Mathematics of Wave Propagation (eBook)

Julian L. Davis (Autor)

eBook Download: PDF

2021
411 Seiten
Princeton University Press (Verlag)
978-0-691-22337-7 (ISBN)

Infos

Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.

Produkt-Details

• Erscheint lt. Verlag: 12.1.2021
• Zusatzinfo: 4 tables, 70 line illus.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: acceleration • Acoustic Impedance • Adiabatic condition • Adjoint operators • Amplitude • Analytical Dynamics • Approximation Theory • Bessel function • Bessel's equation • boundary layer • Boundary value problem • Brachistochrome problem • Bulk modulus • Calculus of Variations • Canonical Transformations • Cartesian coordinate system • Cauchy stress tensor • Caustic or focal curves • Characteristic coordinates • Characteristic equation • Characteristic line element • Characteristics, method of • classical mechanics • coefficient • Configuration space • conservation law • constitutive equation • Continuity equation • Continuum Mechanics • Critical sound speed • Cross section (physics) • Cyclic coordinates • Deformation • Deformation (mechanics) • Degrees of freedom (mechanics) • Derivative • differential equation • Differential operator • Dimension • Directional derivative • Direction field • Displacement field (mechanics) • Displacement (vector) • Dissipation • Divergence Theorem • Doppler Effect • Eigenfunction • eigenfunctions • eigenvalues • Eikonal equation • Elasticity (physics) • Elliptic partial differential equation • Epicycloid • Equation • Equation of State • Equation of state (cosmology) • Equations of motion • Equipartition theorem • Euler equations (fluid dynamics) • Euler's equations (rigid body dynamics) • Fermat's Principle • Finite bar • free surface • Friction, internal • Generalized force • Generalized velocity • hamiltonian • hamiltonian mechanics • Hamilton-Jacoby theory • Hamilton's principle • Harmonic oscillator • Hooke's law • hyperbolic partial differential equation • Ideal or perfect gas • Integral curve • Integral surfaces • inverse Laplace transform • Isothermal condition • jacobian • kinetic energy • Lagrangian (field theory) • lagrangian function • Lagrangian mechanics • Lame constants • Laminar Flow • Laplace's equation • linear differential equation • linear equation • longitudinal wave • Mass flux • Mathematics • Memory Function • Minimizing curve • Monge axis • Monge cone • Navier equations • Navier–Stokes equations • Newtonian fluid • Newton's laws of motion • ordinary differential equation • Oscillation • Oseen approximation • parametric equation • partial derivative • partial differential equation • particle velocity • Perturbation theory (quantum mechanics) • Phase velocity • Phase (waves) • Physics of propagating waves • Plane elastic waves • Poiseuille Flow • Progressing wave • Proportionality (mathematics) • quantum mechanics • Radially symmetric waves • Rayleigh dissipation function • Ray (optics) • Regressing wave • Reversible process (thermodynamics) • Reynold's law • Reynolds Number • Riemann invariant • Schrödinger equation • Self-adjoint operator • shear stress • Shock Wave • Sine Wave • Sinusoidal waves • Statistical Mechanics • Stream Function • surface wave • Tension (physics) • theory • Three-dimensional space (mathematics) • Transverse wave • two-dimensional space • Variational method (quantum mechanics) • Velocity potential • viscosity • wave equation • waveform • Wavefront • wave function • Wavelength • wavenumber • Wave Packet • wave propagation • Wave surface
• ISBN-10: 0-691-22337-8 / 0691223378
• ISBN-13: 978-0-691-22337-7 / 9780691223377