Integral transforms and their applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1985
|
| Edition: | 2. ed. |
| Series: | Applied mathematical sciences
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 411 S. graph. Darst. |
| ISBN: | 0387960805 3540960805 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV006551862 | ||
| 003 | DE-604 | ||
| 005 | 20150129 | ||
| 007 | t | ||
| 008 | 930210s1985 xxud||| |||| 00||| eng d | ||
| 016 | 7 | |a 860470350 |2 DE-101 | |
| 020 | |a 0387960805 |9 0-387-96080-5 | ||
| 020 | |a 3540960805 |9 3-540-96080-5 | ||
| 035 | |a (OCoLC)11030315 | ||
| 035 | |a (DE-599)BVBBV006551862 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c XD-US | ||
| 049 | |a DE-739 |a DE-20 |a DE-521 |a DE-634 |a DE-11 |a DE-188 |a DE-83 | ||
| 050 | 0 | |a QA1 QA432.A647 vol. 25, 1985 | |
| 082 | 0 | |a 510 s 515.7/23 19 | |
| 082 | 0 | |a 515.7/23 |2 19 | |
| 082 | 0 | |a 510 |2 19 | |
| 084 | |a SK 450 |0 (DE-625)143240: |2 rvk | ||
| 084 | |a 42A38 |2 msc | ||
| 084 | |a 35A22 |2 msc | ||
| 084 | |a 27 |2 sdnb | ||
| 084 | |a 44-01 |2 msc | ||
| 100 | 1 | |a Davies, Brian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Integral transforms and their applications |c B. Davies |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1985 | |
| 300 | |a XV, 411 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied mathematical sciences |v 25 | |
| 650 | 7 | |a Analyse fonctionnelle |2 ram | |
| 650 | 7 | |a Intégrales |2 ram | |
| 650 | 4 | |a Transformations intégrales | |
| 650 | 7 | |a fonction spéciale |2 inriac | |
| 650 | 7 | |a transformation intégrale |2 inriac | |
| 650 | 7 | |a transformation multiple |2 inriac | |
| 650 | 7 | |a transformation spéciale |2 inriac | |
| 650 | 7 | |a transformée Fourier |2 inriac | |
| 650 | 7 | |a transformée Hankel |2 inriac | |
| 650 | 4 | |a Integral transforms | |
| 650 | 0 | 7 | |a Integraltransformation |0 (DE-588)4027235-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Integraltransformation |0 (DE-588)4027235-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Applied mathematical sciences |v 25 |w (DE-604)BV000005274 |9 25 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177190&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-004177190 | |
Record in the Search Index
| _version_ | 1808498244024532992 |
|---|---|
| adam_text |
TABLE OF CONTENTS
PAGE
PART I: THE LAPLACE TRANSFORM 1
1. DEFINITION AND ELEMENTARY PROPERTIES 1
1.1. THE LAPLACE TRANSFORM 1
1.2. IMPORTANT PROPERTIES 3
1.3. ASYMPTOTIC PROPERTIES: WATSON'S LEMMA 8
2. THE INVERSION THEOREM 15
2.1. THE RIEMANN-LEBESGUE LEMMA 15
2.2. DIRICHLET INTEGRALS 17
2.3. THE INVERSION INTEGRAL 19
2.4. INVERSION OF RATIONAL FUNCTIONS 20
2.5. TAYLOR SERIES EXPANSION 23
3. ORDINARY DIFFERENTIAL EQUATIONS 26
3.1. FIRST AND SECOND ORDER DIFFERENTIAL
EQUATIONS 26
3.2. HIGHER ORDER DIFFERENTIAL EQUATIONS 29
3.3. SIMULTANEOUS DIFFERENTIAL EQUATIONS 33
3.4. EQUATIONS WITH POLYNOMIAL COEFFICIENTS 42
4. PARTIAL DIFFERENTIAL EQUATIONS 47
4.1. THE DIFFUSION EQUATION 47
4.2. WAVE PROPAGATION 50
5. INTEGRAL EQUATIONS 59
5.1. CONVOLUTION EQUATIONS OF VOLTERRA TYPE 59
5.2. CONVOLUTION EQUATIONS OVER AN INFINITE RANGE 64
5.3. THE PERCUS-YEVICK EQUATION FOR HARD RODS 67
6. THE INVERSION INTEGRAL 76
6.1. INVERSION OF MEROMORPHIC FUNCTIONS 76
6.2. INVERSIONS INVOLVING A BRANCH POINT 79
6.3. WATSON'S LEMMA FOR LOOP INTEGRALS 82
XX
BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/860470350
6.4. ASYMPTOTIC FORMS FOR LARGE T
PAGE
84
6. 5. HEAVISIDE SERIES EXPANSION 86
PART II: THE FOURIER TRANSFORM
7. DEFINITIONS AND ELEMENTARY PROPERTIES 89
7.1. THE EXPONENTIAL, SINE AND COSINE TRANSFORMS 89
7.2. IMPORTANT PROPERTIES 95
7.3. SPECTRAL ANALYSIS 97
7.4. KRAMERS-KRONIG RELATIONS 101
8. APPLICATION TO PARTIAL DIFFERENTIAL EQUATIONS 110
8.1. POTENTIAL PROBLEMS 110
8.2. WATER WAVES: BASIC EQUATIONS 114
8.3. WATER WAVES GENERATED BY AN INITIAL
SURFACE DISPLACEMENT 117
8.4. WAVES DUE TO A PERIODIC DISTURBANCE:
RADIATION CONDITION 120
9. GENERALIZED FUNCTIONS 130
9.1. THE DELTA FUNCTION 130
9.2. TEST FUNCTIONS AND GENERALIZED FUNCTIONS 131
9.3. ELEMENTARY PROPERTIES 136
9.4. ANALYTIC FUNCTIONALS 143
9.5. FOURIER TRANSFORMS OF GENERALIZED FUNCTIONS 145
10. GREEN'S FUNCTIONS 155
10.1. ONE DIMENSIONAL GREEN'S FUNCTIONS 155
10.2. GREEN'S FUNCTIONS AS GENERALIZED FUNCTIONS 159
10.3. POISSON'S EQUATION IN TWO DIMENSIONS 162
10.4. HELMHOLTZ'S EQUATION IN TWO DIMENSIONS 168
11. FOURIER TRANSFORMS IN TWO OR MORE VARIABLES 178
11.1. BASIC NOTATION AND RESULTS 178
11.2. DIFFRACTION OF SCALAR WAVES 182
11.3. RETARDED POTENTIALS OF ELECTROMAGNETISM 185
XII
PAGE
PART III: OTHER IMPORTANT TRANSFORMS
12. MELLIN TRANSFORMS 195
12.1. DEFINITIONS 195
12.2. SIMPLE EXAMPLES 196
12.3. ELEMENTARY PROPERTIES 201
12.4. POTENTIAL PROBLEMS IN WEDGE SHAPED REGIONS 203
12.5. TRANSFORMS INVOLVING POLAR COORDINATES 204
12.6. HERMITE FUNCTIONS 207
13. MELLIN TRANSFORMS IN SUMMATION 214
13.1. MELLIN SUMMATION FORMULA 214
13.2. A PROBLEM OF RAMANUJAN 216
13.3. ASYMPTOTIC BEHAVIOR OF POWER SERIES 219
14. INTEGRALS INVOLVING A PARAMETER 225
14.1. PRELIMINARY EXAMPLE 225
14.2. A GENERAL CLASS OF PROBLEMS 225
14.3. ASCENDING EXPANSIONS FOR FOURIER INTEGRALS 227
14.4. MULTIDIMENSIONAL INTEGRALS 230
15. HANKEL TRANSFORMS 237
15.1. THE HANKEL TRANSFORM PAIR 237
15.2. ELEMENTARY PROPERTIES 240
15.3. SOME EXAMPLES 242
15.4. BOUNDARY VALUE PROBLEMS 243
15.5. WEBER'S INTEGRAL 245
16. DUAL INTEGRAL EQUATIONS 254
16.1. THE ELECTRIFIED DISC 254
16.2. DUAL INTEGRAL EQUATIONS OF TITCHMARSH
TYPE 255
ERDELYI-KOBER OPERATORS
XIII
16.3.
258
PAGE
17. INTEGRAL TRANSFORMS GENERATED BY GREEN'S
FUNCTIONS 267
17.1. THE BASIC FORMULA 267
17.2. FINITE INTERVALS 269
17.3. SOME SINGULAR PROBLEMS 272
17.4. KONTOROVICH-LEBEDEV TRANSFORM 276
17.5. BOUNDARY VALUE PROBLEM IN A WEDGE 278
17.6. DIFFRACTION OF A PULSE BY A TWO-DIMEN
SIONAL HALF-PLANE 280
PART IV: SPECIAL TECHNIQUES
18. THE WIENER-HOPF TECHNIQUE 288
18.1. THE SOMMERFELD DIFFRACTION PROBLEM 289
18.2. THE WIENER-HOPF PROCEDURE: HALF-PLANE
PROBLEMS 299
18.3. INTEGRAL AND INTEGRO-DIFFERENTIAL
EQUATIONS 301
19. METHODS BASED ON CAUCHY INTEGRALS 313
19.1. WIENER-HOPF DECOMPOSITION BY CONTOUR
INTEGRATION 313
19.2. CAUCHY INTEGRALS 315
19.3. THE DISCONTINUITY THEOREM 320
19.4. THE RIEMANN HILBERT PROBLEM 321
19.5. SIMPLE APPLICATIONS 323
19.6. PROBLEMS IN LINEAR TRANSPORT THEORY 324
19.7. THE ALBEDO PROBLEM 329
19.8. A DIFFRACTION PROBLEM 332
20. LAPLACE'S METHOD FOR ORDINARY DIFFERENTIAL
EQUATIONS 342
20.1. INTEGRAL TRANSFORM SOLUTIONS 342
20.2. HERMITE POLYNOMIALS 344
20.3. HERMITE FUNCTIONS 347
XIV
PAGE
20.4. BESSEL FUNCTIONS: INTEGRAL REPRESENTATIONS 351
20.5. BESSEL FUNCTIONS OF THE FIRST KIND 353
20.6. FUNCTIONS OF THE SECOND AND THIRD KINDS 356
20.7. POISSON AND RELATED REPRESENTATIONS 362
20.8. MODIFIED BESSEL FUNCTIONS 364
21. NUMERICAL INVERSION OF LAPLACE TRANSFORMS 374
21.1. GAUSSIAN QUADRATURE FORMULAE FOR THE LAPLACE
INVERSION INTEGRAL 374
21.2. USE OF LAGUERRE POLYNOMIALS 379
21.3. APPROXIMATION OF F(P) BY CHEBYSHEV
POLYNOMIALS FOR REAL P 382
21.4. REPRESENTATION BY FOURIER SERIES 385
21.5. PADD APPROXIMATION 386
21.6. RATIONAL APPROXIMATION OF F(P) 389
APPENDICES
A: THE FACTORIAL FUNCTION 396
B: RIEMANN'S ZETA FUNCTION 399
C: THE EXPONENTIAL INTEGRAL 402
BIBLIOGRAPHY 403
INDEX 406
XV |
| any_adam_object | 1 |
| author | Davies, Brian |
| author_facet | Davies, Brian |
| author_role | aut |
| author_sort | Davies, Brian |
| author_variant | b d bd |
| building | Verbundindex |
| bvnumber | BV006551862 |
| callnumber-first | Q - Science |
| callnumber-label | QA1 QA432 |
| callnumber-raw | QA1 QA432.A647 vol. 25, 1985 |
| callnumber-search | QA1 QA432.A647 vol. 25, 1985 |
| callnumber-sort | QA 11 _Q A432 A647 VOL 225 41985 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 450 |
| ctrlnum | (OCoLC)11030315 (DE-599)BVBBV006551862 |
| dewey-full | 510S515.7/2319 515.7/23 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 s 515.7/23 19 515.7/23 510 |
| dewey-search | 510 s 515.7/23 19 515.7/23 510 |
| dewey-sort | 3510 S 3515.7 223 219 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 cb4500</leader><controlfield tag="001">BV006551862</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20150129</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930210s1985 xxud||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">860470350</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387960805</subfield><subfield code="9">0-387-96080-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540960805</subfield><subfield code="9">3-540-96080-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)11030315</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV006551862</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">XD-US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-521</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA1 QA432.A647 vol. 25, 1985</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510 s 515.7/23 19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.7/23</subfield><subfield code="2">19</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510</subfield><subfield code="2">19</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 450</subfield><subfield code="0">(DE-625)143240:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">42A38</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">35A22</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">27</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">44-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Davies, Brian</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Integral transforms and their applications</subfield><subfield code="c">B. Davies</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">2. ed.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">1985</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 411 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">25</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Analyse fonctionnelle</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Intégrales</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Transformations intégrales</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">fonction spéciale</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">transformation intégrale</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">transformation multiple</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">transformation spéciale</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">transformée Fourier</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">transformée Hankel</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Integral transforms</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Integraltransformation</subfield><subfield code="0">(DE-588)4027235-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Integraltransformation</subfield><subfield code="0">(DE-588)4027235-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Applied mathematical sciences</subfield><subfield code="v">25</subfield><subfield code="w">(DE-604)BV000005274</subfield><subfield code="9">25</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177190&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-004177190</subfield></datafield></record></collection> |
| id | DE-604.BV006551862 |
| illustrated | Illustrated |
| indexdate | 2024-08-27T00:25:25Z |
| institution | BVB |
| isbn | 0387960805 3540960805 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004177190 |
| oclc_num | 11030315 |
| open_access_boolean | |
| owner | DE-739 DE-20 DE-521 DE-634 DE-11 DE-188 DE-83 |
| owner_facet | DE-739 DE-20 DE-521 DE-634 DE-11 DE-188 DE-83 |
| physical | XV, 411 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Springer |
| record_format | marc |
| series | Applied mathematical sciences |
| series2 | Applied mathematical sciences |
| spelling | Davies, Brian Verfasser aut Integral transforms and their applications B. Davies 2. ed. New York [u.a.] Springer 1985 XV, 411 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Applied mathematical sciences 25 Analyse fonctionnelle ram Intégrales ram Transformations intégrales fonction spéciale inriac transformation intégrale inriac transformation multiple inriac transformation spéciale inriac transformée Fourier inriac transformée Hankel inriac Integral transforms Integraltransformation (DE-588)4027235-7 gnd rswk-swf Integraltransformation (DE-588)4027235-7 s DE-604 Applied mathematical sciences 25 (DE-604)BV000005274 25 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177190&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davies, Brian Integral transforms and their applications Applied mathematical sciences Analyse fonctionnelle ram Intégrales ram Transformations intégrales fonction spéciale inriac transformation intégrale inriac transformation multiple inriac transformation spéciale inriac transformée Fourier inriac transformée Hankel inriac Integral transforms Integraltransformation (DE-588)4027235-7 gnd |
| subject_GND | (DE-588)4027235-7 |
| title | Integral transforms and their applications |
| title_auth | Integral transforms and their applications |
| title_exact_search | Integral transforms and their applications |
| title_full | Integral transforms and their applications B. Davies |
| title_fullStr | Integral transforms and their applications B. Davies |
| title_full_unstemmed | Integral transforms and their applications B. Davies |
| title_short | Integral transforms and their applications |
| title_sort | integral transforms and their applications |
| topic | Analyse fonctionnelle ram Intégrales ram Transformations intégrales fonction spéciale inriac transformation intégrale inriac transformation multiple inriac transformation spéciale inriac transformée Fourier inriac transformée Hankel inriac Integral transforms Integraltransformation (DE-588)4027235-7 gnd |
| topic_facet | Analyse fonctionnelle Intégrales Transformations intégrales fonction spéciale transformation intégrale transformation multiple transformation spéciale transformée Fourier transformée Hankel Integral transforms Integraltransformation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004177190&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005274 |
| work_keys_str_mv | AT daviesbrian integraltransformsandtheirapplications |