Buch, Englisch, 270 Seiten, Format (B × H): 178 mm x 235 mm, Gewicht: 1100 g
An Introduction to Continuum Models
Buch, Englisch, 270 Seiten, Format (B × H): 178 mm x 235 mm, Gewicht: 1100 g
Reihe: Springer Undergraduate Mathematics Series
ISBN: 978-1-85233-708-7
Verlag: Springer
This book serves as an introduction to the use of mathematics in describing collective phenomena in physics and biology. Derived from a course of innovative lectures, the book shows students early in their studies how many of the topics they have encountered – partial differential equations, differential equations, Fourier series, and linear algebra – are useful in constructing, analysing and interpreting phenomena present in the real world. Throughout, ideas are developed using worked examples and exercises with solution. The text does not assume a strong background in physics.
Zielgruppe
Lower undergraduate
Autoren/Hrsg.
Fachgebiete
- Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
- Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Naturwissenschaften Physik Physik Allgemein Geschichte der Physik
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Naturwissenschaften Physik Physik Allgemein Experimentalphysik
Weitere Infos & Material
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.
