4.1 INTRODUCTION 405 9.4.2 FREDHOLM ALTERNATIVE 407 9.4.3
GENERALIZED GREEN S FUNCTIONS 409 9.5 GREEN S FUNCTIONS FOR POISSON S
EQUATION 416 9.5.1 INTRODUCTION 416 9.5.2 MULTIDIMENSIONAL DIRAC DELTA
FUNCTION AND GREEN S FUNCTIONS 417 9.5.3 GREEN S FUNCTIONS BY THE METHOD
OF EIGENFUNCTION EXPANSION AND THE FREDHOLM ALTERNATIVE 418 9.5.4 DIRECT
SOLUTION OF GREEN S FUNCTIONS (ONE-DIMENSIONAL EIGENFUNCTIONS) 420 9.5.5
USING GREEN S FUNCTIONS FOR PROBLEMS WITH NONHOMOGENEOUS BOUNDARY
CONDITIONS 422 9.5.6 INFINITE SPACE GREEN S FUNCTIONS 423 9.5.7 GREEN S
FUNCTIONS FOR BOUNDED DOMAINS USING INFINITE SPACE GREEN S FUNCTIONS 426
9.5.8 GREEN S FUNCTIONS FOR A SEMI-INFINITE PLANE (Y 0) USING INFINITE
SPACE GREEN S FUNCTIONS: THE METHOD OF IMAGES 427 9.5.9 GREEN S
FUNCTIONS FOR A CIRCLE: THE METHOD OF IMAGES . . . 430 9.6 PERTURBED
EIGENVALUE PROBLEMS 438 9.6.1 INTRODUCTION 438 9.6.2 MATHEMATICAL
EXAMPLE 438 9.6.3 VIBRATING NEARLY CIRCULAR MEMBRANE 440 9.7 SUMMARY 443
10 INFINITE DOMAIN PROBLEMS: FOURIER TRANSFORM SOLUTIONS OF PARTIAL
DIFFERENTIAL EQUATIONS 445 10.1 INTRODUCTION 445 10.2 HEAT EQUATION ON
AN INFINITE DOMAIN 445 10.3 FOURIER TRANSFORM PAIR 449 10.3.1 MOTIVATION
FROM FOURIER SERIES IDENTITY 449 10.3.2 FOURIER TRANSFORM 450 10.3.3
INVERSE FOURIER TRANSFORM OF A GAUSSIAN 451 10.4 FOURIER TRANSFORM AND
THE HEAT EQUATION 459 10.4.1 HEAT EQUATION 459 XII CONTENTS 10.4.2
FOURIER TRANSFORMING THE HEAT EQUATION: TRANSFORMS OF DERIVATIVES 464
10.4.3 CONVOLUTION THEOREM 466 10.4.4 SUMMARY OF PROPERTIES OF THE
FOURIER TRANSFORM 469 10.5 FOURIER SINE AND COSINE TRANSFORMS: THE HEAT
EQUATION ON SEMI-INFINITE INTERVALS 471 10.5.1 INTRODUCTION 471 10.5.2
HEAT EQUATION ON A SEMI-INFINITE INTERVAL I 471 10.5.3 FOURIER SINE AND
COSINE TRANSFORMS 473 10.5.4 TRANSFORMS OF DERIVATIVES 474 10.5.5 HEAT
EQUATION ON A SEMI-INFINITE INTERVAL II 476 10.5.6 TABLES OF FOURIER
SINE AND COSINE TRANSFORMS 479 10.6 WORKED EXAMPLES USING TRANSFORMS 482
10.6.1 ONE-DIMENSIONAL WAVE EQUATION ON AN INFINITE INTERVAL 482 10.6.2
LAPLACE S EQUATION IN A SEMI-INFINITE STRIP 484 10.6.3 LAPLACE S
EQUATION IN A HALF-PLANE 487 10.6.4 LAPLACE S EQUATION IN A
QUARTER-PLANE 491 10.6.5 HEAT EQUATION IN A PLANE (TWO-DIMENSIONAL
FOURIER TRANSFORMS) 494 10.6.6 TABLE OF DOUBLE-FOURIER TRANSFORMS 498
10.7 SCATTERING AND INVERSE SCATTERING 503 11 GREEN S FUNCTIONS FOR WAVE
AND HEAT EQUATIONS 508 11.1 INTRODUCTION 508 11.2 GREEN S FUNCTIONS FOR
THE WAVE EQUATION 508 11.2.1 INTRODUCTION 508 11.2.2 GREEN S FORMULA 510
11.2.3 RECIPROCITY 511 11.2.4 USING THE GREEN S FUNCTION 513 11.2.5
GREEN S FUNCTION FOR THE WAVE EQUATION 515 11.2.6 ALTERNATE DIFFERENTIAL
EQUATION FOR THE GREEN S FUNCTION 515 11.2.7 INFINITE SPACE GREEN S
FUNCTION FOR THE ONE-DIMENSIONAL WAVE EQUATION AND D ALEMBERT S SOLUTION
516 11.2.8 INFINITE SPACE GREEN S FUNCTION FOR THE THREE- DIMENSIONAL
WAVE EQUATION (HUYGENS PRINCIPLE) 518 11.2.9 TWO-DIMENSIONAL INFINITE
SPACE GREEN S FUNCTION 520 11.2.10 SUMMARY 520 11.3 GREEN S FUNCTIONS
FOR THE HEAT EQUATION 523 11.3.1 INTRODUCTION 523 11.3.2
NON-SELF-ADJOINT NATURE OF THE HEAT EQUATION 524 11.3.3 GREEN S FORMULA
525 11.3.4 ADJOINT GREEN S FUNCTION 527 11.3.5 RECIPROCITY 527 CONTENTS
XIII 11.3.6 REPRESENTATION OF THE SOLUTION USING GREEN S FUNCTIONS 528
11.3.7 ALTERNATE DIFFERENTIAL EQUATION FOR THE GREEN S FUNCTION . . 530
11.3.8 INFINITE SPACE GREEN S FUNCTION FOR THE DIFFUSION EQUATION 530
11.3.9 GREEN S FUNCTION FOR THE HEAT EQUATION (SEMI-INFINITE DOMAIN) 532
11.3.10 GREEN S FUNCTION FOR THE HEAT EQUATION (ON A FINITE REGION) 533
12 THE METHOD OF CHARACTERISTICS FOR LINEAR AND QUASILINEAR WAVE
EQUATIONS 536 12.1 INTRODUCTION 536 12.2 CHARACTERISTICS FOR FIRST-ORDER
WAVE EQUATIONS 537 12.2.1 INTRODUCTION 537 12.2.2 METHOD OF
CHARACTERISTICS FOR FIRST-ORDER PARTIAL DIFFERENTIAL EQUATIONS 538 12.3
METHOD OF CHARACTERISTICS FOR THE ONE-DIMENSIONAL WAVE EQUATION 543
12.3.1 GENERAL SOLUTION 543 12.3.2 INITIAL VALUE PROBLEM (INFINITE
DOMAIN) 545 12.3.3 D ALEMBERT S SOLUTION 549 12.4 SEMI-INFINITE STRINGS
AND REFLECTIONS 552 12.5 METHOD OF CHARACTERISTICS FOR A VIBRATING
STRING OF FIXED LENGTH 557 12.6 THE METHOD OF CHARACTERISTICS FOR
QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS 561 12.6.1 METHOD OF
CHARACTERISTICS 561 12.6.2 TRAFFICFLOW 562 12.6.3 METHOD OF
CHARACTERISTICS (Q = 0) 564 12.6.4 SHOCK WAVES 567 12.6.5 QUASILINEAR
EXAMPLE 579 12.7 FIRST-ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS
585 12.7.1 EIKONAL EQUATION DERIVED FROM THE WAVE EQUATION 585 12.7.2
SOLVING THE EIKONAL EQUATION IN UNIFORM MEDIA AND REFLECTED WAVES 586
12.7.3 FIRST-ORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS .... 589 13
LAPLACE TRANSFORM SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS 591 13.1
INTRODUCTION 591 13.2 PROPERTIES OF THE LAPLACE TRANSFORM 592 13.2.1
INTRODUCTION 592 13.2.2 SINGULARITIES OF THE LAPLACE TRANSFORM 592
13.2.3 TRANSFORMS OF DERIVATIVES 596 F 3.2.4 CONVOLUTION THEOREM 597 XIV
CONTENTS 13.3 GREEN S FUNCTIONS FOR INITIAL VALUE PROBLEMS FOR ORDINARY
DIFFERENTIAL EQUATIONS 601 13.4 A SIGNAL PROBLEM FOR THE WAVE EQUATION
603 13.5 A SIGNAL PROBLEM FOR A VIBRATING STRING OF FINITE LENGTH 606
13.6 THE WAVE EQUATION AND ITS GREEN S FUNCTION 610 13.7 INVERSION OF
LAPLACE TRANSFORMS USING CONTOUR INTEGRALS IN THE COMPLEX PLANE 613 13:8
SOLVING THE WAVE EQUATION USING LAPLACE TRANSFORMS (WITH COMPLEX
VARIABLES) 618 14 DISPERSIVE WAVES: SLOW VARIATIONS, STABILITY,
NONLINEARITY, AND PERTURBATION METHODS 621 14.1 INTRODUCTION 621 14.2
DISPERSIVE WAVES AND GROUP VELOCITY 622 14.2.1 TRAVELING WAVES AND THE
DISPERSION RELATION 622 14.2.2 GROUP VELOCITY I 625 14.3 WAVE GUIDES 628
14.3.1 RESPONSE TO CONCENTRATED PERIODIC SOURCES WITH FREQUENCY UIF 630
14.3.2 GREEN S FUNCTION IF MODE PROPAGATES 631 14.3.3 GREEN S FUNCTION
IF MODE DOES NOT PROPAGATE 632 14.3.4 DESIGN CONSIDERATIONS 632 14.4
FIBER OPTICS 634 14.5 GROUP VELOCITY II AND THE METHOD OF STATIONARY
PHASE 638 14.5.1 METHOD OF STATIONARY PHASE 639 14.5.2 APPLICATION TO
LINEAR DISPERSIVE WAVES 641 14.6 SLOWLY VARYING DISPERSIVE WAVES (GROUP
VELOCITY AND CAUSTICS) . . 645 14.6.1 APPROXIMATE SOLUTIONS OF
DISPERSIVE PARTIAL DIFFERENTIAL EQUATIONS 645 14.6.2 FORMATION OF A
CAUSTIC 648 14.7 WAVE ENVELOPE EQUATIONS (CONCENTRATED WAVE NUMBER) 654
14.7.1 SCHROEDINGER EQUATION 655 14.7.2 LINEARIZED KORTEWEG-DE VRIES
EQUATION 657 14.7.3 NONLINEAR DISPERSIVE WAVES: KORTEWEG-DE VRIES
EQUATION 659 14.7.4 SOLITONS AND INVERSE SCATTERING 662 14.7.5 NONLINEAR
SCHROEDINGER EQUATION 664 14.8 STABILITY AND INSTABILITY 669 14.8.1 BRIEF
ORDINARY DIFFERENTIAL EQUATIONS AND BIFURCATION THEORY 669 14.8.2
ELEMENTARY EXAMPLE OF A STABLE EQUILIBRIUM FOR A PARTIAL DIFFERENTIAL
EQUATION 676 CONTENTS XV 14.8.3 TYPICAL UNSTABLE EQUILIBRIUM FOR A
PARTIAL DIFFERENTIAL EQUATION AND PATTERN FORMATION 677 14.8.4 111 POSED
PROBLEMS 679 14.8.5 SLIGHTLY UNSTABLE DISPERSIVE WAVES AND THE
LINEARIZED COMPLEX GINZBURG-LANDAU EQUATION 680 14.8.6 NONLINEAR COMPLEX
GINZBURG-LANDAU EQUATION 682 14.8.7 LONG WAVE INSTABILITIES 688 14.8.8
PATTERN FORMATION FOR REACTION-DIFFUSION EQUATIONS AND THE TURING
INSTABILITY 689 14.9 SINGULAR PERTURBATION METHODS: MULTIPLE SCALES 696
14.9.1 ORDINARY DIFFERENTIAL EQUATION: WEAKLY NONLINEARLY DAMPED
OSCILLATOR 696 14.9.2 ORDINARY DIFFERENTIAL EQUATION: SLOWLY VARYING
OSCILLATOR 699 14.9.3 SLIGHTLY UNSTABLE PARTIAL DIFFERENTIAL EQUATION ON
FIXED SPATIAL DOMAIN 703 14.9.4 SLOWLY VARYING MEDIUM FOR THE WAVE
EQUATION 705 14.9.5 SLOWLY VARYING LINEAR DISPERSIVE WAVES (INCLUDING
WEAK NONLINEAR EFFECTS) 708 14.10 SINGULAR PERTURBATION METHODS:
BOUNDARY LAYERS METHOD OF MATCHED ASYMPTOTIC EXPANSIONS 713 14.10.1
BOUNDARY LAYER IN AN ORDINARY DIFFERENTIAL EQUATION 713 14.10.2
DIFFUSION OF A POLLUTANT DOMINATED BY CONVECTION 719 BIBLIOGRAPHY 726
ANSWERS TO STARRED EXERCISES 731 INDEX 751
|
| any_adam_object | 1 |
| author | Haberman, Richard |
| author_facet | Haberman, Richard |
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| ctrlnum | (OCoLC)51518593 (DE-599)GBV36001433X |
| dewey-full | 515/.353 |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| edition | 4. ed. |
| format | Book |
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| id | DE-604.BV035910181 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:07:14Z |
| institution | BVB |
| isbn | 0130652431 9780130652430 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018767472 |
| oclc_num | 51518593 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XVIII, 769 S. graph. Darst. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Pearson Prentice Hall, Pearson Education, Inc. |
| record_format | marc |
| spelling | Haberman, Richard Verfasser aut Applied partial differential equations with Fourier series and boundary value problems Richard Haberman 4. ed. Upper Saddle River, NJ Pearson Prentice Hall, Pearson Education, Inc. 2004 XVIII, 769 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Rev. ed. of: Elementary applied partial differential equations. 3rd ed. c1998 Differential equations, Partial Fourier series Boundary value problems Equações diferenciais parciais larpcal Fourier, Séries de Problèmes aux limites Équations aux dérivées partielles Fourier-Reihe (DE-588)4155109-6 gnd rswk-swf Randwertproblem (DE-588)4048395-2 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Anwendung (DE-588)4196864-5 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Randwertproblem (DE-588)4048395-2 s Fourier-Reihe (DE-588)4155109-6 s Anwendung (DE-588)4196864-5 s DE-604 http://www.gbv.de/dms/ilmenau/toc/36001433X.PDF lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018767472&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haberman, Richard Applied partial differential equations with Fourier series and boundary value problems Differential equations, Partial Fourier series Boundary value problems Equações diferenciais parciais larpcal Fourier, Séries de Problèmes aux limites Équations aux dérivées partielles Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Anwendung (DE-588)4196864-5 gnd |
| subject_GND | (DE-588)4155109-6 (DE-588)4048395-2 (DE-588)4044779-0 (DE-588)4196864-5 |
| title | Applied partial differential equations with Fourier series and boundary value problems |
| title_auth | Applied partial differential equations with Fourier series and boundary value problems |
| title_exact_search | Applied partial differential equations with Fourier series and boundary value problems |
| title_full | Applied partial differential equations with Fourier series and boundary value problems Richard Haberman |
| title_fullStr | Applied partial differential equations with Fourier series and boundary value problems Richard Haberman |
| title_full_unstemmed | Applied partial differential equations with Fourier series and boundary value problems Richard Haberman |
| title_short | Applied partial differential equations |
| title_sort | applied partial differential equations with fourier series and boundary value problems |
| title_sub | with Fourier series and boundary value problems |
| topic | Differential equations, Partial Fourier series Boundary value problems Equações diferenciais parciais larpcal Fourier, Séries de Problèmes aux limites Équations aux dérivées partielles Fourier-Reihe (DE-588)4155109-6 gnd Randwertproblem (DE-588)4048395-2 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Anwendung (DE-588)4196864-5 gnd |
| topic_facet | Differential equations, Partial Fourier series Boundary value problems Equações diferenciais parciais Fourier, Séries de Problèmes aux limites Équations aux dérivées partielles Fourier-Reihe Randwertproblem Partielle Differentialgleichung Anwendung |
| url | http://www.gbv.de/dms/ilmenau/toc/36001433X.PDF http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018767472&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT habermanrichard appliedpartialdifferentialequationswithfourierseriesandboundaryvalueproblems |
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