Mathematical Modeling for Industry and Engineering

ISBN-10: 0132608944
ISBN-13: 9780132608947
Edition: 1998
List price: $73.33
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Description: Appropriate for upper level undergraduate and graduate courses in Mathematical Modeling offered in math, engineering departments, and applied math departments. Prerequisite is some exposure to differential equations and to matrices. This accessible  More...

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Book details

List price: $73.33
Copyright year: 1998
Publisher: Prentice Hall PTR
Publication date: 11/24/1997
Binding: Hardcover
Pages: 534
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.694
Language: English

Appropriate for upper level undergraduate and graduate courses in Mathematical Modeling offered in math, engineering departments, and applied math departments. Prerequisite is some exposure to differential equations and to matrices. This accessible and practical text is designed to nurture a "modeling intuition" for a wide range of disciplines, including mathematics, science, engineering, and economics. The numerous examples and mathematical techniques it includes demonstrate that mathematical modeling can be an important tool for revealing the underlying links between apparently disparate phenomena. Its flexible approach also reinforces the idea that there is no fixed set of tools for modeling.

The Modeling Art
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 (�) and 0(�) notation
Fourier Transform
Problems and Recommended Reading
Stability and Bifurcation
Potentials
Bifurcation
Catastrophe
Problems and Recommended Reading
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
Growth and Relaxation
Exponential Growth
The Relaxation Response
Self-Limiting Growth
Autoregulation
Economic Growth
Problems and Recommended Reading
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
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
Random Processes
Processes
Poisson Points and Random Walks
Poisson Points
Stochastic Processes
Markov Chain Models
The Parking Lot Problem
Orbital Debris
Distribution
Continuous-Time Processes
Service Facilities
Orbital Debris
Population Growth
Beyond Markov
General Point Processes
Queues
Cell-cycle Modeling
Simulation and the Monte-Carlo Method
Problems and Recommended Reading
Complex Systems
Coupled Oscillators
Biological Rhythms
Swaying Smokestacks
Dynamo Theory
Problems and Recommended Reading
Snakes and Chains
Snakes and Chains
A Line of Cars
Crystal Vibrations
Fixed-end Boundary Condition
Forced Vibrations
Filters and Ladders
Modeling the Ear
Earthquakes
Snakes versus Chains
Problems and Recommended Reading
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
Birth-Death Processes
First-order 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 Pull-back 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
Diffusion
How It Goes at Small Scales
The Diffusion Equation
The Einstein-Smoluchowski Relation
Conservation Laws
Heat Conduction
Newton's Law of Cooling
Reactions
Solving the Diffusion Equation
Signal Distortion
Steady-state Diffusion Boundary Conditions
Melting and Freezing
Moving Boundaries
Problems and Recommended Reading

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