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Beschreibung
Many phenomena in the physical and biological sciences involve the collective behaviour of (very large) numbers of individual objects. For example, the be haviour of gases ultimately concerns the interacting motions of uncountably many atoms and molecules, but to understand flow in nozzles, around aircraft and in meteorology it is best to treat velocity and density as continuous func tions of position and time and then to analyse the associated flows. Although modern electronics involves ever smaller components, even the semiconduc tor devices used widely in electronic communications and in digital processing involve collective phenomena, such as electric currents and fields, which are continuously varying functions of position and time. Diffusion and reaction between various chemical constituents, the growth and spread of biological or ganisms and the flow of traffic on major highways are all phenomena which may be described and analysed in terms of fields and flows, while sound, light and various other electromagnetic phenomena involve both fields and waves. Treating these using a continuum model, which does not attempt to trace the motion and evolution of individual objects, often gives good predictions. The mathematical concepts and techniques which underlie such treatments are the subject of this book. This book is designed as a first introduction to the use of mathematical techniques, within continuum theories.
Many phenomena in the physical and biological sciences involve the collective behaviour of (very large) numbers of individual objects. For example, the be haviour of gases ultimately concerns the interacting motions of uncountably many atoms and molecules, but to understand flow in nozzles, around aircraft and in meteorology it is best to treat velocity and density as continuous func tions of position and time and then to analyse the associated flows. Although modern electronics involves ever smaller components, even the semiconduc tor devices used widely in electronic communications and in digital processing involve collective phenomena, such as electric currents and fields, which are continuously varying functions of position and time. Diffusion and reaction between various chemical constituents, the growth and spread of biological or ganisms and the flow of traffic on major highways are all phenomena which may be described and analysed in terms of fields and flows, while sound, light and various other electromagnetic phenomena involve both fields and waves. Treating these using a continuum model, which does not attempt to trace the motion and evolution of individual objects, often gives good predictions. The mathematical concepts and techniques which underlie such treatments are the subject of this book. This book is designed as a first introduction to the use of mathematical techniques, within continuum theories.
Zusammenfassung
This book introduces the undergraduate to the diversity and versatility of
fundamental mathematics in the real world, without the need for multiple
preparatory courses first. It illustrates, through examples, how core
undergraduate topics that students have already encountered - such as
linear algebra, matrices and differential equations - are natural tools
for constructing, analysing and interpreting phenomena in the real world.
fundamental mathematics in the real world, without the need for multiple
preparatory courses first. It illustrates, through examples, how core
undergraduate topics that students have already encountered - such as
linear algebra, matrices and differential equations - are natural tools
for constructing, analysing and interpreting phenomena in the real world.
Inhaltsverzeichnis
1. The Continuum Description.- 1.1 Densities and Fluxes.- 1.2 Conservation and Balance Laws in One Dimension.- 1.3 Heat Flow.- 1.4 Steady Radial Flow in Two Dimensions.- 1.5 Steady Radial Flow in Three Dimensions.- 2. Unsteady Heat Flow.- 2.1 Thermal Energy.- 2.2 Effects of Heat Supply.- 2.3 Unsteady, Spherically Symmetric Heat Flow.- 3. Fields and Potentials.- 3.1 Gradient of a Scalar.- 3.2 Gravitational Potential.- 3.3 Continuous Distributions of Mass.- 3.4 Electrostatics.- 4. Laplace's Equation and Poisson's Equation.- 4.1 The Ubiquitous Laplacian.- 4.2 Separable Solutions.- 4.3 Poisson's Equation.- 4.4 Dipole Solutions.- 5. Motion of an Elastic String.- 5.1 Tension and Extension; Kinematics and Dynamics.- 5.2 Planar Motions.- 5.3 Properties of the Wave Equation.- 5.4 D'Alembert's Solution, Travelling Waves and Wave Reflections.- 5.5 Other One-dimensional Waves.- 6. Fluid Flow.- 6.1 Kinematics and Streamlines.- 6.2 Volume Flux and Mass Flux.- 6.3 Two-dimensional Flows of Incompressible Fluids.- 6.4 Pressure in a Fluid.- 6.5 Bernoulli's Equation.- 6.6 Three-dimensional, Incompressible Flows.- 7. Elastic Deformations.- 7.1 The Kinematics of Deformation.- 7.2 Polar Decomposition.- 7.3 Stress.- 7.4 Isotropic Linear Elasticity.- 8. Vibrations and Waves.- 8.2 Guided Waves.- 8.3 Love Waves in Elasticity.- 8.4 Elastic Plane Waves.- 9. Electromagnetic VVaves and Light.- 9.1 Physical Background.- 9.2 Waveguides.- 10. Chemical and Biological Models.- 10.1 Diffusion of Chemical Species.- 10.2 Population Biology.- 10.3 Biological Waves.- Solutions.
Details
| Erscheinungsjahr: | 2003 |
|---|---|
| Fachbereich: | Astronomie |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Taschenbuch |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xii
270 S. 17 s/w Illustr. 270 p. 17 illus. |
| ISBN-13: | 9781852337087 |
| ISBN-10: | 1852337087 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Parker, David F. |
| Hersteller: |
Springer London
Springer-Verlag London Ltd. Springer Undergraduate Mathematics Series |
| Maße: | 235 x 178 x 16 mm |
| Von/Mit: | David F. Parker |
| Erscheinungsdatum: | 05.05.2003 |
| Gewicht: | 0,499 kg |
Zusammenfassung
This book introduces the undergraduate to the diversity and versatility of
fundamental mathematics in the real world, without the need for multiple
preparatory courses first. It illustrates, through examples, how core
undergraduate topics that students have already encountered - such as
linear algebra, matrices and differential equations - are natural tools
for constructing, analysing and interpreting phenomena in the real world.
fundamental mathematics in the real world, without the need for multiple
preparatory courses first. It illustrates, through examples, how core
undergraduate topics that students have already encountered - such as
linear algebra, matrices and differential equations - are natural tools
for constructing, analysing and interpreting phenomena in the real world.
Inhaltsverzeichnis
1. The Continuum Description.- 1.1 Densities and Fluxes.- 1.2 Conservation and Balance Laws in One Dimension.- 1.3 Heat Flow.- 1.4 Steady Radial Flow in Two Dimensions.- 1.5 Steady Radial Flow in Three Dimensions.- 2. Unsteady Heat Flow.- 2.1 Thermal Energy.- 2.2 Effects of Heat Supply.- 2.3 Unsteady, Spherically Symmetric Heat Flow.- 3. Fields and Potentials.- 3.1 Gradient of a Scalar.- 3.2 Gravitational Potential.- 3.3 Continuous Distributions of Mass.- 3.4 Electrostatics.- 4. Laplace's Equation and Poisson's Equation.- 4.1 The Ubiquitous Laplacian.- 4.2 Separable Solutions.- 4.3 Poisson's Equation.- 4.4 Dipole Solutions.- 5. Motion of an Elastic String.- 5.1 Tension and Extension; Kinematics and Dynamics.- 5.2 Planar Motions.- 5.3 Properties of the Wave Equation.- 5.4 D'Alembert's Solution, Travelling Waves and Wave Reflections.- 5.5 Other One-dimensional Waves.- 6. Fluid Flow.- 6.1 Kinematics and Streamlines.- 6.2 Volume Flux and Mass Flux.- 6.3 Two-dimensional Flows of Incompressible Fluids.- 6.4 Pressure in a Fluid.- 6.5 Bernoulli's Equation.- 6.6 Three-dimensional, Incompressible Flows.- 7. Elastic Deformations.- 7.1 The Kinematics of Deformation.- 7.2 Polar Decomposition.- 7.3 Stress.- 7.4 Isotropic Linear Elasticity.- 8. Vibrations and Waves.- 8.2 Guided Waves.- 8.3 Love Waves in Elasticity.- 8.4 Elastic Plane Waves.- 9. Electromagnetic VVaves and Light.- 9.1 Physical Background.- 9.2 Waveguides.- 10. Chemical and Biological Models.- 10.1 Diffusion of Chemical Species.- 10.2 Population Biology.- 10.3 Biological Waves.- Solutions.
Details
| Erscheinungsjahr: | 2003 |
|---|---|
| Fachbereich: | Astronomie |
| Genre: | Physik |
| Rubrik: | Naturwissenschaften & Technik |
| Thema: | Lexika |
| Medium: | Taschenbuch |
| Reihe: | Springer Undergraduate Mathematics Series |
| Inhalt: |
xii
270 S. 17 s/w Illustr. 270 p. 17 illus. |
| ISBN-13: | 9781852337087 |
| ISBN-10: | 1852337087 |
| Sprache: | Englisch |
| Ausstattung / Beilage: | Paperback |
| Einband: | Kartoniert / Broschiert |
| Autor: | Parker, David F. |
| Hersteller: |
Springer London
Springer-Verlag London Ltd. Springer Undergraduate Mathematics Series |
| Maße: | 235 x 178 x 16 mm |
| Von/Mit: | David F. Parker |
| Erscheinungsdatum: | 05.05.2003 |
| Gewicht: | 0,499 kg |
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