Mathematical methods: for students of physics and related fields
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2000
|
| Schriftenreihe: | Undergraduate texts in contemporary physics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 659 S. Ill., graph. Darst. |
| ISBN: | 0387989587 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804128112897687552 |
|---|---|
| adam_text | ATHEMATICAL
METHODS
FOR STUDENTS OF PHYSICS
AND RELATED FIELDS
SADRI HASSANI
WITH 179 ILLUSTRATIONS
SPRINGER
CONTENTS
PREFACE VII
NOTE TO THE READER XI
1 COORDINATE SYSTEMS AND VECTORS 1
1.1 VECTORS IN A PLANE AND IN SPACE 1
1.2 COORDINATE SYSTEMS 10
1.3 VECTORS IN DIFFERENT COORDINATE SYSTEMS 15
1.4 RELATIONS AMONG UNIT VECTORS 32
1.5 PROBLEMS 38
2 DIFFERENTIATION 45
2.1 THE DERIVATIVE 46
2.2 PARTIAL DERIVATIVES 49
2.3 ELEMENTS OF LENGTH, AREA, AND VOLUME 62
2.4 PROBLEMS 71
3 INTEGRATION 77
3.1 / MEANS /UM 77
3.2 PROPERTIES OF INTEGRAL 81
3.3 APPLICATIONS: GENERAL GUIDELINES 92
3.4 APPLICATIONS: SINGLE INTEGRALS 99
3.5 APPLICATIONS: DOUBLE INTEGRALS 115
3.6 APPLICATIONS: TRIPLE INTEGRALS 123
3.7 PROBLEMS 130
XIV CONTENTS
4 VECTORS 139
4.1 VECTORS IN A PLANE REVISITED 140
4.2 VECTORS IN SPACE 160
4.3 DETERMINANT 171
4.4 THEJACOBIAN 176
4.5 FINITE-DIMENSIONAL VECTOR SPACES 180
4.6 ORTHOGONAL POLYNOMIALS 193
4.7 SYSTEMS OF LINEAR EQUATIONS 197
4.8 PROBLEMS 201
5 INFINITE SERIES 205
5.1 INFINITE SEQUENCES 205
5.2 SUMMATIONS 208
5.3 INFINITE SERIES 213
5.4 SEQUENCES AND SERIES OF FUNCTIONS 221
5.5 POWER SERIES . 227
5.6 FOURIER SERIES 243
5.7 MULTIVARIABLE TAYLOR SERIES 249
5.8 APPLICATION TO DIFFERENTIAL EQUATIONS 252
5.9 PROBLEMS 256
6 INTEGRALS AND SERIES AS FUNCTIONS 264
6.1 INTEGRALS AS FUNCTIONS 264
6.2 POWER SERIES AS FUNCTIONS 275
6.3 PROBLEMS 285
7 DIRAC DELTA FUNCTION 289
7.1 ONE-VARIABLE CASE 289
7.2 TWO-VARIABLE CASE 302
7.3 THREE-VARIABLE CASE 308
7.4 PROBLEMS 315
8 VECTOR ANALYSIS 320
8.1 SOLID ANGLE . . . 321
8.2 TIME DERIVATIVE OF VECTORS 328
8.3 THE GRADIENT 334
8.4 FLUX OF A VECTOR FIELD .339
8.5 FLUX DENSITY = DIVERGENCE 344
8.6 THE LINE INTEGRAL 357
8.7 CURL OF A VECTOR FIELD AND STOKES THEOREM 362
8.8 CONSERVATIVE VECTOR FIELDS 370
8.9 DOUBLE DEL OPERATIONS 376
8.10 MAXWELL S EQUATIONS 381
8.11 CURVILINEAR VECTOR ANALYSIS 386
CONTENTS XV
8.12 VECTORS AND INDICES 399
8.13 PROBLEMS 405
9 COMPLEX ARITHMETIC 413
9.1 CARTESIAN FORM OF COMPLEX NUMBERS 413
9.2 POLAR FORM OF COMPLEX NUMBERS 418
9.3 FOURIER SERIES REVISITED 425
9.4 PROBLEMS 428
10 COMPLEX ANALYSIS 432
10.1 COMPLEX FUNCTIONS 432
10.2 COMPLEX SERIES 448
10.3 TAYLOR AND LAURENT SERIES 452
10.4 CALCULUS OF RESIDUES 456
10.5 PROBLEMS 467
11 DIFFERENTIAL EQUATIONS 474
11.1 FROM PDES TO ODES 475
11.2 FIRST-ORDER DIFFERENTIAL EQUATIONS . . 483
11.3 SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS 494
11.4 SOLDES WITH CONSTANT COEFFICIENTS 502
11.5 PROBLEMS 514
12 LAPLACE S EQUATION 519
12.1 UNIQUENESS OF SOLUTIONS 520
12.2 CARTESIAN COORDINATES 522
12.3 SPHERICAL COORDINATES 532
12.4 CYLINDRICAL COORDINATES 562
12.5 PROBLEMS 580
13 OTHER PDES OF MATHEMATICAL PHYSICS 587
13.1 THE HEAT EQUATION 587
13.2 THE SCHRODINGER EQUATION 592
13.3 THE WAVE EQUATION 607
13.4 PROBLEMS 615
14 NONLINEAR DYNAMICS AND CHAOS 618
14.1 SYSTEMS OBEYING ITERATED MAPS 619
14.2 SYSTEMS OBEYING DES 628
14.3 UNIVERSALITY OF CHAOS 639
14.4 PROBLEMS 644
BIBLIOGRAPHY 647
INDEX 649
|
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| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)42690099 (DE-599)BVBBV013338614 |
| dewey-full | 530.15 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.15 |
| dewey-search | 530.15 |
| dewey-sort | 3530.15 |
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| discipline | Physik Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:44:04Z |
| institution | BVB |
| isbn | 0387989587 |
| language | English |
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| physical | XV, 659 S. Ill., graph. Darst. |
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| series2 | Undergraduate texts in contemporary physics |
| spelling | Hassani, Sadri Verfasser (DE-588)114976838X aut Mathematical methods for students of physics and related fields Sadri Hassani New York [u.a.] Springer 2000 XV, 659 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Undergraduate texts in contemporary physics Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009096081&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hassani, Sadri Mathematical methods for students of physics and related fields Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 |
| title | Mathematical methods for students of physics and related fields |
| title_auth | Mathematical methods for students of physics and related fields |
| title_exact_search | Mathematical methods for students of physics and related fields |
| title_full | Mathematical methods for students of physics and related fields Sadri Hassani |
| title_fullStr | Mathematical methods for students of physics and related fields Sadri Hassani |
| title_full_unstemmed | Mathematical methods for students of physics and related fields Sadri Hassani |
| title_short | Mathematical methods |
| title_sort | mathematical methods for students of physics and related fields |
| title_sub | for students of physics and related fields |
| topic | Physique mathématique Mathematische Physik Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Physique mathématique Mathematische Physik Mathematical physics |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009096081&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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