Advanced engineering mathematics with modeling applications:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2009
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XII, 524 S. graph. Darst. |
| ISBN: | 9780849395338 |
Staff View
MARC
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Record in the Search Index
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| adam_text | ADVANCED ENGINEERING MATHEMATICS WITH MODELIN! APPLICATIONS S. GRAHAM
KELLY O ~ ~~F~~~~~ P BOCA RATON LONDON NEW YORK CRC PRESS IS AN IMPRINT
OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE XI
AUTHOR XIII CHAPTER 1 FOUNDATIONS OF MATHEMATICAL MODELING 1 1.1
ENGINEERING ANALYSIS 1 1.2 CONSERVATION LAWS AND MATHEMATICAL MODELING 6
1.3 PROBLEM FORMULATION 10 1.4 NONDIMENSIONALIZATION 27 1.5 SCALING 45
PROBLEMS 56 CHAPTER 2 LINEAR ALGEBRA 65 2.1 INTRODUCTION 65 2.2
THREE-DIMENSIONAL SPACE 66 2.3 VECTOR SPACES 73 2.4 LINEAR INDEPENDENCE
77 2.5 BASIS AND DIMENSION 80 2.6 INNER PRODUCTS 86 2.7 NORMS 93 2.8
GRAM-SCHMIDT ORTHONORMALIZATION 98 2.9 ORTHOGONAL EXPANSIONS 105 2.10
LINEAR OPERATORS 109 2.11 ADJOINT OPERATORS 121 2.12 POSITIVE DEFINITE
OPERATORS 129 2.13 ENERGY INNER PRODUCTS 132 PROBLEMS 139 CHAPTER 3
ORDINARY DIFFERENTIAL EQUATIONS 143 3.1 LINEAR DIFFERENTIAL EQUATIONS
143 3.2 GENERAL THEORY FOR SECOND-ORDER DIFFERENTIAL EQUATIONS 146 3.3
DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS 149 3.4 DIFFERENTIAL
EQUATIONS WITH VARIABLE COEFFICIENTS 167 3.5 SINGULAR POINTS OF
SECOND-ORDER EQUATIONS 173 VIII CONTENTS 3.6 BESSEL FUNCTIONS 180 3.7
DIFFERENTIAL EQUATIONS WHOSE SOLUTIONS ARE EXPRESSIBLE IN TERMS OF
BESSEL FUNCTIONS 193 3.8 LEGENDRE FUNCTIONS 198 PROBLEMS 201 CHAPTER 4
VARIATIONAL METHODS 209 4.1 INTRODUCTION 209 4.2 THE GENERAL VARIATIONAL
PROBLEM 210 4.3 VARIATIONAL SOLUTIONS OF OPERATOR EQUATIONS 224 4.3.1
METHOD OF LEAST SQUARES 224 4.3.2 RAYLEIGH-RITZ METHOD 226 4.4
FINITE-ELEMENT METHOD 242 4.5 GALERKIN SMETHOD 270 PROBLEMS 273
CHAPTER 5 EIGENVALUE PROBLEMS 277 5.1 EIGENVALUE AND EIGENVECTOR
PROBLEMS 277 5.2 EIGENVALUES OF ADJOINT OPERATORS 278 5.3 EIGENVALUES OF
POSITIVE DEFINITE OPERATORS 279 5.4 EIGENVALUE PROBLEMS FOR OPERATORS IN
FINITE-DIMENSIONAL VECTOR SPACES 280 5.5 SECOND-ORDER DIFFERENTIAL
OPERATORS 287 5.6 EIGENVECTOR EXPANSIONS 303 5.6.1 COMPLETENESS THEOREM
303 5.6.2 TRIGONOMETRIE FOURIER SERIES 309 5.6.3 COMPLETENESS OF
EIGENVECTORS FOR SELF-ADJOINT AND NON-SELF-ADJOINT OPERATORS 312 5.6.4
SOLUTION OF NONHOMOGENEOUS EQUATIONS USING EIGENVECTOR EXPANSIONS 314
5.7 FOURTH-ORDER DIFFERENTIAL OPERATORS 318 5.8 DIFFERENTIAL OPERATORS
WITH EIGENVALUES IN BOUNDARY CONDITIONS 329 5.9 EIGENVALUE PROBLEMS
INVOLVING BESSEL FUNCTIONS 336 5.10 EIGENVALUE PROBLEMS IN OTHER
INFINITE-DIMENSIONAL VECTOR SPACES 349 5.11 SOLVABILITY CONDITIONS 354
5.12 ASYMPTOTIC APPROXIMATIONS TO SOLUTIONS OF EIGENVALUE PROBLEMS 358
5.13 RAYLEIGH S QUOTIENT 370 5.14 RAYLEIGH-RITZ METHOD 376 5.15
GREEN SFUNCTIONS 394 PROBLEMS 408 CONTENTS IX CHAPTER 6 PARTIAL
DIFFERENTIAL EQUATIONS 419 6.1 HOMOGENEOUS PARTIAL DIFFERENTIAL
EQUATIONS 419 6.2 SECOND-ORDER STEADY-STATE PROBLEMS, LAPLACE S EQUATION
421 6.3 TIME-DEPENDENT PROBLEMS: INITIAL VALUE PROBLEMS 441 6.4
NONHOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS 455 6.5 PROBLEMS IN
CYLINDRICAL COORDINATES 471 6.6 PROBLEMS IN SPHERICAL COORDINATES 491
PROBLEMS 508 INDEX 517
|
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| dewey-full | 620.001/51 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.001/51 |
| dewey-search | 620.001/51 |
| dewey-sort | 3620.001 251 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035286091 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:30:27Z |
| institution | BVB |
| isbn | 9780849395338 |
| language | English |
| lccn | 2008046267 |
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| physical | XII, 524 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Press |
| record_format | marc |
| spelling | Kelly, S. Graham Verfasser aut Advanced engineering mathematics with modeling applications S. Graham Kelly Boca Raton [u.a.] CRC Press 2009 XII, 524 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Ingenieurwissenschaften Mathematisches Modell Engineering mathematics Engineering Mathematical models Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Mathematik (DE-588)4037944-9 s DE-604 Mathematisches Modell (DE-588)4114528-8 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017091226&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kelly, S. Graham Advanced engineering mathematics with modeling applications Ingenieurwissenschaften Mathematisches Modell Engineering mathematics Engineering Mathematical models Mathematik (DE-588)4037944-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4114528-8 |
| title | Advanced engineering mathematics with modeling applications |
| title_auth | Advanced engineering mathematics with modeling applications |
| title_exact_search | Advanced engineering mathematics with modeling applications |
| title_full | Advanced engineering mathematics with modeling applications S. Graham Kelly |
| title_fullStr | Advanced engineering mathematics with modeling applications S. Graham Kelly |
| title_full_unstemmed | Advanced engineering mathematics with modeling applications S. Graham Kelly |
| title_short | Advanced engineering mathematics with modeling applications |
| title_sort | advanced engineering mathematics with modeling applications |
| topic | Ingenieurwissenschaften Mathematisches Modell Engineering mathematics Engineering Mathematical models Mathematik (DE-588)4037944-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Ingenieurwissenschaften Mathematisches Modell Engineering mathematics Engineering Mathematical models Mathematik |
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