Fields, flows and waves: an introduction to continuum models
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London [u.a.]
Springer
2003
|
| Schriftenreihe: | Springer undergraduate mathematics series
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010206345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XII, 270 S. graph. Darst. |
| ISBN: | 9781852337087 |
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| 100 | 1 | |a Parker, David F. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Fields, flows and waves |b an introduction to continuum models |c D. F. Parker |
| 264 | 1 | |a London [u.a.] |b Springer |c 2003 | |
| 300 | |a XII, 270 S. |b graph. Darst. | ||
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| 490 | 0 | |a Springer undergraduate mathematics series | |
| 520 | 1 | |a "Designed for second-year undergraduate students in mathematics, mathematical physics, and engineering, this book presumes only a limited familiarity with several variable calculus and vector fields. It develops the concepts of flux, conservation law and boundary value problem through simple examples of heat flow, electric potentials and gravitational fields. The ideas are developed through worked examples, and a range of exercises (with solutions) is provided to test understanding."--BOOK JACKET. | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0202 PHY 011f 2003 A 185 |
|---|---|
| DE-BY-TUM_katkey | 1410066 |
| DE-BY-TUM_location | 02 |
| DE-BY-TUM_media_number | 040020729011 040020794361 |
| _version_ | 1821932580425957376 |
| adam_text | Contents
1. The Continuum Description 1
1.1 Densities and Fluxes 1
1.2 Conservation and Balance Laws in One Dimension 3
1.3 Heat Flow 7
1.4 Steady Radial Flow in Two Dimensions 10
1.5 Steady Radial Flow in Three Dimensions 13
2. Unsteady Heat Flow 17
2.1 Thermal Energy 17
2.1.1 Heat Balance in One dimensional Problems 18
2.1.2 Some Special Solutions of Equation (2.3) 20
2.2 Effects of Heat Supply 26
2.3 Unsteady, Spherically Symmetric Heat Flow 30
3. Fields and Potentials 35
3.1 Gradient of a Scalar 35
3.1.1 Some Applications 36
3.2 Gravitational Potential 38
3.2.1 Special Properties of the Function j = r 1 40
3.3 Continuous Distributions of Mass 44
3.4 Electrostatics 46
3.4.1 Gauss s Law of Flux 48
3.4.2 Charge free Regions 48
3.4.3 Surface Charge Density 50
ix
x Contents
4. Laplace s Equation and Poisson s Equation 55
4.1 The Ubiquitous Laplacian 55
4.2 Separable Solutions 58
4.3 Poisson s Equation 66
4.4 Dipole Solutions 70
4.4.1 Uses of Dipole Solutions to V2 £ = 0 72
4.4.2 Spherical Inclusions 73
5. Motion of an Elastic String 77
5.1 Tension and Extension; Kinematics and Dynamics 77
5.1.1 Dynamics 79
5.2 Planar Motions 80
5.2.1 Small Transverse Motions 82
5.2.2 Longitudinal Motions 82
5.3 Properties of the Wave Equation 82
5.3.1 Standing Waves 84
5.3.2 Superposition of Standing Waves 86
5.4 D Alembert s Solution, Travelling Waves and Wave Reflections . 90
5.4.1 Wave Reflections 90
5.5 Other One dimensional Waves 93
5.5.1 Acoustic Vibrations in a Tube 93
5.5.2 Telegraphy and High voltage Transmission 96
6. Fluid Flow 101
6.1 Kinematics and Streamlines 101
6.1.1 Some Important Examples of Steady Flow 102
6.2 Volume Flux and Mass Flux 103
6.2.1 Incompressible Fluids 105
6.2.2 Mass Conservation 106
6.3 Two dimensional Flows of Incompressible Fluids 107
6.3.1 The Continuity Equation 107
6.3.2 Irrotational Flows and the Velocity Potential 108
6.3.3 The Stream Function Ill
6.4 Pressure in a Fluid 116
6.4.1 Resultant Force 116
6.4.2 Hydrostatics and Archimedes Principle 117
6.4.3 Momentum Density and Momentum Flux 119
6.5 Bernoulli s Equation 122
6.5.1 The Material (Advected) Derivative 122
6.5.2 Bernoulli s Equation and Dynamic Pressure 123
6.5.3 The Principle of Aerodynamic Lift 125
6.6 Three dimensional, Incompressible Flows 127
Contents xi
6.6.1 The Continuity Equation 128
6.6.2 Irrotational Flows, the Velocity Potential and Laplace s
Equation 129
7. Elastic Deformations 133
7.1 The Kinematics of Deformation 133
7.1.1 Deformation Gradient 135
7.1.2 Stretch and Rotation 136
7.2 Polar Decomposition 140
7.3 Stress 143
7.3.1 Traction Vectors 144
7.3.2 Components of Stress 144
7.3.3 Traction on a General Surface 146
7.4 Isotropic Linear Elasticity 147
7.4.1 The Constitutive Law 148
7.4.2 Stretching, Shear and Torsion 149
8. Vibrations and Waves 157
8.1 Wave Reflection and Refraction 157
8.1.1 Use of the Complex Exponential 157
8.1.2 Plane Waves 159
8.1.3 Reflection at a Rigid Wall 161
8.1.4 Refraction at an Interface 163
8.1.5 Total Internal Reflection 165
8.2 Guided Waves 167
8.2.1 Acoustic Waves in a Layer 167
8.2.2 Waveguides and Dispersion 169
8.3 Love Waves in Elasticity 174
8.4 Elastic Plane Waves 176
8.4.1 Elastic Shear Waves 176
8.4.2 Dilatational Waves 178
9. Electromagnetic Waves and Light 185
9.1 Physical Background 185
9.1.1 The Origin of Maxwell s Equations 185
9.1.2 Plane Electromagnetic Waves 188
9.1.3 Reflection and Refraction of Electromagnetic Waves .... 192
9.2 Waveguides 195
9.2.1 Rectangular Waveguides 196
9.2.2 Circular Cylindrical Waveguides 198
9.2.3 An Introduction to Fibre Optics 202
xii Contents
10. Chemical and Biological Models 207
10.1 Diffusion of Chemical Species 207
10.1.1 Fick s Law of Diffusion 208
10.1.2 Self similar Solutions 209
10.1.3 Travelling Wavefronts 211
10.2 Population Biology 214
10.2.1 Growth and Dispersal 214
10.2.2 Fisher s Equation and Self limitation 216
10.2.3 Population dependent Dispersivity 219
10.2.4 Competing Species 221
10.2.5 Diffusive Instability 224
10.3 Biological Waves 229
10.3.1 The Logistic Wavefront 229
10.3.2 Travelling Pulses and Spiral Waves 231
Solutions 237
Bibliography 261
Index 263
|
| any_adam_object | 1 |
| author | Parker, David F. |
| author_facet | Parker, David F. |
| author_role | aut |
| author_sort | Parker, David F. |
| author_variant | d f p df dfp |
| building | Verbundindex |
| bvnumber | BV016516338 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA808.2 |
| callnumber-search | QA808.2 |
| callnumber-sort | QA 3808.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | UF 2000 |
| classification_tum | PHY 011f PHY 210f |
| ctrlnum | (OCoLC)51559045 (DE-599)BVBBV016516338 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV016516338 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T11:12:28Z |
| institution | BVB |
| isbn | 9781852337087 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010206345 |
| oclc_num | 51559045 |
| open_access_boolean | |
| owner | DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-29T DE-634 DE-11 DE-188 |
| owner_facet | DE-20 DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-703 DE-29T DE-634 DE-11 DE-188 |
| physical | XII, 270 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer undergraduate mathematics series |
| spellingShingle | Parker, David F. Fields, flows and waves an introduction to continuum models Mathematische fysica gtt Milieux continus, Mécanique des Oneindigheid gtt Wiskundige modellen gtt Continuum mechanics Kontinuumsphysik (DE-588)4165166-2 gnd Strömungsmechanik (DE-588)4077970-1 gnd Vielteilchensystem (DE-588)4063491-7 gnd Kontinuum (DE-588)4032295-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Feld Physik (DE-588)4153902-3 gnd |
| subject_GND | (DE-588)4165166-2 (DE-588)4077970-1 (DE-588)4063491-7 (DE-588)4032295-6 (DE-588)4114528-8 (DE-588)4153902-3 |
| title | Fields, flows and waves an introduction to continuum models |
| title_auth | Fields, flows and waves an introduction to continuum models |
| title_exact_search | Fields, flows and waves an introduction to continuum models |
| title_full | Fields, flows and waves an introduction to continuum models D. F. Parker |
| title_fullStr | Fields, flows and waves an introduction to continuum models D. F. Parker |
| title_full_unstemmed | Fields, flows and waves an introduction to continuum models D. F. Parker |
| title_short | Fields, flows and waves |
| title_sort | fields flows and waves an introduction to continuum models |
| title_sub | an introduction to continuum models |
| topic | Mathematische fysica gtt Milieux continus, Mécanique des Oneindigheid gtt Wiskundige modellen gtt Continuum mechanics Kontinuumsphysik (DE-588)4165166-2 gnd Strömungsmechanik (DE-588)4077970-1 gnd Vielteilchensystem (DE-588)4063491-7 gnd Kontinuum (DE-588)4032295-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd Feld Physik (DE-588)4153902-3 gnd |
| topic_facet | Mathematische fysica Milieux continus, Mécanique des Oneindigheid Wiskundige modellen Continuum mechanics Kontinuumsphysik Strömungsmechanik Vielteilchensystem Kontinuum Mathematisches Modell Feld Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010206345&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT parkerdavidf fieldsflowsandwavesanintroductiontocontinuummodels |
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Teilbibliothek Physik
| Signatur: |
0202 PHY 011f 2003 A 185 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |
| Exemplar 2 | Ausleihbar Am Standort |