
Mathematical Modeling for Industry and Engineering, 1/e
Thomas P. Svobodny, Wright State University Published November, 1997 by Prentice Hall Engineering/Science/Mathematics
 
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What is Modeling? Multiple Models; Shopping Around. An Example of the Modeling Process. Free Radical Formation by Ultrasound. Approximations. Curve Fitting and Parameter Estimating. The O (…Ã) and 0(…Ã) notation. Fourier Transform. Problems and Recommended Reading. 2. Stability and Bifurcation. Potentials. Bifurcation. Catastrophe. Problems and Recommended Reading. 3. Dimensions. Dimensions. Dimensions in Electricity and Magnetism. Scaling and Life. Dimensional Analysis and the Pi Procedure. The Pi Theorem. Limitations and Extensions. Scale Modeling. Problems and Recommended Reading. 4. Growth and Relaxation. Exponential Growth. The Relaxation Response. SelfLimiting Growth. Autoregulation. Economic Growth. Problems and Recommended Reading. 5. Vibrations. Free Vibrations. Mechanical Vibrations. Other Harmonic Oscillators. A Splash of Reality: Nonlinear Oscillations. Forced Vibrations. Linear Response. The Energy Cycle and the Power Absorption Curve. General Resonance. Nonlinear Response. Problems and Recommended Reading. 6. Random Thinking. Probabilities. The Law of Averages. Drunkard's Walk. Counting on Probabilities. Aside on Entropy and Information. Conditional Probabilities. Random Variables. Continuous Random Variables. Time between Random Events. Simulation of Random Variables. Problems and Recommended Reading. 7. Random Processes. Processes: Poisson Points and Random Walks. Poisson Points. Stochastic Processes. Markov Chain Models. The Parking Lot Problem. Orbital Debris: Distribution. ContinuousTime Processes. Service Facilities. Orbital Debris: Population Growth. Beyond Markov. General Point Processes. Queues. Cellcycle Modeling. Simulation and the MonteCarlo Method. Problems and Recommended Reading. 8. Complex Systems. Coupled Oscillators. Biological Rhythms. Swaying Smokestacks. Dynamo Theory. Problems and Recommended Reading. 9. Snakes and Chains. Snakes and Chains. A Line of Cars. Crystal Vibrations. Fixedend Boundary Condition. Forced Vibrations. Filters and Ladders. Modeling the Ear. Earthquakes. Snakes versus Chains. Problems and Recommended Reading. 10. Waves. Waves Here and There. Conservation Laws. An Example of the Method of Characteristics. Constitutive Laws. A nonlinear conservation law. Shocks. Conservation Laws in Higher Dimensions. Population Models. BirthDeath Processes. Firstorder Quasilinear Equations: General Theory. Cauchy Problem. Linear Systems. Blood Flow. Acoustics. Transmission Lines. Solving Linear Hyperbolic Systems. Solving the Transmission Line Equations. Systems of Nonlinear Conservation Laws. Momentum Equation Using Pullback Method. Sound Speed in Gases. Shock as a Dissipative Structure. Conservation of Energy. Quasilinear Hyperbolic Systems: Simple Waves. Water Waves. A Big Bore. Surge on Deep Water. Problems and Recommended Reading. 11. Diffusion. How It Goes at Small Scales. The Diffusion Equation. The EinsteinSmoluchowski Relation. Conservation Laws: Heat Conduction. Newton's Law of Cooling. Reactions. Solving the Diffusion Equation. Signal Distortion. Steadystate Diffusion Boundary Conditions. Melting and Freezing: Moving Boundaries. Problems and Recommended Reading.
