Mathematical methods for engineers and scientists: 3 Fourier analysis, partial differential equations and variational methods
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2007
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| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XI, 438 S. graph. Darst. |
| ISBN: | 9783540446958 3540446958 |
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| 245 | 1 | 0 | |a Mathematical methods for engineers and scientists |n 3 |p Fourier analysis, partial differential equations and variational methods |c K. T. Tang |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2007 | |
| 300 | |a XI, 438 S. |b graph. Darst. | ||
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| adam_text | K.T. TANG MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS 3 FOURIER
ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS AND VARIATIONAL METHODS WITH 79
FIGURES AND 4 TABLES |Y SPRINGER CONTENTS PART I FOURIER ANALYSIS
FOURIER SERIES 3 1.1 FOURIER SERIES OF FUNCTIONS WITH PERIODICITY 2N 3
1.1.1 ORTHOGONALITY OF TRIGONOTRIC FUNCTIONS 3 1.1.2 THE FOURIER
COEFFICIENTS 5 1.1.3 EXPANSION OF FUNCTIONS IN FOURIER SERIES 6 1.2
CONVERGENCE OF FOURIER SERIES 9 1.2.1 DIRICHLET CONDITIONS 9 1.2.2
FOURIER SERIES AND DELTA FUNCTION 10 1.3 FOURIER SERIES OF FUNCTIONS OF
ANY PERIOD 13 1.3.1 CHANGE OF INTERVAL 13 1.3.2 FOURIER SERIES OF EVEN
AND ODD FUNCTIONS 21 1.4 FOURIER SERIES OF NONPERIODIC FUNCTIONS IN
LIMITED RANGE .... 24 1.5 COMPLEX FOURIER SERIES 29 1.6 THE METHOD OF
JUMPS 32 1.7 PROPERTIES OF FOURIER SERIES 37 1.7.1 PARSEVAL S THEOREM 37
1.7.2 SUMS OF RECIPROCAL POWERS OF INTEGERS 39 1.7.3 INTEGRATION OF
FOURIER SERIES 42 1.7.4 DIFFERENTIATION OF FOURIER SERIES 43 1.8 FOURIER
SERIES AND DIFFERENTIAL EQUATIONS 45 1.8.1 DIFFERENTIAL EQUATION WITH
BOUNDARY CONDITIONS 45 1.8.2 PERIODICALLY DRIVEN OSCILLATOR 49 EXERCISES
52 FOURIER TRANSFORMS 61 2.1 FOURIER INTEGRAL AS A LIMIT OF A FOURIER
SERIES 61 2.1.1 FOURIER COSINE AND SINE INTEGRALS 65 2.1.2 FOURIER
COSINE AND SINE TRANSFORMS 67 2.2 TABLES OF TRANSFORMS 72 VIII CONTENTS
2.3 THE FOURIER TRANSFORM 72 2.4 FOURIER TRANSFORM AND DELTA FUNCTION 79
2.4.1 ORTHOGONALITY 79 2.4.2 FOURIER TRANSFORMS INVOLVING DELTA
FUNCTIONS 80 2.4.3 THREE-DIMENSIONAL FOURIER TRANSFORM PAIR 81 2.5 SOME
IMPORTANT TRANSFORM PAIRS 85 2.5.1 RECTANGULAR PULSE FUNCTION 85 2.5.2
GAUSSIAN FUNCTION 85 2.5.3 EXPONENTIALLY DECAYING FUNCTION 87 2.6
PROPERTIES OF FOURIER TRANSFORM 88 2.6.1 SYMMETRY PROPERTY 88 2.6.2
LINEARITY, SHIFTING, SCALING 89 2.6.3 TRANSFORM OF DERIVATIVES 91 2.6.4
TRANSFORM OF INTEGRAL 92 2.6.5 PARSEVAL S THEOREM 92 2.7 CONVOLUTION 94
2.7.1 MATHEMATICAL OPERATION OF CONVOLUTION 94 2.7.2 CONVOLUTION
THEOREMS 96 2.8 FOURIER TRANSFORM AND DIFFERENTIAL EQUATIONS 99 2.9 THE
UNCERTAINTY OF WAVES 103 EXERCISES 105 PART II STURM*LIOUVILLE THEORY
AND SPECIAL FUNCTIONS 3 ORTHOGONAL FUNCTIONS AND STURM*LIOUVILLE
PROBLEMS ILL 3.1 FUNCTIONS AS VECTORS IN INFINITE DIMENSIONAL VECTOR
SPACE .... ILL 3.1.1 VECTOR SPACE ILL 3.1.2 INNER PRODUCT AND
ORTHOGONALITY 113 3.1.3 ORTHOGONAL FUNCTIONS 116 3.2 GENERALIZED FOURIER
SERIES 121 3.3 HERMITIAN OPERATORS 123 3.3.1 ADJOINT AND SELF-ADJOINT
(HERMITIAN) OPERATORS 123 3.3.2 PROPERTIES OF HERMITIAN OPERATORS 125
3.4 STURM-LIOUVILLE THEORY 130 3.4.1 STURM-LIOUVILLE EQUATIONS 130 3.4.2
BOUNDARY CONDITIONS OF STURM-LIOUVILLE PROBLEMS .... 132 3.4.3 REGULAR
STURM-LIOUVILLE PROBLEMS 133 3.4.4 PERIODIC STURM-LIOUVILLE PROBLEMS 141
3.4.5 SINGULAR STURM-LIOUVILLE PROBLEMS 142 3.5 GREEN S FUNCTION 149
3.5.1 GREEN S FUNCTION AND INHOMOGENEOUS DIFFERENTIAL EQUATION 149 3.5.2
GREEN S FUNCTION AND DELTA FUNCTION 150 EXERCISES 157 CONTENTS IX BESSEL
AND LEGENDRE FUNCTIONS 163 4.1 FROBENIUS METHOD OF DIFFERENTIAL
EQUATIONS 164 4.1.1 POWER SERIES SOLUTION OF DIFFERENTIAL EQUATION 164
4.1.2 CLASSIFYING SINGULAR POINTS 166 4.1.3 FROBENIUS SERIES 167 4.2
BESSEL FUNCTIONS 171 4.2.1 BESSEL FUNCTIONS J N (X) OF INTEGER ORDER 172
4.2.2 ZEROS OF THE BESSEL FUNCTIONS 174 4.2.3 GAMMA FUNCTION 175 4.2.4
BESSEL FUNCTION OF NONINTEGER ORDER 177 4.2.5 BESSEL FUNCTION OF
NEGATIVE ORDER 179 4.2.6 NEUMANN FUNCTIONS AND HANKEL FUNCTIONS 179 4.3
PROPERTIES OF BESSEL FUNCTION 182 4.3.1 RECURRENCE RELATIONS 182 4.3.2
GENERATING FUNCTION OF BESSEL FUNCTIONS 185 4.3.3 INTEGRAL
REPRESENTATION 186 4.4 BESSEL FUNCTIONS AS EIGENFUNCTIONS OF
STURM-LIOUVILLE PROBLEMS 187 4.4.1 BOUNDARY CONDITIONS OF BESSEL S
EQUATION 187 4.4.2 ORTHOGONALITY OF BESSEL FUNCTIONS 188 4.4.3
NORMALIZATION OF BESSEL FUNCTIONS 189 4.5 OTHER KINDS OF BESSEL
FUNCTIONS 191 4.5.1 MODIFIED BESSEL FUNCTIONS 191 4.5.2 SPHERICAL BESSEL
FUNCTIONS 192 4.6 LEGENDRE FUNCTIONS 196 4.6.1 SERIES SOLUTION OF
LEGENDRE EQUATION 196 4.6.2 LEGENDRE POLYNOMIALS 200 4.6.3 LEGENDRE
FUNCTIONS OF THE SECOND KIND 202 4.7 PROPERTIES OF LEGENDRE POLYNOMIALS
204 4.7.1 RODRIGUES FORMULA 204 4.7.2 GENERATING FUNCTION OF LEGENDRE
POLYNOMIALS 206 4.7.3 RECURRENCE RELATIONS 208 4.7.4 ORTHOGONALITY AND
NORMALIZATION OF LEGENDRE POLYNOMIALS 211 4.8 ASSOCIATED LEGENDRE
FUNCTIONS AND SPHERICAL HARMONICS 212 4.8.1 ASSOCIATED LEGENDRE
POLYNOMIALS 212 4.8.2 ORTHOGONALITY AND NORMALIZATION OF ASSOCIATED
LEGENDRE FUNCTIONS 214 4.8.3 SPHERICAL HARMONICS 217 4.9 RESOURCES ON
SPECIAL FUNCTIONS 218 EXERCISES 219 X CONTENTS PART III PARTIAL
DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS IN CARTESIAN
COORDINATES .... 229 5.1 ONE-DIMENSIONAL WAVE EQUATIONS 230 5.1.1 THE
GOVERNING EQUATION OF A VIBRATING STRING 230 5.1.2 SEPARATION OF
VARIABLES 232 5.1.3 STANDING WAVE 238 5.1.4 TRAVELING WAVE 242 5.1.5
NONHOMOGENEOUS WAVE EQUATIONS 248 5.1.6 D ALEMBERT S SOLUTION OF WAVE
EQUATIONS 252 5.2 TWO-DIMENSIONAL WAVE EQUATIONS 261 5.2.1 THE GOVERNING
EQUATION OF A VIBRATING MEMBRANE .... 261 5.2.2 VIBRATION OF A
RECTANGULAR MEMBRANE 262 5.3 THREE-DIMENSIONAL WAVE EQUATIONS 267 5.3.1
PLANE WAVE 268 5.3.2 PARTICLE WAVE IN A RECTANGULAR BOX 270 5.4 EQUATION
OF HEAT CONDUCTION 272 5.5 ONE-DIMENSIONAL DIFFUSION EQUATIONS 274 5.5.1
TEMPERATURE DISTRIBUTIONS WITH SPECIFIED VALUES AT THE BOUNDARIES 275
5.5.2 PROBLEMS INVOLVING INSULATED BOUNDARIES 278 5.5.3 HEAT EXCHANGE AT
THE BOUNDARY 280 5.6 TWO-DIMENSIONAL DIFFUSION EQUATIONS: HEAT TRANSFER
IN A RECTANGULAR PLATE 284 5.7 LAPLACE S EQUATIONS 286 5.7.1
TWO-DIMENSIONAL LAPLACE S EQUATION: STEADY-STATE TEMPERATURE IN A
RECTANGULAR PLATE 287 5.7.2 THREE-DIMENSIONAL LAPLACE S EQUATION:
STEADY-STATE TEMPERATURE IN A RECTANGULAR PARALLELEPIPED 289 5.8
HELMHOLTZ S EQUATIONS 291 EXERCISES 292 PARTIAL DIFFERENTIAL EQUATIONS
WITH CURVED BOUNDARIES .... 301 6.1 THE LAPLACIAN 302 6.2
TWO-DIMENSIONAL LAPLACE S EQUATIONS 304 6.2.1 LAPLACE S EQUATION IN
POLAR COORDINATES 304 6.2.2 POISSON S INTEGRAL FORMULA 312 6.3
TWO-DIMENSIONAL HELMHOLTZ S EQUATIONS IN POLAR COORDINATES. 315 6.3.1
VIBRATION OF A DRUMHEAD: TWO DIMENSIONAL WAVE EQUATION IN POLAR
COORDINATES 316 6.3.2 HEAT CONDUCTION IN A DISK: TWO DIMENSIONAL
DIFFUSION EQUATION IN POLAR COORDINATES 322 6.3.3 LAPLACE S EQUATIONS IN
CYLINDRICAL COORDINATES 326 6.3.4 HELMHOLTZ S EQUATIONS IN CYLINDRICAL
COORDINATES 331 CONTENTS XI 6.4 THREE-DIMENSIONAL LAPLACIAN IN SPHERICAL
COORDINATES 334 6.4.1 LAPLACE S EQUATIONS IN SPHERICAL COORDINATES 334
6.4.2 HELMHOLTZ S EQUATIONS IN SPHERICAL COORDINATES 345 6.4.3 WAVE
EQUATIONS IN SPHERICAL COORDINATES 346 6.5 POISSON S EQUATIONS 349 6.5.1
POISSON S EQUATION AND GREEN S FUNCTION 351 6.5.2 GREEN S FUNCTION FOR
BOUNDARY VALUE PROBLEMS 355 EXERCISES 359 PART IV VARIATIONAL METHODS 7
CALCULUS OF VARIATION 367 7.1 THE EULER-LAGRANGE EQUATION 368 7.1.1
STATIONARY VALUE OF A FUNCTIONAL 368 7.1.2 FUNDAMENTAL THEOREM OF
VARIATIONAL CALCULUS 370 7.1.3 VARIATIONAL NOTATION 372 7.1.4 SPECIAL
CASES 373 7.2 CONSTRAINED VARIATION 377 7.3 SOLUTIONS TO SOME FAMOUS
PROBLEMS 380 7.3.1 THE BRACHISTOCHRONE PROBLEM 380 7.3.2 ISOPERIMETRIC
PROBLEMS 384 7.3.3 THE CATENARY 386 7.3.4 MINIMUM SURFACE OF REVOLUTION
391 7.3.5 FERMAT S PRINCIPLE 394 7.4 SOME EXTENSIONS 397 7.4.1
FUNCTIONALS WITH HIGHER DERIVATIVES 397 7.4.2 SEVERAL DEPENDENT
VARIABLES 399 7.4.3 SEVERAL INDEPENDENT VARIABLES 401 7.5
STURM-LIOUVILLE PROBLEMS AND VARIATIONAL PRINCIPLES 403 7.5.1
VARIATIONAL FORMULATION OF STURM-LIOUVILLE PROBLEMS . . 403 7.5.2
VARIATIONAL CALCULATIONS OF EIGENVALUES AND EIGENFUNCTIONS 405 7.6
RAYLEIGH-RITZ METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 410 7.6.1
LAPLACE S EQUATION 411 7.6.2 POISSON S EQUATION 415 7.6.3 HELMHOLTZ S
EQUATION 417 7.7 HAMILTON S PRINCIPLE 420 EXERCISES 425 REFERENCES 431
INDEX 433
|
| adam_txt |
K.T. TANG MATHEMATICAL METHODS FOR ENGINEERS AND SCIENTISTS 3 FOURIER
ANALYSIS, PARTIAL DIFFERENTIAL EQUATIONS AND VARIATIONAL METHODS WITH 79
FIGURES AND 4 TABLES |Y SPRINGER CONTENTS PART I FOURIER ANALYSIS
FOURIER SERIES 3 1.1 FOURIER SERIES OF FUNCTIONS WITH PERIODICITY 2N 3
1.1.1 ORTHOGONALITY OF TRIGONOTRIC FUNCTIONS 3 1.1.2 THE FOURIER
COEFFICIENTS 5 1.1.3 EXPANSION OF FUNCTIONS IN FOURIER SERIES 6 1.2
CONVERGENCE OF FOURIER SERIES 9 1.2.1 DIRICHLET CONDITIONS 9 1.2.2
FOURIER SERIES AND DELTA FUNCTION 10 1.3 FOURIER SERIES OF FUNCTIONS OF
ANY PERIOD 13 1.3.1 CHANGE OF INTERVAL 13 1.3.2 FOURIER SERIES OF EVEN
AND ODD FUNCTIONS 21 1.4 FOURIER SERIES OF NONPERIODIC FUNCTIONS IN
LIMITED RANGE . 24 1.5 COMPLEX FOURIER SERIES 29 1.6 THE METHOD OF
JUMPS 32 1.7 PROPERTIES OF FOURIER SERIES 37 1.7.1 PARSEVAL'S THEOREM 37
1.7.2 SUMS OF RECIPROCAL POWERS OF INTEGERS 39 1.7.3 INTEGRATION OF
FOURIER SERIES 42 1.7.4 DIFFERENTIATION OF FOURIER SERIES 43 1.8 FOURIER
SERIES AND DIFFERENTIAL EQUATIONS 45 1.8.1 DIFFERENTIAL EQUATION WITH
BOUNDARY CONDITIONS 45 1.8.2 PERIODICALLY DRIVEN OSCILLATOR 49 EXERCISES
52 FOURIER TRANSFORMS 61 2.1 FOURIER INTEGRAL AS A LIMIT OF A FOURIER
SERIES 61 2.1.1 FOURIER COSINE AND SINE INTEGRALS 65 2.1.2 FOURIER
COSINE AND SINE TRANSFORMS 67 2.2 TABLES OF TRANSFORMS 72 VIII CONTENTS
2.3 THE FOURIER TRANSFORM 72 2.4 FOURIER TRANSFORM AND DELTA FUNCTION 79
2.4.1 ORTHOGONALITY 79 2.4.2 FOURIER TRANSFORMS INVOLVING DELTA
FUNCTIONS 80 2.4.3 THREE-DIMENSIONAL FOURIER TRANSFORM PAIR 81 2.5 SOME
IMPORTANT TRANSFORM PAIRS 85 2.5.1 RECTANGULAR PULSE FUNCTION 85 2.5.2
GAUSSIAN FUNCTION 85 2.5.3 EXPONENTIALLY DECAYING FUNCTION 87 2.6
PROPERTIES OF FOURIER TRANSFORM 88 2.6.1 SYMMETRY PROPERTY 88 2.6.2
LINEARITY, SHIFTING, SCALING 89 2.6.3 TRANSFORM OF DERIVATIVES 91 2.6.4
TRANSFORM OF INTEGRAL 92 2.6.5 PARSEVAL'S THEOREM 92 2.7 CONVOLUTION 94
2.7.1 MATHEMATICAL OPERATION OF CONVOLUTION 94 2.7.2 CONVOLUTION
THEOREMS 96 2.8 FOURIER TRANSFORM AND DIFFERENTIAL EQUATIONS 99 2.9 THE
UNCERTAINTY OF WAVES 103 EXERCISES 105 PART II STURM*LIOUVILLE THEORY
AND SPECIAL FUNCTIONS 3 ORTHOGONAL FUNCTIONS AND STURM*LIOUVILLE
PROBLEMS ILL 3.1 FUNCTIONS AS VECTORS IN INFINITE DIMENSIONAL VECTOR
SPACE . ILL 3.1.1 VECTOR SPACE ILL 3.1.2 INNER PRODUCT AND
ORTHOGONALITY 113 3.1.3 ORTHOGONAL FUNCTIONS 116 3.2 GENERALIZED FOURIER
SERIES 121 3.3 HERMITIAN OPERATORS 123 3.3.1 ADJOINT AND SELF-ADJOINT
(HERMITIAN) OPERATORS 123 3.3.2 PROPERTIES OF HERMITIAN OPERATORS 125
3.4 STURM-LIOUVILLE THEORY 130 3.4.1 STURM-LIOUVILLE EQUATIONS 130 3.4.2
BOUNDARY CONDITIONS OF STURM-LIOUVILLE PROBLEMS . 132 3.4.3 REGULAR
STURM-LIOUVILLE PROBLEMS 133 3.4.4 PERIODIC STURM-LIOUVILLE PROBLEMS 141
3.4.5 SINGULAR STURM-LIOUVILLE PROBLEMS 142 3.5 GREEN'S FUNCTION 149
3.5.1 GREEN'S FUNCTION AND INHOMOGENEOUS DIFFERENTIAL EQUATION 149 3.5.2
GREEN'S FUNCTION AND DELTA FUNCTION 150 EXERCISES 157 CONTENTS IX BESSEL
AND LEGENDRE FUNCTIONS 163 4.1 FROBENIUS METHOD OF DIFFERENTIAL
EQUATIONS 164 4.1.1 POWER SERIES SOLUTION OF DIFFERENTIAL EQUATION 164
4.1.2 CLASSIFYING SINGULAR POINTS 166 4.1.3 FROBENIUS SERIES 167 4.2
BESSEL FUNCTIONS 171 4.2.1 BESSEL FUNCTIONS J N (X) OF INTEGER ORDER 172
4.2.2 ZEROS OF THE BESSEL FUNCTIONS 174 4.2.3 GAMMA FUNCTION 175 4.2.4
BESSEL FUNCTION OF NONINTEGER ORDER 177 4.2.5 BESSEL FUNCTION OF
NEGATIVE ORDER 179 4.2.6 NEUMANN FUNCTIONS AND HANKEL FUNCTIONS 179 4.3
PROPERTIES OF BESSEL FUNCTION 182 4.3.1 RECURRENCE RELATIONS 182 4.3.2
GENERATING FUNCTION OF BESSEL FUNCTIONS 185 4.3.3 INTEGRAL
REPRESENTATION 186 4.4 BESSEL FUNCTIONS AS EIGENFUNCTIONS OF
STURM-LIOUVILLE PROBLEMS 187 4.4.1 BOUNDARY CONDITIONS OF BESSEL'S
EQUATION 187 4.4.2 ORTHOGONALITY OF BESSEL FUNCTIONS 188 4.4.3
NORMALIZATION OF BESSEL FUNCTIONS 189 4.5 OTHER KINDS OF BESSEL
FUNCTIONS 191 4.5.1 MODIFIED BESSEL FUNCTIONS 191 4.5.2 SPHERICAL BESSEL
FUNCTIONS 192 4.6 LEGENDRE FUNCTIONS 196 4.6.1 SERIES SOLUTION OF
LEGENDRE EQUATION 196 4.6.2 LEGENDRE POLYNOMIALS 200 4.6.3 LEGENDRE
FUNCTIONS OF THE SECOND KIND 202 4.7 PROPERTIES OF LEGENDRE POLYNOMIALS
204 4.7.1 RODRIGUES' FORMULA 204 4.7.2 GENERATING FUNCTION OF LEGENDRE
POLYNOMIALS 206 4.7.3 RECURRENCE RELATIONS 208 4.7.4 ORTHOGONALITY AND
NORMALIZATION OF LEGENDRE POLYNOMIALS 211 4.8 ASSOCIATED LEGENDRE
FUNCTIONS AND SPHERICAL HARMONICS 212 4.8.1 ASSOCIATED LEGENDRE
POLYNOMIALS 212 4.8.2 ORTHOGONALITY AND NORMALIZATION OF ASSOCIATED
LEGENDRE FUNCTIONS 214 4.8.3 SPHERICAL HARMONICS 217 4.9 RESOURCES ON
SPECIAL FUNCTIONS 218 EXERCISES 219 X CONTENTS PART III PARTIAL
DIFFERENTIAL EQUATIONS PARTIAL DIFFERENTIAL EQUATIONS IN CARTESIAN
COORDINATES . 229 5.1 ONE-DIMENSIONAL WAVE EQUATIONS 230 5.1.1 THE
GOVERNING EQUATION OF A VIBRATING STRING 230 5.1.2 SEPARATION OF
VARIABLES 232 5.1.3 STANDING WAVE 238 5.1.4 TRAVELING WAVE 242 5.1.5
NONHOMOGENEOUS WAVE EQUATIONS 248 5.1.6 D'ALEMBERT'S SOLUTION OF WAVE
EQUATIONS 252 5.2 TWO-DIMENSIONAL WAVE EQUATIONS 261 5.2.1 THE GOVERNING
EQUATION OF A VIBRATING MEMBRANE . 261 5.2.2 VIBRATION OF A
RECTANGULAR MEMBRANE 262 5.3 THREE-DIMENSIONAL WAVE EQUATIONS 267 5.3.1
PLANE WAVE 268 5.3.2 PARTICLE WAVE IN A RECTANGULAR BOX 270 5.4 EQUATION
OF HEAT CONDUCTION 272 5.5 ONE-DIMENSIONAL DIFFUSION EQUATIONS 274 5.5.1
TEMPERATURE DISTRIBUTIONS WITH SPECIFIED VALUES AT THE BOUNDARIES 275
5.5.2 PROBLEMS INVOLVING INSULATED BOUNDARIES 278 5.5.3 HEAT EXCHANGE AT
THE BOUNDARY 280 5.6 TWO-DIMENSIONAL DIFFUSION EQUATIONS: HEAT TRANSFER
IN A RECTANGULAR PLATE 284 5.7 LAPLACE'S EQUATIONS 286 5.7.1
TWO-DIMENSIONAL LAPLACE'S EQUATION: STEADY-STATE TEMPERATURE IN A
RECTANGULAR PLATE 287 5.7.2 THREE-DIMENSIONAL LAPLACE'S EQUATION:
STEADY-STATE TEMPERATURE IN A RECTANGULAR PARALLELEPIPED 289 5.8
HELMHOLTZ'S EQUATIONS 291 EXERCISES 292 PARTIAL DIFFERENTIAL EQUATIONS
WITH CURVED BOUNDARIES . 301 6.1 THE LAPLACIAN 302 6.2
TWO-DIMENSIONAL LAPLACE'S EQUATIONS 304 6.2.1 LAPLACE'S EQUATION IN
POLAR COORDINATES 304 6.2.2 POISSON'S INTEGRAL FORMULA 312 6.3
TWO-DIMENSIONAL HELMHOLTZ'S EQUATIONS IN POLAR COORDINATES. 315 6.3.1
VIBRATION OF A DRUMHEAD: TWO DIMENSIONAL WAVE EQUATION IN POLAR
COORDINATES 316 6.3.2 HEAT CONDUCTION IN A DISK: TWO DIMENSIONAL
DIFFUSION EQUATION IN POLAR COORDINATES 322 6.3.3 LAPLACE'S EQUATIONS IN
CYLINDRICAL COORDINATES 326 6.3.4 HELMHOLTZ'S EQUATIONS IN CYLINDRICAL
COORDINATES 331 CONTENTS XI 6.4 THREE-DIMENSIONAL LAPLACIAN IN SPHERICAL
COORDINATES 334 6.4.1 LAPLACE'S EQUATIONS IN SPHERICAL COORDINATES 334
6.4.2 HELMHOLTZ'S EQUATIONS IN SPHERICAL COORDINATES 345 6.4.3 WAVE
EQUATIONS IN SPHERICAL COORDINATES 346 6.5 POISSON'S EQUATIONS 349 6.5.1
POISSON'S EQUATION AND GREEN'S FUNCTION 351 6.5.2 GREEN'S FUNCTION FOR
BOUNDARY VALUE PROBLEMS 355 EXERCISES 359 PART IV VARIATIONAL METHODS 7
CALCULUS OF VARIATION 367 7.1 THE EULER-LAGRANGE EQUATION 368 7.1.1
STATIONARY VALUE OF A FUNCTIONAL 368 7.1.2 FUNDAMENTAL THEOREM OF
VARIATIONAL CALCULUS 370 7.1.3 VARIATIONAL NOTATION 372 7.1.4 SPECIAL
CASES 373 7.2 CONSTRAINED VARIATION 377 7.3 SOLUTIONS TO SOME FAMOUS
PROBLEMS 380 7.3.1 THE BRACHISTOCHRONE PROBLEM 380 7.3.2 ISOPERIMETRIC
PROBLEMS 384 7.3.3 THE CATENARY 386 7.3.4 MINIMUM SURFACE OF REVOLUTION
391 7.3.5 FERMAT'S PRINCIPLE 394 7.4 SOME EXTENSIONS 397 7.4.1
FUNCTIONALS WITH HIGHER DERIVATIVES 397 7.4.2 SEVERAL DEPENDENT
VARIABLES 399 7.4.3 SEVERAL INDEPENDENT VARIABLES 401 7.5
STURM-LIOUVILLE PROBLEMS AND VARIATIONAL PRINCIPLES 403 7.5.1
VARIATIONAL FORMULATION OF STURM-LIOUVILLE PROBLEMS . . 403 7.5.2
VARIATIONAL CALCULATIONS OF EIGENVALUES AND EIGENFUNCTIONS 405 7.6
RAYLEIGH-RITZ METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 410 7.6.1
LAPLACE'S EQUATION 411 7.6.2 POISSON'S EQUATION 415 7.6.3 HELMHOLTZ'S
EQUATION 417 7.7 HAMILTON'S PRINCIPLE 420 EXERCISES 425 REFERENCES 431
INDEX 433 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Tang, Kwong-Tin |
| author_facet | Tang, Kwong-Tin |
| author_role | aut |
| author_sort | Tang, Kwong-Tin |
| author_variant | k t t ktt |
| building | Verbundindex |
| bvnumber | BV022425660 |
| classification_rvk | SK 400 SK 950 |
| ctrlnum | (OCoLC)180089416 (DE-599)BVBBV022425660 |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| genre | (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV022425660 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:27:23Z |
| indexdate | 2024-07-09T20:57:19Z |
| institution | BVB |
| isbn | 9783540446958 3540446958 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015633917 |
| oclc_num | 180089416 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-634 DE-92 |
| owner_facet | DE-29T DE-703 DE-634 DE-92 |
| physical | XI, 438 S. graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Springer |
| record_format | marc |
| spelling | Tang, Kwong-Tin Verfasser aut Mathematical methods for engineers and scientists 3 Fourier analysis, partial differential equations and variational methods K. T. Tang Berlin [u.a.] Springer 2007 XI, 438 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Variationsprinzip (DE-588)4062354-3 gnd rswk-swf Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Harmonische Analyse (DE-588)4023453-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Harmonische Analyse (DE-588)4023453-8 s Partielle Differentialgleichung (DE-588)4044779-0 s Variationsprinzip (DE-588)4062354-3 s DE-604 (DE-604)BV021879823 3 http://www.agi-imc.de/intelligentSEARCH.nsf/alldocs/28BD0A0F2111D113C12571C400673BF7/$File/000000016507067.PDF?OpenElement Inhaltsverzeichnis HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tang, Kwong-Tin Mathematical methods for engineers and scientists Variationsprinzip (DE-588)4062354-3 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| subject_GND | (DE-588)4062354-3 (DE-588)4044779-0 (DE-588)4023453-8 (DE-588)4123623-3 |
| title | Mathematical methods for engineers and scientists |
| title_auth | Mathematical methods for engineers and scientists |
| title_exact_search | Mathematical methods for engineers and scientists |
| title_exact_search_txtP | Mathematical methods for engineers and scientists |
| title_full | Mathematical methods for engineers and scientists 3 Fourier analysis, partial differential equations and variational methods K. T. Tang |
| title_fullStr | Mathematical methods for engineers and scientists 3 Fourier analysis, partial differential equations and variational methods K. T. Tang |
| title_full_unstemmed | Mathematical methods for engineers and scientists 3 Fourier analysis, partial differential equations and variational methods K. T. Tang |
| title_short | Mathematical methods for engineers and scientists |
| title_sort | mathematical methods for engineers and scientists fourier analysis partial differential equations and variational methods |
| topic | Variationsprinzip (DE-588)4062354-3 gnd Partielle Differentialgleichung (DE-588)4044779-0 gnd Harmonische Analyse (DE-588)4023453-8 gnd |
| topic_facet | Variationsprinzip Partielle Differentialgleichung Harmonische Analyse Lehrbuch |
| url | http://www.agi-imc.de/intelligentSEARCH.nsf/alldocs/28BD0A0F2111D113C12571C400673BF7/$File/000000016507067.PDF?OpenElement http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021879823 |
| work_keys_str_mv | AT tangkwongtin mathematicalmethodsforengineersandscientists3 |
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