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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 | |