Quaternionic and Clifford calculus for physicists and engineers:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
John Wiley & Sons
1997
|
| Series: | Mathematical Methods in Practice
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 371 Seiten |
| ISBN: | 0471962007 |
Staff View
MARC
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| 245 | 1 | 0 | |a Quaternionic and Clifford calculus for physicists and engineers |c Klaus Gürlebeck, Bauhaus-University Weimar, Germany, Wolfgang Sprössig, Frieberg University of Mining and Technology, Germany |
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| 300 | |a XI, 371 Seiten | ||
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| 490 | 1 | |a Mathematical Methods in Practice |v 1 | |
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| 650 | 4 | |a Differential equations, Partial | |
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Record in the Search Index
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| adam_text | Contents
Preface vii
Series Perface xi
1 Quaternions and multivectors 1
1.1 Real and complex quaternions 2
1.2 Quaternions and vector algebra relations 8
1.3 Rotations 13
1.4 General Clifford algebras 19
1.5 ... Tensors andcliffors 26
1.6 Multivectors 29
1.7 Quaternionic matrices 32
2 Clifford valued functions and forms 35
2.1 Classes of regular functions 36
2.2 Different approaches to regular functions 45
2.3 Paravector valued elementary functions 49
2.4 Regular functions in symmetric domains 58
2.5 Uniqueness of Clifford regular functions 62
2.6 Hypercomplex exterior calculus 64
2.7 Wirtinger Calculus 70
3 Clifford operator calculus 74
3.1 Teodorescu transform 75
3.2 Around Cauchy s integral formula 84
3.3 Function series expansions 92
3.4 Singular integrals of Cauchy s type 99
3.5 Formulae of Plemelj Sokhotzki type 104
3.6 Decomposition of the C70,,, valued Hilbert space 109
3.7 Remarks on residues in Clifford analysis 113
3.8 Mobius transformations in IR 116
3.9 Fourier transform and related transforms 121
V
vi CONTENTS
4 Boundary value problems 127
4.1 First order boundary value problems 128
4.2 Dirichlet problems and orthoprojections 134
4.3 Vekua type problems 139
4.4 Higher order boundary value problems 155
4.5 Weak time dependent Maxwell equations 162
4.6 A coupled problem of thermo elasticity 167
4.7 Stokes equations 170
4.8 Navier Stokes equations and related equations 178
4.9 Problems with non linear right hand side 184
4.10 On strong non linear problems 191
4.11 Riemann Hilbert problems 196
4.12 Domain perturbation problems 201
4.13 Transmission problems 206
4.14 Hypercomplex Beltrami equation 213
4.15 Lower bounds for eigenvalues 220
4.16 Kernel functions 229
5 Numerical Clifford analysis 233
5.1 Discrete quaternionic calculus 234
5.2 Discrete fundamental solutions 245
5.3 Discrete reprokernels 258
5.4 Convergence results 262
5.5 Functional analytic theorems 277
5.6 Special systems of C/On regular functions 280
5.7 A Gram Schmidt procedure 284
5.8 Boundary collocation methods 288
6 Further results and research problems 298
6.1 Parabolic problems 299
6.2 On field equations 303
6.3 On recent problems in Clifford analysis 310
A Exact computations of the Teodorescu transform 322
B Discrete fundamental solutions 338
C Discrete Teodorescu transform 343
D Bibliography 348
Index 365
|
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| id | DE-604.BV011591407 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:12:23Z |
| institution | BVB |
| isbn | 0471962007 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007807369 |
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| owner_facet | DE-703 DE-29T DE-91G DE-BY-TUM DE-83 DE-188 |
| physical | XI, 371 Seiten |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | John Wiley & Sons |
| record_format | marc |
| series | Mathematical Methods in Practice |
| series2 | Mathematical Methods in Practice |
| spelling | Gürlebeck, Klaus 1954- Verfasser (DE-588)1015214991 aut Quaternionic and Clifford calculus for physicists and engineers Klaus Gürlebeck, Bauhaus-University Weimar, Germany, Wolfgang Sprössig, Frieberg University of Mining and Technology, Germany Chichester [u.a.] John Wiley & Sons 1997 XI, 371 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical Methods in Practice 1 Boundary value problems Clifford algebras Differential equations, Partial Quaternions Quaternion (DE-588)4176653-2 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Clifford-Analysis (DE-588)4484012-3 gnd rswk-swf Quaternion (DE-588)4176653-2 s Algebra (DE-588)4001156-2 s DE-604 Clifford-Analysis (DE-588)4484012-3 s Sprößig, Wolfgang 1946- Verfasser (DE-588)1055083103 aut Mathematical Methods in Practice 1 (DE-604)BV035419231 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007807369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gürlebeck, Klaus 1954- Sprößig, Wolfgang 1946- Quaternionic and Clifford calculus for physicists and engineers Mathematical Methods in Practice Boundary value problems Clifford algebras Differential equations, Partial Quaternions Quaternion (DE-588)4176653-2 gnd Algebra (DE-588)4001156-2 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| subject_GND | (DE-588)4176653-2 (DE-588)4001156-2 (DE-588)4484012-3 |
| title | Quaternionic and Clifford calculus for physicists and engineers |
| title_auth | Quaternionic and Clifford calculus for physicists and engineers |
| title_exact_search | Quaternionic and Clifford calculus for physicists and engineers |
| title_full | Quaternionic and Clifford calculus for physicists and engineers Klaus Gürlebeck, Bauhaus-University Weimar, Germany, Wolfgang Sprössig, Frieberg University of Mining and Technology, Germany |
| title_fullStr | Quaternionic and Clifford calculus for physicists and engineers Klaus Gürlebeck, Bauhaus-University Weimar, Germany, Wolfgang Sprössig, Frieberg University of Mining and Technology, Germany |
| title_full_unstemmed | Quaternionic and Clifford calculus for physicists and engineers Klaus Gürlebeck, Bauhaus-University Weimar, Germany, Wolfgang Sprössig, Frieberg University of Mining and Technology, Germany |
| title_short | Quaternionic and Clifford calculus for physicists and engineers |
| title_sort | quaternionic and clifford calculus for physicists and engineers |
| topic | Boundary value problems Clifford algebras Differential equations, Partial Quaternions Quaternion (DE-588)4176653-2 gnd Algebra (DE-588)4001156-2 gnd Clifford-Analysis (DE-588)4484012-3 gnd |
| topic_facet | Boundary value problems Clifford algebras Differential equations, Partial Quaternions Quaternion Algebra Clifford-Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007807369&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035419231 |
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