Applied vector analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press
2001
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| Series: | Electrical engineering textbook series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 272 S. graph. Darst. |
| ISBN: | 0849310881 |
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MARC
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Record in the Search Index
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| adam_text | * * *: APPLIED VECTOR ANALYSIS MATIUR RAHMAN DEPARTMENT OF ENGINEERING
MATHEMATICS DALHOUSIE UNIVERSITY HALIFAX, NOVA SCOTIA, CANADA ISAAC
MULOLANI DEPARTMENT OF ENGINEERING MATHEMATICS DALHOUSIE UNIVERSITY
HALIFAX, NOVA SCOTIA, CANADA (G) CRC PRESS BOCA RATON LONDON NEW YORK
WASHINGTON, D.C. CONTENTS ACKNOWLEDGMENTS V PREFACE X 1 HISTORICAL
BACKGROUND 1 1.1 INTRODUCTION 1 1.2 HAMILTON S QUATERNIONS 2 1.3
GRASSMANN S CALCULUS OF EXTENSION 3 1.4 THE WORK OF MAXWELL 4 1.5 MODERN
VECTOR ANALYSIS 5 1.6 OTHER CONTRIBUTIONS 6 2 THE ALGEBRA OF VECTORS 9
2.1 ADDITION AND SUBTRACTION OF VECTORS 11 2.2 SCALAR AND VECTOR
PRODUCTS 12 2.3 SCALAR AND VECTOR PROJECTIONS 15 2.4 CARTESIAN FRAME OF
REFERENCE 17 2.4.1 DEFINITION OF A POSITION VECTOR R 17 2.5 VECTOR
ALGEBRA USING COORDINATES 18 2.6 MIXED PRODUCT IN COORDINATE FORM 22 2.7
VECTOR REPRESENTATION USING COORDINATES 31 2.8 LINES AND PLANES USING
VECTOR ALGEBRA 34 2.8.1 LINES 34 2.8.2 THE EQUATION OF A PLANE 37 2.9
PARTIAL DERIVATIVES 37 2.10 ITERATED PARTIAL DERIVATIVES 40 EXERCISES 43
3 VECTOR FUNCTIONS OF ONE VARIABLE 49 3.1 VECTOR DIFFERENTIATION 50 3.2
GEOMETRIE INTERPRETATION OF R 51 3.3 HIGHER-ORDER DERIVATIVES 53 3.4
CURVES, LENGTH AND ARE LENGTH 54 VII VLLL 3.5 MOTION ON A CURVE,
VELOCITY AND ACCELERATION 56 3.6 CURVATURE, COMPONENTS OF ACCELERATION
57 3.7 CURVATURE, TANGENTIAL AND NORMAL COMPONENTS OF ACCELERATION 61
EXERCISES 70 4 THE DEL OPERATOR 75 4.1 GRADIENT CHARACTERIZES MAXIMUM
INCREASE 80 4.2 TANGENT PLANES AND NORMAL LINES 83 4.3 TANGENT PLANE 87
4.4 NORMAL LINES 88 4.5 DIVERGENCE AND CURL OF A VECTOR FIELD 90 4.6
PHYSICAL INTERPRETATION OF DIVERGENCE 91 4.7 PHYSICAL INTERPRETATION OF
THE CURL 93 4.8 THE LAPLACIAN OPERATOR 96 4.9 VECTOR IDENTITIES 98
EXERCISES 102 5 LINE, SURFACE AND VOLUME INTEGRALS 107 5.1 INTRODUCTION
107 5.2 LINE INTEGRALS AND VECTOR FUNCTIONS 118 5.3 WORK 120 5.4 LINE
INTEGRALS INDEPENDENT OF PATH 123 5.5 CONSERVATIVE VECTOR FIELDS 130 5.6
SURFACE INTEGRALS 131 5.7 ORIENTATION OF A SURFACE 136 5.8 VOLUME
INTEGRATION 138 5.9 TRIPLE INTEGRALS IN CYLINDRICAL COORDINATES 144 5.10
TRIPLE INTEGRALS IN SPHERICAL COORDINATES 149 EXERCISES 156 6 INTEGRAL
THEOREMS 163 6.1 GREEN S THEOREM 163 6.2 REGION WITH HOLES 170 6.3
INTEGRALS OVER VECTOR FIELDS 176 6.4 STOKES THEOREM 181 6.5 GREEN S
THEOREM IN 3-D 182 6.6 THE DIVERGENCE THEOREM 193 EXERCISES 202 7
APPLICATIONS 207 7.1 INTRODUCTION 207 7.2 ACCELERATION VECTOR 207 7.3
CONTINUITY EQUATION OF FLUID FLOW 212 7.3.1 EULER S EQUATION OF MOTION
217 IX 7.4 CONTINUITY EQUATION AND HEAT CONDUCTION 220 7.5 POISSON S
EQUATION 221 7.6 VECTORS IN ELECTROMAGNETIC THEORY 224 7.7 THE
CONTINUITY EQUATION REVISITED 224 7.8 MAXWELL S EQUATIONS FOR
ELECTROMAGNETIC FIELDS 226 7.9 WAVES SOLUTIONS OF MAXWELL S EQUATIONS
234 7.10 OCEAN WAVE INTERACTIONS 243 7.11 SOLUTION TECHNIQUES FOR S N I
245 7.12 GRAPHICAL SIMULATION OF A VECTOR FIELD 248 EXERCISES 250
BIBLIOGRAPHY 255 A ANSWERS TO ODD-NUMBERED EXERCISES 257 B VECTOR
FORMULAE AT A GLANCE 265 INDEX 269
|
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| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:53:10Z |
| institution | BVB |
| isbn | 0849310881 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009474575 |
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| physical | XI, 272 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Electrical engineering textbook series |
| spelling | Rahman, Matiur Verfasser aut Applied vector analysis Matiur Rahman ; Isaac Mulolani Boca Raton [u.a.] CRC Press 2001 XI, 272 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Electrical engineering textbook series Vector analysis Vektoranalysis (DE-588)4191992-0 gnd rswk-swf Vektoranalysis (DE-588)4191992-0 s DE-604 Mulolani, Isaac Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009474575&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rahman, Matiur Mulolani, Isaac Applied vector analysis Vector analysis Vektoranalysis (DE-588)4191992-0 gnd |
| subject_GND | (DE-588)4191992-0 |
| title | Applied vector analysis |
| title_auth | Applied vector analysis |
| title_exact_search | Applied vector analysis |
| title_full | Applied vector analysis Matiur Rahman ; Isaac Mulolani |
| title_fullStr | Applied vector analysis Matiur Rahman ; Isaac Mulolani |
| title_full_unstemmed | Applied vector analysis Matiur Rahman ; Isaac Mulolani |
| title_short | Applied vector analysis |
| title_sort | applied vector analysis |
| topic | Vector analysis Vektoranalysis (DE-588)4191992-0 gnd |
| topic_facet | Vector analysis Vektoranalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009474575&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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