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  • 1
    Online-Ressource
    Online-Ressource
    Fields, Flows and Waves : An Introduction to Continuum Models (2003)
    London :Springer London :
    Details
    UID:
    almahu_9947362728202882
    Umfang: XII, 270 p. 17 illus. , online resource.
    ISBN: 9781447100195
    Serie: Springer Undergraduate Mathematics Series,
    Inhalt: 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.
    Anmerkung: 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.
    In: Springer eBooks
    Weitere Ausg.: Printed edition: ISBN 9781852337087
    Sprache: Englisch
    DOI: 10.1007/978-1-4471-0019-5
    URL: http://dx.doi.org/10.1007/978-1-4471-0019-5
    URL: Volltext
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Online Zugang
    Open Access Wunsch
    HU Berlin
    BTU Cottbus
  • 2
    Online-Ressource
    Online-Ressource
    Fields, Flows and Waves : An Introduction to Continuum Models (2003)
    London : Springer
    Details
    UID:
    gbv_1655428942
    Umfang: Online-Ressource (XII, 270 p, online resource)
    ISBN: 9781447100195
    Serie: Springer Undergraduate Mathematics Series
    Inhalt: This book, derived from an innovative course of lectures, is a first introduction to the mathematical description of fields, flows and waves. It shows students, early in their studies, how many of the topics they have encountered are useful in constructing, analysing and interpreting phenomena in the real world. Designed for second-year undergraduate students in mathematics, mathematical physics, and engineering, it 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. Chapters 1-7 contain ample material for an introductory lecture course, while later chapters on waves in fluids, solids and electromagnetism, and on bio-mathematics, show how the extension of earlier ideas leads to the description and explanation of important topics in modern technology and science
    Weitere Ausg.: ISBN 9781852337087
    Weitere Ausg.: Erscheint auch als Druck-Ausgabe Parker, D. F., 1940 - Fields, flows and waves London : Springer, 2003 ISBN 1852337087
    Weitere Ausg.: ISBN 9781852337087
    Sprache: Englisch
    Fachgebiete: Physik
    RVK:
    UF 2000
    Schlagwort(e): Kontinuumsphysik ; Vielteilchensystem ; Mathematisches Modell ; Kontinuum ; Kontinuumsphysik ; Mathematisches Modell
    DOI: 10.1007/978-1-4471-0019-5
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    URL: Inhaltstext
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
    BibTip Andere fanden auch interessant ...
    Online-Ressource
    Online Zugang
    Open Access Wunsch
    UB Potsdam
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