Partial differential equations of applied mathematics:
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| Main Author: | |
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| Format: | Book |
| Language: | German |
| Published: |
Hoboken, NJ
Wiley
2006
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| Edition: | 3. ed. |
| Series: | Pure and applied mathematics
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVII, 930 S. graph. Darst. |
| ISBN: | 0471690732 9780471690733 |
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| 245 | 1 | 0 | |a Partial differential equations of applied mathematics |c Erich Zauderer |
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| _version_ | 1804135260359753728 |
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| adam_text | PARTIAL DIFFERENTIAL EQUATIONS OF APPLIED MATHEMATICS THIRD EDITION
ERICH ZAUDERER EMERITUS PROFESSOR OF MATHEMATICS POLYTECHNIC UNIVERSITY
NEW YORK IWILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XXIII 1 RANDOM WALKS AND PARTIAL DIFFERENTIAL EQUATIONS
1 1.1 THE DIFFUSION EQUATION AND BROWNIAN MOTION 2 UNRESTRICTED RANDOM
WALKS AND THEIR LIMITS 2 BROWNIAN MOTION 3 RESTRICTED RANDOM WALKS AND
THEIR LIMITS 8 FOKKER-PLANCK AND KOLMOGOROV EQUATIONS 9 PROPERTIES OF
PARTIAL DIFFERENCE EQUATIONS AND RELATED PDES 11 LANGEVIN EQUATION 12
EXERCISES 1.1 12 1.2 THE TELEGRAPHER S EQUATION AND DIFFUSION 15
CORRELATED RANDOM WALKS AND THEIR LIMITS 15 PARTIAL DIFFERENCE EQUATIONS
FOR CORRELATED RANDOM WALKS AND THEIR LIMITS 17 TELEGRAPHER S,
DIFFUSION, AND WAVE EQUATIONS 20 POSITION-DEPENDENT CORRELATED RANDOM
WALKS AND THEIR LIMITS 23 EXERCISES 1.2 25 VII VIH CONTENTS 1.3
LAPLACE S EQUATION AND GREEN S FUNCTION 27 TIME-INDEPENDENT RANDOM WALKS
AND THEIR LIMITS 28 GREEN S FUNCTION 29 MEAN FIRST PASSAGE TIMES AND
POISSON S EQUATION 32 POSITION-DEPENDENT RANDOM WALKS AND THEIR LIMITS
33 PROPERTIES OF PARTIAL DIFFERENCE EQUATIONS AND RELATED PDES 34
EXERCISES 1.3 34 1.4 RANDOM WALKS AND FIRST ORDER PDES 37 RANDOM WALKS
AND LINEAR FIRST ORDER PDES: CONSTANT TRANSITION PROBABILITIES 37 RANDOM
WALKS AND LINEAR FIRST ORDER PDES: VARIABLE TRANSITION PROBABILITIES 39
RANDOM WALKS AND NONLINEAR FIRST ORDER PDES 41 EXERCISES 1.4 42 1.5
SIMULATION OF RANDOM WALKS USING MAPLE 42 UNRESTRICTED RANDOM WALKS 43
RESTRICTED RANDOM WALKS 48 CORRELATED RANDOM WALKS 51 TIME-INDEPENDENT
RANDOM WALKS 54 RANDOM WALKS WITH VARIABLE TRANSITION PROBABILITIES 60
EXERCISES 1.5 62 FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 63 2.1
INTRODUCTION 63 EXERCISES 2.1 65 2.2 LINEAR FIRST ORDER PARTIAL
DIFFERENTIAL EQUATIONS 66 METHOD OF CHARACTERISTICS 66 EXAMPLES 67
GENERALIZED SOLUTIONS 72 CHARACTERISTIC INITIAL VALUE PROBLEMS 76
EXERCISES 2.2 78 2.3 QUASILINEAR FIRST ORDER PARTIAL DIFFERENTIAL
EQUATIONS 82 METHOD OF CHARACTERISTICS 82 WAVE MOTION AND BREAKING 84
UNIDIRECTIONAL NONLINEAR WAVE MOTION: AN EXAMPLE 88 GENERALIZED
SOLUTIONS AND SHOCK WAVES 92 EXERCISES 2.3 99 2.4 NONLINEAR FIRST ORDER
PARTIAL DIFFERENTIAL EQUATIONS 102 CONTENTS IX METHOD OF CHARACTERISTICS
, 102 GEOMETRICAL OPTICS: THE EICONAL EQUATION 108 EXERCISES 2.4 111 2.5
MAPLE METHODS 113 LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 114
QUASILINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 116 NONLINEAR
FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 118 EXERCISES 2.5 119
APPENDIX: ENVELOPES OF CURVES AND SURFACES 120 3 CLASSIFICATION OF
EQUATIONS AND CHARACTERISTICS 123 3.1 LINEAR SECOND ORDER PARTIAL
DIFFERENTIAL EQUATIONS 124 CANONICAL FORMS FOR EQUATIONS OF HYPERBOLIC
TYPE 125 CANONICAL FORMS FOR EQUATIONS OF PARABOLIC TYPE 127 CANONICAL
FORMS FOR EQUATIONS OF ELLIPTIC TYPE 128 EQUATIONS OF MIXED TYPE 128
EXERCISES 3.1 130 3.2 CHARACTERISTIC CURVES 131 FIRST ORDER PDES 131
SECOND ORDER PDES 134 EXERCISES 3.2 135 3.3 CLASSIFICATION OF EQUATIONS
IN GENERAL 137 CLASSIFICATION OF SECOND ORDER PDES 137 CHARACTERISTIC
SURFACES FOR SECOND ORDER PDES 140 FIRST ORDER SYSTEMS OF LINEAR PDES:
CLASSIFICATION AND CHARACTERISTICS 142 SYSTEMS OF HYPERBOLIC TYPE 144
HIGHER-ORDER AND NONLINEAR PDES 147 QUASILINEAR FIRST ORDER SYSTEMS AND
NORMAL FORMS 149 EXERCISES 3.3 151 3.4 FORMULATION OF INITIAL AND
BOUNDARY VALUE PROBLEMS 153 WELL-POSED PROBLEMS 154 EXERCISES 3.4 156
3.5 STABILITY THEORY, ENERGY CONSERVATION, AND DISPERSION 157 NORMAL
MODES AND WELL-POSEDNESS 157 STABILITY 159 ENERGY CONSERVATION AND
DISPERSION 160 CONTENTS DISSIPATION 161 EXERCISES 3.5 162 3.6 ADJOINT
DIFFERENTIAL OPERATORS 163 SCALAR PDES 164 SYSTEMS OF PDES 166
QUASILINEAR PDES 167 EXERCISES 3.6 167 3.7 MAPLE METHODS 168
CLASSIFICATION OF EQUATIONS AND CANONICAL FORMS 168 CLASSIFICATION AND
SOLUTION OF LINEAR SYSTEMS 170 QUASILINEAR HYPERBOLIC SYSTEMS IN TWO
INDEPENDENT VARIABLES 172 WELL-POSEDNESS AND STABILITY 172 EXERCISES 3.7
173 INITIAL AND BOUNDARY VALUE PROBLEMS IN BOUNDED REGIONS 175 4.1
INTRODUCTION 175 BALANCE LAW FOR HEAT CONDUCTION AND DIFFUSION 176 BASIC
EQUATIONS OF PARABOLIC, ELLIPTIC, AND HYPERBOLIC TYPES 177 BOUNDARY
CONDITIONS 179 EXERCISES 4.1 180 4.2 SEPARATION OF VARIABLES 180
SELF-ADJOINT AND POSITIVE OPERATORS 183 EIGENVALUES, EIGENFUNCTIONS, AND
EIGENFUNCTION EXPANSIONS 185 EXERCISES 4.2 189 4.3 THE STURM-LIOUVILLE
PROBLEM AND FOURIER SERIES 191 STURM-LIOUVILLE PROBLEM 191 PROPERTIES OF
EIGENVALUES AND EIGENFUNCTIONS 194 DETERMINATION OF EIGENVALUES AND
EIGENFUNCTIONS 196 TRIGONOMETRIC EIGENFUNCTIONS 196 FOURIER SINE SERIES
197 FOURIER COSINE SERIES 197 FOURIER SERIES 198 PROPERTIES OF
TRIGONOMETRIC FOURIER SERIES 199 BESSEL EIGENFUNCTIONS AND THEIR SERIES
202 LEGENDRE POLYNOMIAL EIGENFUNCTIONS AND THEIR SERIES 203 EXERCISES
4.3 204 4.4 SERIES SOLUTIONS OF BOUNDARY AND INITIAL AND BOUNDARY VALUE
PROBLEMS 207 CONTENTS XJ EXERCISES 4.4 215 4.5 INHOMOGENEOUS EQUATIONS:
DUHAMEL S PRINCIPLE 218 EXAMPLES 219 EXERCISES 4.5 223 4.6 EIGENFUNCTION
EXPANSIONS: FINITE FOURIER TRANSFORMS 224 PDES WITH GENERAL
INHOMOGENEOUS TERMS AND DATA 225 EXAMPLES 227 TIME-DEPENDENT PDES WITH
STATIONARY INHOMOGENEITIES 230 CONVERSION TO PROBLEMS WITH HOMOGENEOUS
BOUNDARY DATA 232 EXERCISES 4.6 233 4.7 NONLINEAR STABILITY THEORY:
EIGENFUNCTION EXPANSIONS 235 NONLINEAR HEAT EQUATION: STABILITY THEORY
235 NONLINEAR HEAT EQUATION: CAUCHY PROBLEM 236 NONLINEAR HEAT EQUATION:
INITIAL AND BOUNDARY VALUE PROBLEM 237 EXERCISES 4.7 240 4.8 MAPLE
METHODS 241 EIGENVALUE PROBLEMS FOR ODES 242 TRIGONOMETRIC FOURIER
SERIES 245 FOURIER-BESSEL AND FOURIER-LEGENDRE SERIES 247 FINITE FOURIER
TRANSFORMS: EIGENFUNCTION EXPANSIONS 248 STATIONARY INHOMOGENEITIES AND
MODIFIED EIGENFUNCTION EXPANSIONS 250 EXERCISES 4.8 252 INTEGRAL
TRANSFORMS 253 5.1 INTRODUCTION 253 5.2 ONE-DIMENSIONAL FOURIER
TRANSFORMS 255 GENERAL PROPERTIES 256 APPLICATIONS TO ODES AND PDES 257
EXERCISES 5.2 267 5.3 FOURIER SINE AND COSINE TRANSFORMS 270 GENERAL
PROPERTIES , 271 APPLICATIONS TO PDES 272 EXERCISES 5.3 279 5.4
HIGHER-DIMENSIONAL FOURIER TRANSFORMS 281 CAUCHY PROBLEM FOR THE
THREE-DIMENSIONAL WAVE EQUATION: SPHERICAL MEANS AND STOKES RULE 282 XII
CONTENTS CAUCHY PROBLEM FOR THE TWO-DIMENSIONAL WAVE EQUATION:
HADAMARD S METHOD OF DESCENT 284 HUYGENS PRINCIPLE 285 HELMHOLTZ AND
MODIFIED HELMHOLTZ EQUATIONS 287 EXERCISES 5.4 289 5.5 HANKEL TRANSFORMS
290 GENERAL PROPERTIES 291 APPLICATIONS TO PDES 292 EXERCISES 5.5 . 296
5.6 LAPLACE TRANSFORMS . 297 GENERAL PROPERTIES 298 APPLICATIONS TO PDES
299 ABELIAN AND TAUBERIAN THEORIES 302 EXERCISES 5.6 304 5.7 ASYMPTOTIC
APPROXIMATION METHODS FOR FOURIER INTEGRALS 306 METHOD OF STATIONARY
PHASE 307 DISPERSIVE PDES: KLEIN-GORDON EQUATION 308 SIROVICH S METHOD
312 DISSIPATIVE PDES: DISSIPATIVE WAVE EQUATION 313 EXERCISES 5.7 317
5.8 MAPLE METHODS 318 FOURIER TRANSFORMS T 319 FOURIER SINE AND COSINE
TRANSFORMS 321 HIGHER-DIMENSIONAL FOURIER TRANSFORMS 323 HANKEL
TRANSFORMS 324 LAPLACE TRANSFORMS 325 ASYMPTOTIC APPROXIMATION METHODS
FOR FOURIER INTEGRALS 327 DISCRETE FOURIER TRANSFORM AND FAST FOURIER
TRANSFORM 328 EXERCISES 5.8 331 INTEGRAL RELATIONS 333 6.1 INTRODUCTION
334 INTEGRAL RELATION: HYPERBOLIC PDE 335 INTEGRAL RELATION: PARABOLIC
AND ELLIPTIC PDES 337 EXERCISES 6.1 338 6.2 COMPOSITE MEDIA:
DISCONTINUOUS COEFFICIENTS 338 CAUCHY AND INITIAL AND BOUNDARY VALUE
PROBLEMS 340 EIGENVALUE PROBLEMS AND EIGENFUNCTION EXPANSIONS 343
CONTENTS XIH EXERCISES 6.2 345 6.3 SOLUTIONS WITH DISCONTINUOUS FIRST
DERIVATIVES 347 EXERCISES 6.3 351 6.4 WEAK SOLUTIONS 352 INITIAL AND
BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC EQUATIONS 352 INITIAL VALUE
PROBLEMS FOR HYPERBOLIC EQUATIONS 354 WEAK SOLUTIONS OF PARABOLIC AND
ELLIPTIC EQUATIONS 354 EXAMPLES 355 EXERCISES 6.4 358 6.5 THE INTEGRAL
WAVE EQUATION 360 CHARACTERISTIC QUADRILATERALS AND TRIANGLES 360
EXAMPLES 363 SPACELIKE AND TIMELIKE CURVES 369 CHARACTERISTIC INITIAL
VALUE PROBLEM 370 EXERCISES 6.5 372 6.6 CONCENTRATED SOURCE OR FORCE
TERMS 373 HYPERBOLIC EQUATIONS 373 ONE-DIMENSIONAL HYPERBOLIC EQUATIONS:
STATIONARY CONCENTRATED FORCES 375 ONE-DIMENSIONAL HYPERBOLIC EQUATIONS:
MOVING CONCENTRATED FORCES 376 EXERCISES 6.6 379 6.7 POINT SOURCES AND
FUNDAMENTAL SOLUTIONS 380 HYPERBOLIC AND PARABOLIC EQUATIONS: STATIONARY
POINT SOURCES 381 POINT SOURCES AND INSTANTANEOUS POINT SOURCES 385
FUNDAMENTAL SOLUTIONS 387 FUNDAMENTAL SOLUTIONS OF ELLIPTIC EQUATIONS
388 FUNDAMENTAL SOLUTIONS OF HYPERBOLIC EQUATIONS 392 FUNDAMENTAL
SOLUTIONS OF PARABOLIC EQUATIONS 395 EXERCISES 6.7 397 6.8 ENERGY
INTEGRALS 398 ENERGY INTEGRALS FOR.HYPERBOLIC EQUATIONS 398 ENERGY
INTEGRALS FOR PARABOLIC EQUATIONS 402 ENERGY INTEGRALS FOR ELLIPTIC
EQUATIONS 403 EXERCISES 6.8 . 404 6.9 MAPLE METHODS 406 INTEGRAL WAVE
EQUATION 406 FUNDAMENTAL SOLUTIONS - 407 XIV CONTENTS EXERCISES 6.9 408
7 GREEN S FUNCTIONS 409 7.1 INTEGRAL THEOREMS AND GREEN S FUNCTIONS 410
INTEGRAL THEOREMS AND GREEN S FUNCTIONS FOR ELLIPTIC EQUATIONS 410
INTEGRAL THEOREMS AND GREEN S FUNCTIONS FOR HYPERBOLIC EQUATIONS 412
INTEGRAL THEOREMS AND GREEN S FUNCTIONS FOR PARABOLIC EQUATIONS 415
CAUSAL FUNDAMENTAL SOLUTIONS AND GREEN S FUNCTIONS FOR CAUCHY PROBLEMS
416 GREEN S FUNCTIONS FOR HYPERBOLIC AND PARABOLIC EQUATIONS: AN
ALTERNATIVE CONSTRUCTION 417 INTEGRAL THEOREMS AND GREEN S FUNCTIONS IN
ONE DIMENSION 418 GREEN S FUNCTIONS FOR NONSELF-ADJOINT ELLIPTIC
EQUATIONS 421 EXERCISES 7.1 423 7.2 GENERALIZED FUNCTIONS 425 TEST
FUNCTIONS AND LINEAR FUNCTIONALS 425 PROPERTIES OF GENERALIZED FUNCTIONS
427 FOURIER TRANSFORMS OF GENERALIZED FUNCTIONS 433 WEAK CONVERGENCE OF
SERIES 435 PROPERTIES OF THE DIRAC DELTA FUNCTION 438 EXERCISES 7.2 441
7.3 GREEN S FUNCTIONS FOR BOUNDED REGIONS 443 GREEN S FUNCTIONS FOR
ELLIPTIC PDES 444 MODIFIED GREEN S FUNCTIONS FOR ELLIPTIC PDES 451
GREEN S FUNCTIONS FOR HYPERBOLIC PDES 456 GREEN S FUNCTIONS FOR
PARABOLIC PDES 457 EXERCISES 7.3 458 7.4 GREEN S FUNCTIONS FOR UNBOUNDED
REGIONS 462 GREEN S FUNCTIONS FOR THE HEAT EQUATION IN AN UNBOUNDED
REGION 462 GREEN S FUNCTIONS FOR THE WAVE EQUATION IN AN UNBOUNDED
REGION 464 GREEN S FUNCTIONS FOR THE KLEIN-GORDON EQUATION AND THE
MODIFIED TELEGRAPHER S EQUATION 467 GREEN S FUNCTIONS FOR PARABOLIC AND
HYPERBOLIC PDES 470 GREEN S FUNCTIONS FOR THE REDUCED WAVE EQUATION:
OCEAN ACOUSTICS 471 EXERCISES 7.4 473 CONTENTS XV 7.5 THE METHOD OF
IMAGES 476 LAPLACE S EQUATION IN A HALF-SPACE 476 HYPERBOLIC EQUATIONS
IN A SEMI-INFINITE INTERVAL 480 HEAT EQUATION IN A FINITE INTERVAL 481
GREEN S FUNCTION FOR LAPLACE S EQUATION IN A SPHERE 482 EXERCISES 7.5
486 7.6 MAPLE METHODS 488 GENERALIZED FUNCTIONS 488 GREEN S FUNCTIONS
FOR ODES 489 ADJOINT DIFFERENTIAL OPERATORS 490 EXERCISES 7.6 490 8
VARIATIONAL AND OTHER METHODS 491 8.1 VARIATIONAL PROPERTIES OF
EIGENVALUES AND EIGENFUNCTIONS 492 ENERGY INTEGRALS AND RAYLEIGH
QUOTIENTS 492 COURANT S MAXIMUM-MINIMUM PRINCIPLE 496 VARIATIONAL
FORMULATION OF THE EIGENVALUE PROBLEM 497 DISTRIBUTION OF THE
EIGENVALUES 500 DIRICHLET EIGENVALUE PROBLEMS FOR ELLIPTIC EQUATIONS
WITH CONSTANT COEFFICIENTS 503 COMPLETENESS OF THE EIGENFUNCTIONS 506
EXERCISES 8.1 508 8.2 THE RAYLEIGH-RITZ METHOD 511 APPLICATION OF THE
RAYLEIGH-RITZ METHOD 514 DIFFUSION PROCESS WITH A CHAIN REACTION 516
RAYLEIGH-RITZ METHOD FOR STURM-LIOUVILLE PROBLEMS 517 EXERCISES 8.2 521
8.3 RIEMANN S METHOD 523 EXERCISES 8.3 528 8.4 MAXIMUM AND MINIMUM
PRINCIPLES 528 MAXIMUM AND MINIMUM PRINCIPLES FOR THE DIFFUSION EQUATION
528 MAXIMUM AND MINIMUM PRINCIPLE FOR POISSON S AND LAPLACE S EQUATIONS
531 POSITIVITY PRINCIPLE FOR THE TELEGRAPHER S EQUATION 533 EXERCISES
8.4 534 8.5 SOLUTION METHODS FOR HIGHER-ORDER PDES AND SYSTEMS OF PDES
537 LATERAL VIBRATION OF A ROD OF INFINITE LENGTH 537 LATERAL VIBRATION
OF A ROD OF FINITE LENGTH 539 XVI CONTENTS VIBRATION OF A PLATE 541
STATIC DEFLECTION OF A PLATE: THE BIHARMONIC EQUATION 544 EULER S
EQUATIONS OF INVISCID FLUID DYNAMICS 546 INCOMPRESSIBLE AND IRROTATIONAL
FLUID FLOW 548 LINEARIZATION OF EULER S EQUATIONS: ACOUSTICS 549 EULER S
EQUATIONS FOR ONE-DIMENSIONAL FLUID FLOW 551 NAVIER-STOKES EQUATIONS FOR
ONE-DIMENSIONAL VISCOUS FLUID HOW 552 STEADY TWO-DIMENSIONAL ISENTROPIC
FLOW 554 MAXWELL S EQUATIONS OF ELECTROMAGNETIC THEORY 555 MAXWELL S
EQUATIONS IN A VACUUM 558 NAVIER S EQUATION OF ELASTICITY THEORY 559
EXERCISES 8.5 561 8.6 MAPLE METHODS 565 RAYLEIGH-RITZ METHOD: ONE
DIMENSION 565 RAYLEIGH-RITZ METHOD: TWO AND THREE DIMENSIONS 566
EXERCISES 8.6 568 9 PERTURBATION METHODS 569 9.1 INTRODUCTION 569 9.2
REGULAR PERTURBATION METHODS 572 PERTURBATION METHOD IN A BOUNDED REGION
575 PERTURBATION METHOD IN AN UNBOUNDED REGION: METHODS OF MULTIPLE
SCALES AND RENORMALIZATION 577 HYPERBOLIC EQUATION WITH SLOWLY VARYING
COEFFICIENTS 582 BOUNDARY PERTURBATION METHODS 585 PERTURBATION METHOD
FOR EIGENVALUE PROBLEMS 588 NONLINEAR DISPERSIVE WAVE MOTION 590
EXERCISES 9.2 594 9.3 SINGULAR PERTURBATION METHODS AND BOUNDARY LAYER
THEORY 597 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR FIRST ORDER
PDES 598 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR HYPERBOLIC PDES
606 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR LINEAR ELLIPTIC PDES:
A SIMPLE EXAMPLE 611 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR
ELLIPTIC PDES: A GENERAL DISCUSSION 617 CONTENTS XVII PARABOLIC EQUATION
METHOD 623 PARABOLIC EQUATION METHOD: SPECIFIC EXAMPLES 626 SINGULAR
PERTURBATION OF AN ELLIPTIC PDE IN AN EXTERIOR REGION 630 EXERCISES 9.3
632 9.4 MAPLE METHODS 635 REGULAR PERTURBATION EXPANSIONS 635 SINGULAR
PERTURBATIONS AND BOUNDARY LAYER METHODS 636 PARABOLIC EQUATION METHOD
637 EXERCISES 9.4 638 10 ASYMPTOTIC METHODS 639 10.1 EQUATIONS WITH A
LARGE PARAMETER 640 LINEAR REDUCED WAVE EQUATION 640 EICONAL AND
TRANSPORT EQUATIONS OF GEOMETRICAL OPTICS 641 EXACT AND ASYMPTOTIC
REPRESENTATIONS OF THE FREE-SPACE GREENVFUNCTION 642 EXACT AND
ASYMPTOTIC REPRESENTATIONS OF THE HALF-PLANE GREEN S FUNCTION 644 RAY
EQUATIONS FOR THE ASYMPTOTIC PHASE TERM 646 RAYS IN A STRATIFIED MEDIUM
647 GENERAL INITIAL VALUE PROBLEMS FOR THE RAY EQUATIONS 649 TRANSPORT
EQUATIONS: RAYS AND WAVE FRONTS 652 SPECIFIC RAY SYSTEMS AND WAVE FRONTS
655 BOUNDARY VALUE PROBLEMS FOR THE REDUCED WAVE EQUATION 658 REFLECTION
OF A CYLINDRICAL WAVE BY A PARABOLA 659 ASYMPTOTIC EXPANSION AT A
CAUSTIC 663 SCATTERING BY A HALF-PLANE 671 SCATTERING BY A CIRCULAR
CYLINDER 676 PROPAGATION OF A GAUSSIAN BEAM 680 NONLINEAR REDUCED WAVE
EQUATION AND NONLINEAR GEOMETRICAL OPTICS 682 SELF-FOCUSING AND
SELF-TRAPPING OF BEAMS IN A NONLINEAR MEDIUM 683 PROPAGATION OF A BEAM
IN A NONLINEAR MEDIUM 687 EXERCISES 10.1 697 10.2 THE PROPAGATION OF
DISCONTINUITIES AND SINGULARITIES FOR HYPERBOLIC EQUATIONS 700 SOLUTIONS
WITH JUMP DISCONTINUITIES 700 XVIII CONTENTS BICHARACTERISTICS AND THE
PROPAGATION OF JUMP DISCONTINUITIES 701 FUNCTIONS WITH JUMP
DISCONTINUITIES AND HEAVISIDE FUNCTIONS 704 INITIAL VALUE PROBLEM FOR
THE TELEGRAPHER S EQUATION: JUMP DISCONTINUITIES 705 INITIAL VALUE
PROBLEM FOR THE TELEGRAPHER S EQUATION: SINGULAR SOLUTIONS 707 GENERAL
SINGULARITY EXPANSIONS 708 INITIAL VALUE PROBLEM FOR THE TWO-DIMENSIONAL
WAVE EQUATION: JUMP DISCONTINUITIES 709 MODIFIED SINGULARITY EXPANSIONS:
FUNDAMENTAL SOLUTION OF THE KLEIN-GORDON EQUATION 711 MODIFIED
SINGULARITY EXPANSIONS: FUNDAMENTAL SOLUTIONS OF HYPERBOLIC EQUATIONS
713 EXERCISES 10.2 715 10.3 ASYMPTOTIC SIMPLIFICATION OF EQUATIONS 717
ASYMPTOTIC SIMPLIFICATION OF THE DISSIPATIVE WAVE EQUATION 717
EIGENSPACES AND PROJECTION MATRICES 719 ASYMPTOTIC SIMPLIFICATION OF THE
SYSTEM FORM OF THE DISSIPATIVE WAVE EQUATION 720 ASYMPTOTIC
SIMPLIFICATION OF SYSTEMS OF EQUATIONS 722 NAVIER-STOKES EQUATIONS 724
ASYMPTOTIC SIMPLIFICATION OF THE NAVIER-STOKES EQUATIONS: BURGERS AND
HEAT EQUATIONS 726 BURGERS EQUATION: SIMPLE WAVES AND SHOCK WAVES 729
BURGERS EQUATION: SHOCK STRUCTURE 731 SHALLOW WATER THEORY: BOUSSINESQ
EQUATIONS 734 ASYMPTOTIC SIMPLIFICATION OF THE SHALLOW WATER EQUATIONS:
KORTEWEG-DEVRIES EQUATION 735 SOLITARY WAVE SOLUTION OF THE
KORTEWEG-DEVRIES EQUATION 736 EXERCISES 10.3 737 10.4 MAPLE METHODS 738
EQUATIONS WITH A LARGE PARAMETER 738 PROPAGATION OF DISCONTINUITIES AND
SINGULARITIES FOR HYPERBOLIC EQUATIONS 738 ASYMPTOTIC SIMPLIFICATION OF
EQUATIONS 739 EXERCISES 10.4 740 CONTENTS XIX 11 FINITE DIFFERENCE
METHODS 741 11.1 FINITE DIFFERENCE OPERATORS 743 FORWARD, BACKWARD, AND
CENTERED DIFFERENCES: MAPLE PROCEDURES 743 EXERCISES 11.1 746 11.2
FINITE DIFFERENCE METHODS FOR THE ONE-DIMENSIONAL HEAT EQUATION 746
EXPLICIT FORWARD DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL HEAT EQUATION
747 IMPLICIT BACKWARD DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL HEAT
EQUATION 755 ADDITIONAL DIFFERENCE METHODS FOR THE ONE-DIMENSIONAL HEAT
EQUATION 759 METHOD OF LINES FOR THE ONE-DIMENSIONAL HEAT EQUATION 763
EXERCISES 11.2 767 11.3 FINITE DIFFERENCE METHODS FOR THE
ONE-DIMENSIONAL WAVE EQUATION 768 EXPLICIT FORWARD DIFFERENCE METHOD FOR
THE ONE-DIMENSIONAL WAVE EQUATION 768 IMPLICIT BACKWARD DIFFERENCE
METHODS FOR THE ONE-DIMENSIONAL WAVE EQUATION 772 METHOD OF LINES FOR
THE ONE-DIMENSIONAL WAVE EQUATION 775 EXERCISES 11.3 777 11.4 FINITE
DIFFERENCE METHODS FOR TWO-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 778
JACOBI, GAUSS-SEIDEL, AND RELAXATION METHODS FOR TWO- DIMENSIONAL
LAPLACE AND POISSON EQUATIONS 785 ALTERNATING-DIRECTION IMPLICIT METHOD
FOR TWO-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 790 EXERCISES 11.4 792
11.5 VON NEUMANN STABILITY OF DIFFERENCE METHODS FOR PDES 793 VON
NEUMANN STABILITY FOR THE HEAT EQUATION 795 VON NEUMANN STABILITY FOR
THE WAVE EQUATION 797 EXERCISES 11.5 798 11.6 STABILITY AND CONVERGENCE
OF MATRIX DIFFERENCE METHODS FOR PDES 799 MATRIX STABILITY FOR THE HEAT
EQUATION 801 XX CONTENTS CONVERGENCE OF MATRIX ITERATION METHODS FOR
LAPLACE S AND POISSON S EQUATIONS 805 EXERCISES 11.6 807 11.7 FINITE
DIFFERENCE METHODS FOR FIRST ORDER HYPERBOLIC EQUATIONS AND SYSTEMS .
807 FIRST ORDER SCALAR PDES 808 FIRST ORDER HYPERBOLIC SYSTEMS 815 VON
NEUMANN STABILITY FOR FIRST ORDER PDES AND HYPERBOLIC SYSTEMS OF PDES
819 EXERCISES 11.7 821 11.8 FINITE DIFFERENCE METHODS FOR PDES WITH
VARIABLE COEFFICIENTS 821 METHOD OF LINES FOR LINEAR AND SEMILINEAR
PARABOLIC EQUATIONS 822 METHOD OF LINES FOR LINEAR AND SEMILINEAR
HYPERBOLIC EQUATIONS 825 SECOND ORDER QUASILINEAR HYPERBOLIC EQUATIONS:
METHOD OF CHARACTERISTICS FOR INITIAL VALUE PROBLEMS 827 METHOD OF
CHARACTERISTICS FOR HYPERBOLIC SYSTEMS OF TWO QUASILINEAR EQUATIONS IN
TWO UNKNOWNS 830 CHARACTERISTIC DIFFERENCE METHODS FOR LINEAR HYPERBOLIC
SYSTEMS 831 CHARACTERISTIC DIFFERENCE METHODS FOR QUASILINEAR HYPERBOLIC
SYSTEMS 834 DIFFERENCE METHODS FOR THE SOLUTION OF BVPS FOR SEMILINEAR
ELLIPTIC EQUATIONS WITH VARIABLE COEFFICIENTS 835 EXERCISES 11.8 839
11.9 FINITE DIFFERENCE METHODS FOR HIGHER-DIMENSIONAL PDES 839 EXPLICIT
FORWARD DIFFERENCE METHOD FOR THE TWO-DIMENSIONAL HEAT EQUATION 840
IMPLICIT BACKWARD DIFFERENCE METHODS FOR THE TWO-DIMENSIONAL HEAT
EQUATION 842 PEACEMAN-RACHFORD AND DOUGLAS-RACHFORD ADI DIFFERENCE
METHODS FOR THE TWO-DIMENSIONAL HEAT EQUATION 843 METHOD OF LINES FOR
THE TWO-DIMENSIONAL HEAT EQUATION 845 EXPLICIT FORWARD DIFFERENCE METHOD
FOR THE TWO-DIMENSIONAL WAVE EQUATION 846 IMPLICIT BACKWARD DIFFERENCE
METHOD FOR THE TWO-DIMENSIONAL WAVE EQUATION 848 METHOD OF LINES FOR THE
TWO-DIMENSIONAL WAVE EQUATION 849 METHOD OF LINES FOR THE
THREE-DIMENSIONAL HEAT EQUATION 850 CONTENTS XXI METHOD OF LINES FOR THE
THREE-DIMENSIONAL WAVE EQUATION 852 DIFFERENCE METHODS FOR THE
THREE-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 853 EXERCISES 11.9 854
11.10 MAPLE FINITE DIFFERENCE METHODS FOR PARABOLIC AND HYPERBOLIC PDES
855 EXERCISES 11.10 858 12 FINITE ELEMENT METHODS IN TWO DIMENSIONS 859
12.1 INTRODUCTION 859 12.2 THE TRIANGULATION OF A REGION 860
TRIANGULATION OF A POLYGON AND ITS REFINEMENT 861 PLOTS OF
TRIANGULATIONS 863 MAXIMUM AND MINIMUM AREAS OF THE TRIANGLES IN A
TRIANGULATION 865 LOCATION OF A POINT IN A TRIANGULATED REGION 866
PARTIAL REFINEMENT OF A TRIANGULATION 866 BOUNDING LINES FOR TRIANGLES
DETERMINED BY VERTICES 868 EXERCISES 12.2 869 12.3 FINITE ELEMENT
OPERATIONS 870 PLANE ELEMENTS FOR A TRIANGLE 871 FINITE ELEMENT BASIS
FUNCTIONS 872 PLOTS OF BASIS FUNCTIONS 874 FULL SET OF FINITE ELEMENT
BASIS FUNCTIONS 874 FINITE ELEMENT REPRESENTATIONS IN TERMS OF BASIS
FUNCTIONS AND THEIR PLOTS 876 REPRESENTATION OF A FUNCTION OVER A
TRIANGULATED REGION AND ITS EVALUATION 877 FINITE ELEMENT CENTROID- AND
MIDPOINT-VALUED FUNCTIONS 879 INTEGRAL OF A FINITE ELEMENT FUNCTION OVER
A TRIANGULATED REGION 880 LINE INTEGRAL OF A FINITE ELEMENT FUNCTION
OVER A FULL OR PARTIAL BOUNDARY 882 EXERCISES 12.3 , 884 12.4 THE FINITE
ELEMENT METHOD FOR ELLIPTIC EQUATIONS IN TWO DIMENSIONS 885 GALERKIN
INTEGRALS FOR ELLIPTIC EQUATIONS 885 FINITE ELEMENT METHOD FOR ELLIPTIC
EQUATIONS 887 EXERCISES 12.4 893 XXII CONTENTS 12.5 THE FINITE ELEMENT
METHOD FOR PARABOLIC EQUATIONS IN TWO DIMENSIONS 894 GALERKIN INTEGRALS
FOR PARABOLIC EQUATIONS 894 FINITE ELEMENT METHOD FOR PARABOLIC
EQUATIONS 896 EXERCISES 12.5 * 899 12.6 FINITE ELEMENT SOLUTIONS FOR
HYPERBOLIC EQUATIONS IN TWO DIMENSIONS 900 GALERKIN INTEGRALS FOR
HYPERBOLIC EQUATIONS 900 FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS
901 EXERCISES 12.6 904 12.7 FINITE ELEMENT SOLUTIONS FOR PDE EIGENVALUE
PROBLEMS IN TWO DIMENSIONS 905 GALERKIN INTEGRALS FOR PDE EIGENVALUE
PROBLEMS 905 FINITE ELEMENT METHOD FOR THE PDE EIGENVALUE PROBLEM 906
EXERCISES 12.7 910 BIBLIOGRAPHY 911 INDEX 919
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PARTIAL DIFFERENTIAL EQUATIONS OF APPLIED MATHEMATICS THIRD EDITION
ERICH ZAUDERER EMERITUS PROFESSOR OF MATHEMATICS POLYTECHNIC UNIVERSITY
NEW YORK IWILEY- INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
CONTENTS PREFACE XXIII 1 RANDOM WALKS AND PARTIAL DIFFERENTIAL EQUATIONS
1 1.1 THE DIFFUSION EQUATION AND BROWNIAN MOTION 2 UNRESTRICTED RANDOM
WALKS AND THEIR LIMITS 2 BROWNIAN MOTION 3 RESTRICTED RANDOM WALKS AND
THEIR LIMITS 8 FOKKER-PLANCK AND KOLMOGOROV EQUATIONS 9 PROPERTIES OF
PARTIAL DIFFERENCE EQUATIONS AND RELATED PDES 11 LANGEVIN EQUATION 12
EXERCISES 1.1 12 1.2 THE TELEGRAPHER'S EQUATION AND DIFFUSION 15
CORRELATED RANDOM WALKS AND THEIR LIMITS 15 PARTIAL DIFFERENCE EQUATIONS
FOR CORRELATED RANDOM WALKS AND THEIR LIMITS 17 TELEGRAPHER'S,
DIFFUSION, AND WAVE EQUATIONS 20 POSITION-DEPENDENT CORRELATED RANDOM
WALKS AND THEIR LIMITS 23 EXERCISES 1.2 25 VII VIH CONTENTS 1.3
LAPLACE'S EQUATION AND GREEN'S FUNCTION 27 TIME-INDEPENDENT RANDOM WALKS
AND THEIR LIMITS 28 GREEN'S FUNCTION 29 MEAN FIRST PASSAGE TIMES AND
POISSON'S EQUATION 32 POSITION-DEPENDENT RANDOM WALKS AND THEIR LIMITS
33 PROPERTIES OF PARTIAL DIFFERENCE EQUATIONS AND RELATED PDES 34
EXERCISES 1.3 34 1.4 RANDOM WALKS AND FIRST ORDER PDES 37 RANDOM WALKS
AND LINEAR FIRST ORDER PDES: CONSTANT TRANSITION PROBABILITIES 37 RANDOM
WALKS AND LINEAR FIRST ORDER PDES: VARIABLE TRANSITION PROBABILITIES 39
RANDOM WALKS AND NONLINEAR FIRST ORDER PDES 41 EXERCISES 1.4 42 1.5
SIMULATION OF RANDOM WALKS USING MAPLE 42 UNRESTRICTED RANDOM WALKS 43
RESTRICTED RANDOM WALKS 48 CORRELATED RANDOM WALKS 51 TIME-INDEPENDENT
RANDOM WALKS 54 RANDOM WALKS WITH VARIABLE TRANSITION PROBABILITIES 60
EXERCISES 1.5 62 FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 63 2.1
INTRODUCTION 63 EXERCISES 2.1 65 2.2 LINEAR FIRST ORDER PARTIAL
DIFFERENTIAL EQUATIONS 66 METHOD OF CHARACTERISTICS 66 EXAMPLES 67
GENERALIZED SOLUTIONS 72 CHARACTERISTIC INITIAL VALUE PROBLEMS 76
EXERCISES 2.2 78 2.3 QUASILINEAR FIRST ORDER PARTIAL DIFFERENTIAL
EQUATIONS 82 METHOD OF CHARACTERISTICS 82 WAVE MOTION AND BREAKING 84
UNIDIRECTIONAL NONLINEAR WAVE MOTION: AN EXAMPLE 88 GENERALIZED
SOLUTIONS AND SHOCK WAVES 92 EXERCISES 2.3 99 2.4 NONLINEAR FIRST ORDER
PARTIAL DIFFERENTIAL EQUATIONS 102 CONTENTS IX METHOD OF CHARACTERISTICS
, 102 GEOMETRICAL OPTICS: THE EICONAL EQUATION 108 EXERCISES 2.4 111 2.5
MAPLE METHODS 113 LINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 114
QUASILINEAR FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 116 NONLINEAR
FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS 118 EXERCISES 2.5 119
APPENDIX: ENVELOPES OF CURVES AND SURFACES 120 3 CLASSIFICATION OF
EQUATIONS AND CHARACTERISTICS 123 3.1 LINEAR SECOND ORDER PARTIAL
DIFFERENTIAL EQUATIONS 124 CANONICAL FORMS FOR EQUATIONS OF HYPERBOLIC
TYPE 125 CANONICAL FORMS FOR EQUATIONS OF PARABOLIC TYPE 127 CANONICAL
FORMS FOR EQUATIONS OF ELLIPTIC TYPE 128 EQUATIONS OF MIXED TYPE 128
EXERCISES 3.1 130 3.2 CHARACTERISTIC CURVES 131 FIRST ORDER PDES 131
SECOND ORDER PDES 134 EXERCISES 3.2 135 3.3 CLASSIFICATION OF EQUATIONS
IN GENERAL 137 CLASSIFICATION OF SECOND ORDER PDES 137 CHARACTERISTIC
SURFACES FOR SECOND ORDER PDES 140 FIRST ORDER SYSTEMS OF LINEAR PDES:
CLASSIFICATION AND CHARACTERISTICS 142 SYSTEMS OF HYPERBOLIC TYPE 144
HIGHER-ORDER AND NONLINEAR PDES 147 QUASILINEAR FIRST ORDER SYSTEMS AND
NORMAL FORMS 149 EXERCISES 3.3 151 3.4 FORMULATION OF INITIAL AND
BOUNDARY VALUE PROBLEMS 153 WELL-POSED PROBLEMS 154 EXERCISES 3.4 156
3.5 STABILITY THEORY, ENERGY CONSERVATION, AND DISPERSION 157 NORMAL
MODES AND WELL-POSEDNESS 157 STABILITY 159 ENERGY CONSERVATION AND
DISPERSION 160 CONTENTS DISSIPATION 161 EXERCISES 3.5 162 3.6 ADJOINT
DIFFERENTIAL OPERATORS 163 SCALAR PDES 164 SYSTEMS OF PDES 166
QUASILINEAR PDES 167 EXERCISES 3.6 167 3.7 MAPLE METHODS 168
CLASSIFICATION OF EQUATIONS AND CANONICAL FORMS 168 CLASSIFICATION AND
SOLUTION OF LINEAR SYSTEMS 170 QUASILINEAR HYPERBOLIC SYSTEMS IN TWO
INDEPENDENT VARIABLES 172 WELL-POSEDNESS AND STABILITY 172 EXERCISES 3.7
173 INITIAL AND BOUNDARY VALUE PROBLEMS IN BOUNDED REGIONS 175 4.1
INTRODUCTION 175 BALANCE LAW FOR HEAT CONDUCTION AND DIFFUSION 176 BASIC
EQUATIONS OF PARABOLIC, ELLIPTIC, AND HYPERBOLIC TYPES 177 BOUNDARY
CONDITIONS 179 EXERCISES 4.1 180 4.2 SEPARATION OF VARIABLES 180
SELF-ADJOINT AND POSITIVE OPERATORS 183 EIGENVALUES, EIGENFUNCTIONS, AND
EIGENFUNCTION EXPANSIONS 185 EXERCISES 4.2 189 4.3 THE STURM-LIOUVILLE
PROBLEM AND FOURIER SERIES 191 STURM-LIOUVILLE PROBLEM 191 PROPERTIES OF
EIGENVALUES AND EIGENFUNCTIONS 194 DETERMINATION OF EIGENVALUES AND
EIGENFUNCTIONS 196 TRIGONOMETRIC EIGENFUNCTIONS 196 FOURIER SINE SERIES
197 FOURIER COSINE SERIES 197 FOURIER SERIES 198 PROPERTIES OF
TRIGONOMETRIC FOURIER SERIES 199 BESSEL EIGENFUNCTIONS AND THEIR SERIES
202 LEGENDRE POLYNOMIAL EIGENFUNCTIONS AND THEIR SERIES 203 EXERCISES
4.3 204 4.4 SERIES SOLUTIONS OF BOUNDARY AND INITIAL AND BOUNDARY VALUE
PROBLEMS 207 CONTENTS XJ EXERCISES 4.4 215 4.5 INHOMOGENEOUS EQUATIONS:
DUHAMEL'S PRINCIPLE 218 EXAMPLES 219 EXERCISES 4.5 223 4.6 EIGENFUNCTION
EXPANSIONS: FINITE FOURIER TRANSFORMS 224 PDES WITH GENERAL
INHOMOGENEOUS TERMS AND DATA 225 EXAMPLES 227 TIME-DEPENDENT PDES WITH
STATIONARY INHOMOGENEITIES 230 CONVERSION TO PROBLEMS WITH HOMOGENEOUS
BOUNDARY DATA 232 EXERCISES 4.6 233 4.7 NONLINEAR STABILITY THEORY:
EIGENFUNCTION EXPANSIONS 235 NONLINEAR HEAT EQUATION: STABILITY THEORY
235 NONLINEAR HEAT EQUATION: CAUCHY PROBLEM 236 NONLINEAR HEAT EQUATION:
INITIAL AND BOUNDARY VALUE PROBLEM 237 EXERCISES 4.7 240 4.8 MAPLE
METHODS 241 EIGENVALUE PROBLEMS FOR ODES ' 242 TRIGONOMETRIC FOURIER
SERIES 245 FOURIER-BESSEL AND FOURIER-LEGENDRE SERIES 247 FINITE FOURIER
TRANSFORMS: EIGENFUNCTION EXPANSIONS 248 STATIONARY INHOMOGENEITIES AND
MODIFIED EIGENFUNCTION EXPANSIONS 250 EXERCISES 4.8 252 INTEGRAL
TRANSFORMS 253 5.1 INTRODUCTION 253 5.2 ONE-DIMENSIONAL FOURIER
TRANSFORMS 255 GENERAL PROPERTIES 256 APPLICATIONS TO ODES AND PDES 257
EXERCISES 5.2 267 5.3 FOURIER SINE AND COSINE TRANSFORMS 270 GENERAL
PROPERTIES ,' 271 APPLICATIONS TO PDES 272 EXERCISES 5.3 279 5.4
HIGHER-DIMENSIONAL FOURIER TRANSFORMS 281 CAUCHY PROBLEM FOR THE
THREE-DIMENSIONAL WAVE EQUATION: SPHERICAL MEANS AND STOKES'RULE 282 XII
CONTENTS CAUCHY PROBLEM FOR THE TWO-DIMENSIONAL WAVE EQUATION:
HADAMARD'S METHOD OF DESCENT 284 HUYGENS' PRINCIPLE 285 HELMHOLTZ AND
MODIFIED HELMHOLTZ EQUATIONS 287 EXERCISES 5.4 289 5.5 HANKEL TRANSFORMS
290 GENERAL PROPERTIES 291 APPLICATIONS TO PDES 292 EXERCISES 5.5 . 296
5.6 LAPLACE TRANSFORMS . 297 GENERAL PROPERTIES 298 APPLICATIONS TO PDES
299 ABELIAN AND TAUBERIAN THEORIES 302 EXERCISES 5.6 304 5.7 ASYMPTOTIC
APPROXIMATION METHODS FOR FOURIER INTEGRALS 306 METHOD OF STATIONARY
PHASE 307 DISPERSIVE PDES: KLEIN-GORDON EQUATION 308 SIROVICH'S METHOD "
312 DISSIPATIVE PDES: DISSIPATIVE WAVE EQUATION 313 EXERCISES 5.7 317
5.8 MAPLE METHODS 318 FOURIER TRANSFORMS T 319 FOURIER SINE AND COSINE
TRANSFORMS 321 HIGHER-DIMENSIONAL FOURIER TRANSFORMS 323 HANKEL
TRANSFORMS 324 LAPLACE TRANSFORMS 325 ASYMPTOTIC APPROXIMATION METHODS
FOR FOURIER INTEGRALS 327 DISCRETE FOURIER TRANSFORM AND FAST FOURIER
TRANSFORM 328 EXERCISES 5.8 331 INTEGRAL RELATIONS 333 6.1 INTRODUCTION
334 INTEGRAL RELATION: HYPERBOLIC PDE 335 INTEGRAL RELATION: PARABOLIC
AND ELLIPTIC PDES 337 EXERCISES 6.1 338 6.2 COMPOSITE MEDIA:
DISCONTINUOUS COEFFICIENTS 338 CAUCHY AND INITIAL AND BOUNDARY VALUE
PROBLEMS 340 EIGENVALUE PROBLEMS AND EIGENFUNCTION EXPANSIONS 343
CONTENTS XIH EXERCISES 6.2 345 6.3 SOLUTIONS WITH DISCONTINUOUS FIRST
DERIVATIVES 347 EXERCISES 6.3 351 6.4 WEAK SOLUTIONS 352 INITIAL AND
BOUNDARY VALUE PROBLEMS FOR HYPERBOLIC EQUATIONS 352 INITIAL VALUE
PROBLEMS FOR HYPERBOLIC EQUATIONS 354 WEAK SOLUTIONS OF PARABOLIC AND
ELLIPTIC EQUATIONS 354 EXAMPLES 355 EXERCISES 6.4 358 6.5 THE INTEGRAL
WAVE EQUATION 360 CHARACTERISTIC QUADRILATERALS AND TRIANGLES 360
EXAMPLES 363 SPACELIKE AND TIMELIKE CURVES 369 CHARACTERISTIC INITIAL
VALUE PROBLEM 370 EXERCISES 6.5 372 6.6 CONCENTRATED SOURCE OR FORCE
TERMS 373 HYPERBOLIC EQUATIONS 373 ONE-DIMENSIONAL HYPERBOLIC EQUATIONS:
STATIONARY CONCENTRATED FORCES 375 ONE-DIMENSIONAL HYPERBOLIC EQUATIONS:
MOVING CONCENTRATED FORCES 376 EXERCISES 6.6 379 6.7 POINT SOURCES AND
FUNDAMENTAL SOLUTIONS 380 HYPERBOLIC AND PARABOLIC EQUATIONS: STATIONARY
POINT SOURCES 381 POINT SOURCES AND INSTANTANEOUS POINT SOURCES 385
FUNDAMENTAL SOLUTIONS 387 FUNDAMENTAL SOLUTIONS OF ELLIPTIC EQUATIONS
388 FUNDAMENTAL SOLUTIONS OF HYPERBOLIC EQUATIONS 392 FUNDAMENTAL
SOLUTIONS OF PARABOLIC EQUATIONS 395 EXERCISES 6.7 397 6.8 ENERGY
INTEGRALS 398 ENERGY INTEGRALS FOR.HYPERBOLIC EQUATIONS 398 ENERGY
INTEGRALS FOR PARABOLIC EQUATIONS 402 ENERGY INTEGRALS FOR ELLIPTIC
EQUATIONS 403 EXERCISES 6.8 . 404 6.9 MAPLE METHODS 406 INTEGRAL WAVE
EQUATION 406 FUNDAMENTAL SOLUTIONS - 407 XIV CONTENTS EXERCISES 6.9 408
7 GREEN'S FUNCTIONS 409 7.1 INTEGRAL THEOREMS AND GREEN'S FUNCTIONS 410
INTEGRAL THEOREMS AND GREEN'S FUNCTIONS FOR ELLIPTIC EQUATIONS 410
INTEGRAL THEOREMS AND GREEN'S FUNCTIONS FOR HYPERBOLIC EQUATIONS 412
INTEGRAL THEOREMS AND GREEN'S FUNCTIONS FOR PARABOLIC EQUATIONS 415
CAUSAL FUNDAMENTAL SOLUTIONS AND GREEN'S FUNCTIONS FOR CAUCHY PROBLEMS
416 GREEN'S FUNCTIONS FOR HYPERBOLIC AND PARABOLIC EQUATIONS: AN
ALTERNATIVE CONSTRUCTION 417 INTEGRAL THEOREMS AND GREEN'S FUNCTIONS IN
ONE DIMENSION 418 GREEN'S FUNCTIONS FOR NONSELF-ADJOINT ELLIPTIC
EQUATIONS 421 EXERCISES 7.1 423 7.2 GENERALIZED FUNCTIONS 425 TEST
FUNCTIONS AND LINEAR FUNCTIONALS 425 PROPERTIES OF GENERALIZED FUNCTIONS
427 FOURIER TRANSFORMS OF GENERALIZED FUNCTIONS 433 WEAK CONVERGENCE OF
SERIES 435 PROPERTIES OF THE DIRAC DELTA FUNCTION 438 EXERCISES 7.2 441
7.3 GREEN'S FUNCTIONS FOR BOUNDED REGIONS 443 GREEN'S FUNCTIONS FOR
ELLIPTIC PDES 444 MODIFIED GREEN'S FUNCTIONS FOR ELLIPTIC PDES 451
GREEN'S FUNCTIONS FOR HYPERBOLIC PDES 456 GREEN'S FUNCTIONS FOR
PARABOLIC PDES 457 EXERCISES 7.3 458 7.4 GREEN'S FUNCTIONS FOR UNBOUNDED
REGIONS 462 GREEN'S FUNCTIONS FOR THE HEAT EQUATION IN AN UNBOUNDED
REGION 462 GREEN'S FUNCTIONS FOR THE WAVE EQUATION IN AN UNBOUNDED
REGION 464 GREEN'S FUNCTIONS FOR THE KLEIN-GORDON EQUATION AND THE
MODIFIED TELEGRAPHER'S EQUATION 467 GREEN'S FUNCTIONS FOR PARABOLIC AND
HYPERBOLIC PDES 470 GREEN'S FUNCTIONS FOR THE REDUCED WAVE EQUATION:
OCEAN ACOUSTICS 471 EXERCISES 7.4 473 CONTENTS XV 7.5 THE METHOD OF
IMAGES 476 LAPLACE'S EQUATION IN A HALF-SPACE 476 HYPERBOLIC EQUATIONS
IN A SEMI-INFINITE INTERVAL 480 HEAT EQUATION IN A FINITE INTERVAL 481
GREEN'S FUNCTION FOR LAPLACE'S EQUATION IN A SPHERE 482 EXERCISES 7.5
486 7.6 MAPLE METHODS 488 GENERALIZED FUNCTIONS 488 GREEN'S FUNCTIONS
FOR ODES 489 ADJOINT DIFFERENTIAL OPERATORS 490 EXERCISES 7.6 490 8
VARIATIONAL AND OTHER METHODS 491 8.1 VARIATIONAL PROPERTIES OF
EIGENVALUES AND EIGENFUNCTIONS 492 ENERGY INTEGRALS AND RAYLEIGH
QUOTIENTS 492 COURANT'S MAXIMUM-MINIMUM PRINCIPLE 496 VARIATIONAL
FORMULATION OF THE EIGENVALUE PROBLEM 497 DISTRIBUTION OF THE
EIGENVALUES 500 DIRICHLET EIGENVALUE PROBLEMS FOR ELLIPTIC EQUATIONS
WITH CONSTANT COEFFICIENTS 503 COMPLETENESS OF THE EIGENFUNCTIONS 506
EXERCISES 8.1 508 8.2 THE RAYLEIGH-RITZ METHOD 511 APPLICATION OF THE
RAYLEIGH-RITZ METHOD 514 DIFFUSION PROCESS WITH A CHAIN REACTION 516
RAYLEIGH-RITZ METHOD FOR STURM-LIOUVILLE PROBLEMS 517 EXERCISES 8.2 521
8.3 RIEMANN'S METHOD 523 EXERCISES 8.3 528 8.4 MAXIMUM AND MINIMUM
PRINCIPLES 528 MAXIMUM AND MINIMUM PRINCIPLES FOR THE DIFFUSION EQUATION
528 MAXIMUM AND MINIMUM PRINCIPLE FOR POISSON'S AND LAPLACE'S EQUATIONS
531 POSITIVITY PRINCIPLE FOR THE TELEGRAPHER'S EQUATION 533 EXERCISES
8.4 534 8.5 SOLUTION METHODS FOR HIGHER-ORDER PDES AND SYSTEMS OF PDES
537 LATERAL VIBRATION OF A ROD OF INFINITE LENGTH 537 LATERAL VIBRATION
OF A ROD OF FINITE LENGTH 539 XVI CONTENTS VIBRATION OF A PLATE 541
STATIC DEFLECTION OF A PLATE: THE BIHARMONIC EQUATION 544 EULER'S
EQUATIONS OF INVISCID FLUID DYNAMICS 546 INCOMPRESSIBLE AND IRROTATIONAL
FLUID FLOW 548 LINEARIZATION OF EULER'S EQUATIONS: ACOUSTICS 549 EULER'S
EQUATIONS FOR ONE-DIMENSIONAL FLUID FLOW 551 NAVIER-STOKES EQUATIONS FOR
ONE-DIMENSIONAL VISCOUS FLUID HOW 552 STEADY TWO-DIMENSIONAL ISENTROPIC
FLOW 554 MAXWELL'S EQUATIONS OF ELECTROMAGNETIC THEORY 555 MAXWELL'S
EQUATIONS IN A VACUUM 558 NAVIER'S EQUATION OF ELASTICITY THEORY 559
EXERCISES 8.5 561 8.6 MAPLE METHODS 565 RAYLEIGH-RITZ METHOD: ONE
DIMENSION 565 RAYLEIGH-RITZ METHOD: TWO AND THREE DIMENSIONS 566
EXERCISES 8.6 568 9 PERTURBATION METHODS 569 9.1 INTRODUCTION 569 9.2
REGULAR PERTURBATION METHODS 572 PERTURBATION METHOD IN A BOUNDED REGION
575 PERTURBATION METHOD IN AN UNBOUNDED REGION: METHODS OF MULTIPLE
SCALES AND RENORMALIZATION 577 HYPERBOLIC EQUATION WITH SLOWLY VARYING
COEFFICIENTS 582 BOUNDARY PERTURBATION METHODS 585 PERTURBATION METHOD
FOR EIGENVALUE PROBLEMS 588 NONLINEAR DISPERSIVE WAVE MOTION 590
EXERCISES 9.2 594 9.3 SINGULAR PERTURBATION METHODS AND BOUNDARY LAYER
THEORY 597 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR FIRST ORDER
PDES 598 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR HYPERBOLIC PDES
606 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR LINEAR ELLIPTIC PDES:
A SIMPLE EXAMPLE 611 SINGULAR PERTURBATIONS AND BOUNDARY LAYERS FOR
ELLIPTIC PDES: A GENERAL DISCUSSION 617 CONTENTS XVII PARABOLIC EQUATION
METHOD 623 PARABOLIC EQUATION METHOD: SPECIFIC EXAMPLES 626 SINGULAR
PERTURBATION OF AN ELLIPTIC PDE IN AN EXTERIOR REGION 630 EXERCISES 9.3
632 9.4 MAPLE METHODS 635 REGULAR PERTURBATION EXPANSIONS 635 SINGULAR
PERTURBATIONS AND BOUNDARY LAYER METHODS 636 PARABOLIC EQUATION METHOD
637 EXERCISES 9.4 638 10 ASYMPTOTIC METHODS 639 10.1 EQUATIONS WITH A
LARGE PARAMETER 640 LINEAR REDUCED WAVE EQUATION 640 EICONAL AND
TRANSPORT EQUATIONS OF GEOMETRICAL OPTICS 641 EXACT AND ASYMPTOTIC
REPRESENTATIONS OF THE FREE-SPACE GREENVFUNCTION 642 EXACT AND
ASYMPTOTIC REPRESENTATIONS OF THE HALF-PLANE GREEN'S FUNCTION 644 RAY
EQUATIONS FOR THE ASYMPTOTIC PHASE TERM 646 RAYS IN A STRATIFIED MEDIUM
647 GENERAL INITIAL VALUE PROBLEMS FOR THE RAY EQUATIONS 649 TRANSPORT
EQUATIONS: RAYS AND WAVE FRONTS 652 SPECIFIC RAY SYSTEMS AND WAVE FRONTS
655 BOUNDARY VALUE PROBLEMS FOR THE REDUCED WAVE EQUATION 658 REFLECTION
OF A CYLINDRICAL WAVE BY A PARABOLA 659 ASYMPTOTIC EXPANSION AT A
CAUSTIC 663 SCATTERING BY A HALF-PLANE 671 SCATTERING BY A CIRCULAR
CYLINDER 676 PROPAGATION OF A GAUSSIAN BEAM 680 NONLINEAR REDUCED WAVE
EQUATION AND NONLINEAR GEOMETRICAL OPTICS 682 SELF-FOCUSING AND
SELF-TRAPPING OF BEAMS IN A NONLINEAR MEDIUM 683 PROPAGATION OF A BEAM
IN A NONLINEAR MEDIUM 687 EXERCISES 10.1 697 10.2 THE PROPAGATION OF
DISCONTINUITIES AND SINGULARITIES FOR HYPERBOLIC EQUATIONS 700 SOLUTIONS
WITH JUMP DISCONTINUITIES 700 XVIII CONTENTS BICHARACTERISTICS AND THE
PROPAGATION OF JUMP DISCONTINUITIES 701 FUNCTIONS WITH JUMP
DISCONTINUITIES AND HEAVISIDE FUNCTIONS 704 INITIAL VALUE PROBLEM FOR
THE TELEGRAPHER'S EQUATION: JUMP DISCONTINUITIES 705 INITIAL VALUE
PROBLEM FOR THE TELEGRAPHER'S EQUATION: SINGULAR SOLUTIONS 707 GENERAL
SINGULARITY EXPANSIONS 708 INITIAL VALUE PROBLEM FOR THE TWO-DIMENSIONAL
WAVE EQUATION: JUMP DISCONTINUITIES 709 MODIFIED SINGULARITY EXPANSIONS:
FUNDAMENTAL SOLUTION OF THE KLEIN-GORDON EQUATION 711 MODIFIED
SINGULARITY EXPANSIONS: FUNDAMENTAL SOLUTIONS OF HYPERBOLIC EQUATIONS
713 EXERCISES 10.2 715 10.3 ASYMPTOTIC SIMPLIFICATION OF EQUATIONS 717
ASYMPTOTIC SIMPLIFICATION OF THE DISSIPATIVE WAVE EQUATION 717
EIGENSPACES AND PROJECTION MATRICES 719 ASYMPTOTIC SIMPLIFICATION OF THE
SYSTEM FORM OF THE DISSIPATIVE WAVE EQUATION 720 ASYMPTOTIC
SIMPLIFICATION OF SYSTEMS OF EQUATIONS 722 NAVIER-STOKES EQUATIONS 724
ASYMPTOTIC SIMPLIFICATION OF THE NAVIER-STOKES EQUATIONS: BURGERS' AND
HEAT EQUATIONS 726 BURGERS' EQUATION: SIMPLE WAVES AND SHOCK WAVES 729
BURGERS'EQUATION: SHOCK STRUCTURE 731 SHALLOW WATER THEORY: BOUSSINESQ
EQUATIONS 734 ASYMPTOTIC SIMPLIFICATION OF THE SHALLOW WATER EQUATIONS:
KORTEWEG-DEVRIES EQUATION 735 SOLITARY WAVE SOLUTION OF THE
KORTEWEG-DEVRIES EQUATION 736 EXERCISES 10.3 737 10.4 MAPLE METHODS 738
EQUATIONS WITH A LARGE PARAMETER 738 PROPAGATION OF DISCONTINUITIES AND
SINGULARITIES FOR HYPERBOLIC EQUATIONS 738 ASYMPTOTIC SIMPLIFICATION OF
EQUATIONS 739 EXERCISES 10.4 740 CONTENTS XIX 11 FINITE DIFFERENCE
METHODS 741 11.1 FINITE DIFFERENCE OPERATORS 743 FORWARD, BACKWARD, AND
CENTERED DIFFERENCES: MAPLE PROCEDURES 743 EXERCISES 11.1 746 11.2
FINITE DIFFERENCE METHODS FOR THE ONE-DIMENSIONAL HEAT EQUATION 746
EXPLICIT FORWARD DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL HEAT EQUATION
747 IMPLICIT BACKWARD DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL HEAT
EQUATION 755 ADDITIONAL DIFFERENCE METHODS FOR THE ONE-DIMENSIONAL HEAT
EQUATION 759 METHOD OF LINES FOR THE ONE-DIMENSIONAL HEAT EQUATION 763
EXERCISES 11.2 767 11.3 FINITE DIFFERENCE METHODS FOR THE
ONE-DIMENSIONAL WAVE EQUATION 768 EXPLICIT FORWARD DIFFERENCE METHOD FOR
THE ONE-DIMENSIONAL WAVE EQUATION 768 IMPLICIT BACKWARD DIFFERENCE
METHODS FOR THE ONE-DIMENSIONAL WAVE EQUATION 772 METHOD OF LINES FOR
THE ONE-DIMENSIONAL WAVE EQUATION 775 EXERCISES 11.3 777 11.4 FINITE
DIFFERENCE METHODS FOR TWO-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 778
JACOBI, GAUSS-SEIDEL, AND RELAXATION METHODS FOR TWO- DIMENSIONAL
LAPLACE AND POISSON EQUATIONS 785 ALTERNATING-DIRECTION IMPLICIT METHOD
FOR TWO-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 790 EXERCISES 11.4 792
11.5 VON NEUMANN STABILITY OF DIFFERENCE METHODS FOR PDES 793 VON
NEUMANN STABILITY FOR THE HEAT EQUATION 795 VON NEUMANN STABILITY FOR
THE WAVE EQUATION 797 EXERCISES 11.5 798 11.6 STABILITY AND CONVERGENCE
OF MATRIX DIFFERENCE METHODS FOR PDES 799 MATRIX STABILITY FOR THE HEAT
EQUATION 801 XX CONTENTS CONVERGENCE OF MATRIX ITERATION METHODS FOR
LAPLACE'S AND POISSON'S EQUATIONS 805 EXERCISES 11.6 807 11.7 FINITE
DIFFERENCE METHODS FOR FIRST ORDER HYPERBOLIC EQUATIONS AND SYSTEMS .
807 FIRST ORDER SCALAR PDES 808 FIRST ORDER HYPERBOLIC SYSTEMS 815 VON
NEUMANN STABILITY FOR FIRST ORDER PDES AND HYPERBOLIC SYSTEMS OF PDES
819 EXERCISES 11.7 821 11.8 FINITE DIFFERENCE METHODS FOR PDES WITH
VARIABLE COEFFICIENTS 821 METHOD OF LINES FOR LINEAR AND SEMILINEAR
PARABOLIC EQUATIONS 822 METHOD OF LINES FOR LINEAR AND SEMILINEAR
HYPERBOLIC EQUATIONS 825 SECOND ORDER QUASILINEAR HYPERBOLIC EQUATIONS:
METHOD OF CHARACTERISTICS FOR INITIAL VALUE PROBLEMS 827 METHOD OF
CHARACTERISTICS FOR HYPERBOLIC SYSTEMS OF TWO QUASILINEAR EQUATIONS IN
TWO UNKNOWNS 830 CHARACTERISTIC DIFFERENCE METHODS FOR LINEAR HYPERBOLIC
SYSTEMS 831 CHARACTERISTIC DIFFERENCE METHODS FOR QUASILINEAR HYPERBOLIC
SYSTEMS 834 DIFFERENCE METHODS FOR THE SOLUTION OF BVPS FOR SEMILINEAR
ELLIPTIC EQUATIONS WITH VARIABLE COEFFICIENTS 835 EXERCISES 11.8 839
11.9 FINITE DIFFERENCE METHODS FOR HIGHER-DIMENSIONAL PDES 839 EXPLICIT
FORWARD DIFFERENCE METHOD FOR THE TWO-DIMENSIONAL HEAT EQUATION 840
IMPLICIT BACKWARD DIFFERENCE METHODS FOR THE TWO-DIMENSIONAL HEAT
EQUATION 842 PEACEMAN-RACHFORD AND DOUGLAS-RACHFORD ADI DIFFERENCE
METHODS FOR THE TWO-DIMENSIONAL HEAT EQUATION 843 METHOD OF LINES FOR
THE TWO-DIMENSIONAL HEAT EQUATION 845 EXPLICIT FORWARD DIFFERENCE METHOD
FOR THE TWO-DIMENSIONAL WAVE EQUATION 846 IMPLICIT BACKWARD DIFFERENCE
METHOD FOR THE TWO-DIMENSIONAL WAVE EQUATION 848 METHOD OF LINES FOR THE
TWO-DIMENSIONAL WAVE EQUATION 849 METHOD OF LINES FOR THE
THREE-DIMENSIONAL HEAT EQUATION 850 CONTENTS XXI METHOD OF LINES FOR THE
THREE-DIMENSIONAL WAVE EQUATION 852 DIFFERENCE METHODS FOR THE
THREE-DIMENSIONAL LAPLACE AND POISSON EQUATIONS 853 EXERCISES 11.9 854
11.10 MAPLE FINITE DIFFERENCE METHODS FOR PARABOLIC AND HYPERBOLIC PDES
855 EXERCISES 11.10 858 12 FINITE ELEMENT METHODS IN TWO DIMENSIONS 859
12.1 INTRODUCTION 859 12.2 THE TRIANGULATION OF A REGION 860
TRIANGULATION OF A POLYGON AND ITS REFINEMENT 861 PLOTS OF
TRIANGULATIONS 863 MAXIMUM AND MINIMUM AREAS OF THE TRIANGLES IN A
TRIANGULATION 865 LOCATION OF A POINT IN A TRIANGULATED REGION 866
PARTIAL REFINEMENT OF A TRIANGULATION 866 BOUNDING LINES FOR TRIANGLES
DETERMINED BY VERTICES 868 EXERCISES 12.2 869 12.3 FINITE ELEMENT
OPERATIONS 870 PLANE ELEMENTS FOR A TRIANGLE 871 FINITE ELEMENT BASIS
FUNCTIONS 872 PLOTS OF BASIS FUNCTIONS 874 FULL SET OF FINITE ELEMENT
BASIS FUNCTIONS 874 FINITE ELEMENT REPRESENTATIONS IN TERMS OF BASIS
FUNCTIONS AND THEIR PLOTS 876 REPRESENTATION OF A FUNCTION OVER A
TRIANGULATED REGION AND ITS EVALUATION 877 FINITE ELEMENT CENTROID- AND
MIDPOINT-VALUED FUNCTIONS 879 INTEGRAL OF A FINITE ELEMENT FUNCTION OVER
A TRIANGULATED REGION 880 LINE INTEGRAL OF A FINITE ELEMENT FUNCTION
OVER A FULL OR PARTIAL BOUNDARY 882 EXERCISES 12.3 , 884 12.4 THE FINITE
ELEMENT METHOD FOR ELLIPTIC EQUATIONS IN TWO DIMENSIONS 885 GALERKIN
INTEGRALS FOR ELLIPTIC EQUATIONS 885 FINITE ELEMENT METHOD FOR ELLIPTIC
EQUATIONS 887 EXERCISES 12.4 893 XXII CONTENTS 12.5 THE FINITE ELEMENT
METHOD FOR PARABOLIC EQUATIONS IN TWO DIMENSIONS 894 GALERKIN INTEGRALS
FOR PARABOLIC EQUATIONS 894 FINITE ELEMENT METHOD FOR PARABOLIC
EQUATIONS 896 EXERCISES 12.5' * 899 12.6 FINITE ELEMENT SOLUTIONS FOR
HYPERBOLIC EQUATIONS IN TWO DIMENSIONS 900 GALERKIN INTEGRALS FOR
HYPERBOLIC EQUATIONS 900 FINITE ELEMENT METHOD FOR HYPERBOLIC EQUATIONS
901 EXERCISES 12.6 904 12.7 FINITE ELEMENT SOLUTIONS FOR PDE EIGENVALUE
PROBLEMS IN TWO DIMENSIONS 905 GALERKIN INTEGRALS FOR PDE EIGENVALUE
PROBLEMS 905 FINITE ELEMENT METHOD FOR THE PDE EIGENVALUE PROBLEM 906
EXERCISES 12.7 910 BIBLIOGRAPHY 911 INDEX 919 |
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| author | Zauderer, Erich |
| author_facet | Zauderer, Erich |
| author_role | aut |
| author_sort | Zauderer, Erich |
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| building | Verbundindex |
| bvnumber | BV021519761 |
| callnumber-first | Q - Science |
| callnumber-label | QA377 |
| callnumber-raw | QA377 |
| callnumber-search | QA377 |
| callnumber-sort | QA 3377 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 540 |
| classification_tum | MAT 350f MAT 671f |
| ctrlnum | (OCoLC)70158521 (DE-599)BVBBV021519761 |
| dewey-full | 515/.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.353 |
| dewey-search | 515/.353 |
| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV021519761 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:22:09Z |
| indexdate | 2024-07-09T20:37:41Z |
| institution | BVB |
| isbn | 0471690732 9780471690733 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014736272 |
| oclc_num | 70158521 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM |
| physical | XXVII, 930 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley |
| record_format | marc |
| series2 | Pure and applied mathematics |
| spelling | Zauderer, Erich Verfasser aut Partial differential equations of applied mathematics Erich Zauderer 3. ed. Hoboken, NJ Wiley 2006 XXVII, 930 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics Differential equations, Partial Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 s Angewandte Mathematik (DE-588)4142443-8 s DE-604 Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014736272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Zauderer, Erich Partial differential equations of applied mathematics Differential equations, Partial Angewandte Mathematik (DE-588)4142443-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4142443-8 (DE-588)4044779-0 (DE-588)4042805-9 |
| title | Partial differential equations of applied mathematics |
| title_auth | Partial differential equations of applied mathematics |
| title_exact_search | Partial differential equations of applied mathematics |
| title_exact_search_txtP | Partial differential equations of applied mathematics |
| title_full | Partial differential equations of applied mathematics Erich Zauderer |
| title_fullStr | Partial differential equations of applied mathematics Erich Zauderer |
| title_full_unstemmed | Partial differential equations of applied mathematics Erich Zauderer |
| title_short | Partial differential equations of applied mathematics |
| title_sort | partial differential equations of applied mathematics |
| topic | Differential equations, Partial Angewandte Mathematik (DE-588)4142443-8 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Differential equations, Partial Angewandte Mathematik Partielle Differentialgleichung Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014736272&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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