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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 | |