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The Modeling Art | |
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What is Modeling? Multiple Models; Shopping Around | |
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An Example of the Modeling Process | |
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Free Radical Formation by Ultrasound | |
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Approximations | |
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Curve Fitting and Parameter Estimating | |
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The O (�) and 0(�) notation | |
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Fourier Transform | |
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Problems and Recommended Reading | |
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Stability and Bifurcation | |
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Potentials | |
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Bifurcation | |
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Catastrophe | |
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Problems and Recommended Reading | |
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Dimensions | |
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Dimensions | |
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Dimensions in Electricity and Magnetism | |
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Scaling and Life | |
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Dimensional Analysis and the Pi Procedure | |
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The Pi Theorem | |
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Limitations and Extensions | |
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Scale Modeling | |
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Problems and Recommended Reading | |
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Growth and Relaxation | |
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Exponential Growth | |
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The Relaxation Response | |
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Self-Limiting Growth | |
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Autoregulation | |
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Economic Growth | |
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Problems and Recommended Reading | |
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Vibrations | |
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Free Vibrations | |
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Mechanical Vibrations | |
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Other Harmonic Oscillators | |
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A Splash of Reality | |
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Nonlinear Oscillations | |
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Forced Vibrations | |
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Linear Response | |
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The Energy Cycle and the Power Absorption Curve | |
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General Resonance | |
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Nonlinear Response | |
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Problems and Recommended Reading | |
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Random Thinking | |
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Probabilities | |
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The Law of Averages | |
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Drunkard's Walk | |
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Counting on Probabilities | |
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Aside on Entropy and Information | |
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Conditional Probabilities | |
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Random Variables | |
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Continuous Random Variables | |
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Time between Random Events | |
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Simulation of Random Variables | |
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Problems and Recommended Reading | |
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Random Processes | |
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Processes | |
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Poisson Points and Random Walks | |
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Poisson Points | |
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Stochastic Processes | |
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Markov Chain Models | |
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The Parking Lot Problem | |
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Orbital Debris | |
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Distribution | |
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Continuous-Time Processes | |
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Service Facilities | |
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Orbital Debris | |
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Population Growth | |
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Beyond Markov | |
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General Point Processes | |
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Queues | |
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Cell-cycle Modeling | |
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Simulation and the Monte-Carlo Method | |
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Problems and Recommended Reading | |
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Complex Systems | |
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Coupled Oscillators | |
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Biological Rhythms | |
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Swaying Smokestacks | |
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Dynamo Theory | |
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Problems and Recommended Reading | |
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Snakes and Chains | |
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Snakes and Chains | |
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A Line of Cars | |
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Crystal Vibrations | |
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Fixed-end Boundary Condition | |
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Forced Vibrations | |
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Filters and Ladders | |
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Modeling the Ear | |
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Earthquakes | |
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Snakes versus Chains | |
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Problems and Recommended Reading | |
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Waves | |
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Waves Here and There | |
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Conservation Laws | |
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An Example of the Method of Characteristics | |
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Constitutive Laws | |
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A nonlinear conservation law | |
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Shocks | |
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Conservation Laws in Higher Dimensions | |
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Population Models | |
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Birth-Death Processes | |
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First-order Quasilinear Equations | |
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General Theory | |
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Cauchy Problem | |
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Linear Systems | |
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Blood Flow | |
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Acoustics | |
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Transmission Lines | |
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Solving Linear Hyperbolic Systems | |
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Solving the Transmission Line Equations | |
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Systems of Nonlinear Conservation Laws | |
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Momentum Equation Using Pull-back Method | |
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Sound Speed in Gases | |
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Shock as a Dissipative Structure | |
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Conservation of Energy | |
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Quasilinear Hyperbolic Systems | |
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Simple Waves | |
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Water Waves | |
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A Big Bore | |
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Surge on Deep Water | |
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Problems and Recommended Reading | |
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Diffusion | |
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How It Goes at Small Scales | |
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The Diffusion Equation | |
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The Einstein-Smoluchowski Relation | |
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Conservation Laws | |
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Heat Conduction | |
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Newton's Law of Cooling | |
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Reactions | |
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Solving the Diffusion Equation | |
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Signal Distortion | |
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Steady-state Diffusion Boundary Conditions | |
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Melting and Freezing | |
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Moving Boundaries | |
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Problems and Recommended Reading | |