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Introduction to First Edition | |

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Introduction to Second Edition | |

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Introduction to Third Edition | |

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Introduction to Fourth Edition | |

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Introduction to Fifth Edition | |

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Introduction to Sixth Edition | |

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Simple Harmonic Motion | |

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Displacement in Simple Harmonic Motion | |

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Velocity and Acceleration in Simple Harmonic Motion | |

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Energy of a Simple Harmonic Oscillator | |

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Simple Harmonic Oscillations in an Electrical System | |

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Superposition of Two Simple Harmonic Vibrations in One Dimension | |

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Superposition of Two Perpendicular Simple Harmonic Vibrations | |

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*Polarization | |

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Superposition of a Large Number n of Simple Harmonic Vibrations of Equal Amplitude a and Equal Successive Phase Difference [delta] | |

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*Superposition of n Equal SHM Vectors of Length a with Random Phase | |

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Some Useful Mathematics | |

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Damped Simple Harmonic Motion | |

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Methods of Describing the Damping of an Oscillator | |

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The Forced Oscillator | |

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The Operation of i upon a Vector | |

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Vector form of Ohm's Law | |

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The Impedance of a Mechanical Circuit | |

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Behaviour of a Forced Oscillator | |

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Behaviour of Velocity [upsilon] in Magnitude and Phase versus Driving Force Frequency [omega] | |

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Behaviour of Displacement versus Driving Force Frequency [omega] | |

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Problem on Vibration Insulation | |

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Significance of the Two Components of the Displacement Curve | |

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Power Supplied to Oscillator by the Driving Force | |

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Variation of P[subscript av] with [omega]. Absorption Resonance Curve | |

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The Q-Value in Terms of the Resonance Absorption Bandwidth | |

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The Q-Value as an Amplification Factor | |

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The Effect of the Transient Term | |

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Coupled Oscillations | |

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Stiffness (or Capacitance) Coupled Oscillators | |

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Normal Coordinates, Degrees of Freedom and Normal Modes of Vibration | |

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The General Method for Finding Normal Mode Frequencies, Matrices, Eigenvectors and Eigenvalues | |

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Mass or Inductance Coupling | |

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Coupled Oscillations of a Loaded String | |

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The Wave Equation | |

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Transverse Wave Motion | |

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Partial Differentiation | |

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Waves | |

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Velocities in Wave Motion | |

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The Wave Equation | |

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Solution of the Wave Equation | |

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Characteristic Impedance of a String (the string as a forced oscillator) | |

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Reflection and Transmission of WAves on a String at a Boundary | |

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Reflection and Transmission of Energy | |

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The Reflected and Transmitted Intensity Coefficients | |

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The Matching of Impedances | |

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Standing Waves on a String of Fixed Length | |

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Energy of a Vibrating String | |

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Energy in Each Normal Mode of a Vibrating String | |

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Standing Wave Ratio | |

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Wave Groups and Group Velocity | |

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Wave Group of Many Components. The Bandwidth Theorem | |

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Transverse Waves in a Periodic Structure | |

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Linear Array of Two Kinds of Atoms in an Ionic Crystal | |

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Absorption of Infrared Radiation by Ionic Crystals | |

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Doppler Effect | |

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Longitudinal Waves | |

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Sound Waves in Gases | |

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Energy Distribution in Sound Waves | |

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Intensity of Sound Waves | |

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Longitudinal Waves in a Solid | |

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Application to Earthquakes | |

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Longitudinal Waves in a Periodic Structure | |

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Reflection and Transmission of Sound Waves at Boundaries | |

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Reflection and Transmission of Sound Intensity | |

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Waves on Transmission Lines | |

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Ideal or Lossless Transmission Line | |

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Coaxial Cables | |

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Characteristic Impedance of a Transmission Line | |

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Reflections from the End of a Transmission Line | |

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Short Circuited Transmission Line (Z[subscript L] = 0) | |

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The Transmission Line as a Filter | |

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Effect of Resistance in a Transmission Line | |

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Characteristic Impedance of a Transmission Line with Resistance | |

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The Diffusion Equation and Energy Absorption in Waves | |

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Wave Equation with Diffusion Effects | |

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Appendix | |

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Electromagnetic Waves | |

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Maxwell's Equations | |

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Electromagnetic Waves in a Medium having Finite Permeability [mu] and Permittivity [epsilon] but with Conductivity [sigma] = 0 | |

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The Wave Equation for Electromagnetic Waves | |

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Illustration of Poynting Vector | |

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Impedance of a Dielectric to Electromagnetic Waves | |

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Electromagnetic Waves in a Medium of Properties [mu], [epsilon] and [sigma] (where [sigma] [not equal] 0) | |

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Skin Depth | |

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Electromagnetic Wave Velocity in a Conductor and Anomalous Dispersion | |

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When is a Medium a Conductor or a Dielectric? | |

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Why will an Electromagnetic Wave not Propagate into a Conductor? | |

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Impedance of a Conducting Medium to Electromagnetic Waves | |

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Reflection and Transmission of Electromagnetic Waves at a Boundary | |

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Reflection from a Conductor (Normal Incidence) | |

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Electromagnetic Waves in a Plasma | |

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Electromagnetic Waves in the Ionosphere | |

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Waves in More than One Dimension | |

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Plane Wave Representation in Two and Three Dimensions | |

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Wave Equation in Two Dimensions | |

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Wave Guides | |

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Normal Modes and the Method of Separation of Variables | |

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Two-Dimensional Case | |

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Three-Dimensional Case | |

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Normal Modes in Two Dimensions on a Rectangular Membrane | |

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Normal Modes in Three Dimensions | |

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Frequency Distribution of Energy Radiated from a Hot Body. Planck's Law | |

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Debye Theory of Specific Heats | |

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Reflection and Transmission of a Three-Dimensional Wave at a Plane Boundary | |

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Total Internal Reflection and Evanescent Waves | |

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Fourier Methods | |

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Fourier Series | |

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Application of Fourier Sine Series to a Triangular Function | |

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Application to the Energy in the Normal Modes of a Vibrating String | |

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Fourier Series Analysis of a Rectangular Velocity Pulse on a String | |

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The Spectrum of a Fourier Series | |

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Fourier Integral | |

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Fourier Transforms | |

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Examples of Fourier Transforms | |

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The Slit Function | |

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The Fourier Transform Applied to Optical Diffraction from a Single Slit | |

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The Gaussian Curve | |

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The Dirac Delta Function, its Sifting Property and its Fourier Transform | |

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Convolution | |

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The Convolution Theorem | |

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Waves in Optical Systems | |

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Light. Waves or Rays? | |

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Fermat's Principle | |

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The Laws of Reflection | |

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The Law of Refraction | |

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Rays and Wavefronts | |

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Ray Optics and Optical Systems | |

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Power of a Spherical Surface | |

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Magnification by the Spherical Surface | |

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Power of Two Optically Refracting Surfaces | |

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Power of a Thin Lens in Air (Figure 11.12) | |

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Principal Planes and Newton's Equation | |

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Optical Helmholtz Equation for a Conjugate Plane at Infinity | |

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The Deviation Method for (a) Two Lenses and (b) a Thick Lens | |

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The Matrix Method | |

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Interference and Diffraction | |

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Interference | |

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Division of Amplitude | |

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Newton's Rings | |

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Michelson's Spectral Interferometer | |

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The Structure of Spectral Lines | |

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Fabry - Perot Interferometer | |

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Resolving Power of the Fabry - Perot Interferometer | |

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Division of Wavefront | |

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Interference from Two Equal Sources of Separation f | |

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Interference from Linear Array of N Equal Sources | |

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Diffraction | |

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Scale of the Intensity Distribution | |

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Intensity Distribution for Interference with Diffraction from N Identical Slits | |

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Fraunhofer Diffraction for Two Equal Slits (N = 2) | |

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Transmission Diffraction Grating (N Large) | |

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Resolving Power of Diffraction Grating | |

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Resolving Power in Terms of the Bandwidth Theorem | |

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Fraunhofer Diffraction from a Rectangular Aperture | |

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Fraunhofer Diffraction from a Circular Aperture | |

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Fraunhofer Far Field Diffraction | |

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The Michelson Stellar Interferometer | |

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The Convolution Array Theorem | |

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The Optical Transfer Function | |

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Fresnel Diffraction | |

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Holography | |

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Wave Mechanics | |

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Origins of Modern Quantum Theory | |

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Heisenberg's Uncertainty Principle | |

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Schrodinger's Wave Equation | |

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One-dimensional Infinite Potential Well | |

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Significance of the Amplitude [psi subscript n](x) of the Wave Function | |

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Particle in a Three-dimensional Box | |

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Number of Energy States in Interval E to E + dE | |

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The Potential Step | |

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The Square Potential Well | |

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The Harmonic Oscillator | |

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Electron Waves in a Solid | |

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Phonons | |

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Non-linear Oscillations and Chaos | |

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Free Vibrations of an Anharmonic Oscillator - Large Amplitude Motion of a Simple Pendulum | |

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Forced Oscillations - Non-linear Restoring Force | |

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Thermal Expansion of a Crystal | |

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Non-linear Effects in Electrical Devices | |

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Electrical Relaxation Oscillators | |

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Chaos in Population Biology | |

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Chaos in a Non-linear Electrical Oscillator | |

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Phase Space | |

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Repellor and Limit Cycle | |

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The Torus in Three-dimensional (x,x,t) Phase Space | |

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Chaotic Response of a Forced Non-linear Mechanical Oscillator | |

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A Brief Review | |

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Chaos in Fluids | |

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Recommended Further Reading | |

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References | |

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Non-linear Waves, Shocks and Solitons | |

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Non-linear Effects in Acoustic Waves | |

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Shock Front Thickness | |

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Equations of Conservation | |

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Mach Number | |

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Ratios of Gas Properties Across a Shock Front | |

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Strong Shocks | |

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Solitons | |

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Bibliography | |

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References | |

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Normal Modes, Phase Space and Statistical Physics | |

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Mathematical Derivation of the Statistical Distributions | |

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Kirchhoff's Integral Theorem | |

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Non-Linear Schrodinger Equation | |

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Index | |