Mathematical and experimental modeling of physical and biological processes /

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Bibliographic Details
Author / Creator:Banks, H. T. (Harvey Thomas), 1940-
Imprint:Boca Raton : CRC Press, c2009.
Description:299 p. : ill. ; 25 cm. + 1 CD-ROM (4 3/4 in.).
Language:English
Series:Textbooks in mathematics
Textbooks in mathematics (Boca Raton, Fla.)
Subject:
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7630834
Hidden Bibliographic Details
Other authors / contributors:Tran, H. T.
ISBN:9781420073379 (hardcover : alk. paper)
1420073370 (hardcover : alk. paper)
Notes:"A Chapman & Hall book."
Includes bibliographical references and index.
Table of Contents:
  • 1. Introduction: The Iterative Modeling Process
  • 2. Modeling and Inverse Problems
  • 2.1. Mechanical Vibrations
  • 2.2. Inverse Problems
  • References
  • 3. Mathematical and Statistical Aspects of Inverse Problems
  • 3.1. Probability and Statistics Overview
  • 3.1.1. Probability
  • 3.1.2. Random Variables
  • 3.1.3. Statistical Averages of Random Variables
  • 3.1.4. Special Probability Distributions
  • 3.2. Parameter Estimation or Inverse Problems
  • 3.2.1. The Mathematical Model
  • 3.2.2. The Statistical Model
  • 3.2.3. Known Error Processes: Maximum Likelihood Estimators
  • 3.2.3.1. Normally Distributed Errors
  • 3.2.4. Unspecified Error Distributions and Asymptotic Theory
  • 3.2.5. Ordinary Least Squares (OLS)
  • 3.2.6. Numerical Implementation of the Vector OLS Procedure
  • 3.2.7. Generalized Least Squares (GLS)
  • 3.2.8. GLS Motivation
  • 3.2.9. Numerical Implementation of the GLS Procedure
  • 3.3. Computation of , Standard Errors and Confidence Intervals
  • 3.4. Investigation of Statistical Assumptions
  • 3.4.1. Residual Plots
  • 3.4.2. An Example Using Residual Plots
  • 3.5. Statistically Based Model Comparison Techniques
  • 3.5.1. RSS Based Statistical Tests
  • 3.5.1.1. P-Values
  • 3.5.1.2. Alternative Statement
  • 3.5.2. Application: Cat-Brain Diffusion/Convection Problem
  • References
  • 4. Mass Balance and Mass Transport
  • 4.1. Introduction
  • 4.2. Compartmental Concepts
  • 4.3. Compartment Modeling
  • 4.4. General Mass Transport Equations
  • 4.4.1. Mass Flux Law in a Stationary (Non-Moving) Fluid
  • 4.4.2. Mass Flux in a Moving Fluid
  • References
  • 5. Heat Conduction
  • 5.1. Motivating Problems
  • 5.1.1. Radio-Frequency Bonding of Adhesives
  • 5.1.2. Thermal Testing of Structures
  • 5.2. Mathematical Modeling of Heat Transfer
  • 5.2.1. Introduction
  • 5.2.2. Fourier's Law of Heat Conduction
  • 5.2.3. Heat Equation
  • 5.2.4. Boundary Conditions and Initial Conditions
  • 5.2.5. Properties of Solutions
  • 5.3. Experimental Modeling of Heat Transfer
  • 5.3.1. The Thermocouple as a Temperature Measuring Device
  • 5.3.2. Detailed Hardware and Software Lists
  • References
  • 6. Structural Modeling: Force/Moments Balance
  • 6.1. Motivation: Control of Acoustics/Structural Interactions
  • 6.2. Introduction to Mechanics of Elastic Solids
  • 6.2.1. Normal Stress and Strain
  • 6.2.2. Stress and Strain Relationship (Hooke's Law)
  • 6.2.3. Shear Stress and Strain
  • 6.3. Deformations of Beams
  • 6.3.1. Differential Equations of Thin Beam Deflections
  • 6.3.1.1. Force Balance
  • 6.3.1.2. Moment Balance
  • 6.3.1.3. Moment Computation
  • 6.3.1.4. Initial Conditions
  • 6.3.1.5. Boundary Conditions
  • 6.4. Separation of Variables: Modes and Mode Shapes
  • 6.5. Numerical Approximations: Galerkin's Method
  • 6.6. Energy Functional Formulation
  • 6.7. The Finite Element Method
  • 6.8. Experimental Beam Vibration Analysis
  • References
  • 7. Beam Vibrational Control and Real-Time Implementation
  • 7.1. Introduction
  • 7.2. Controllability and Observability of Linear Systems
  • 7.2.1. Controllability
  • 7.2.1.1. Time-Varying Case
  • 7.2.1.2. Time-Invariant Case
  • 7.2.2. Observability
  • 7.2.2.1. Time-Varying Case
  • 7.2.2.2. Time-Invariant Case
  • 7.3. Design of State Feedback Control Systems and State Estimators
  • 7.3.1. Effect of State Feedback on System Properties
  • 7.3.1.1. Stability
  • 7.3.1.2. Controllability
  • 7.3.1.3. Observability
  • 7.4. Pole Placement (Relocation) Problem
  • 7.4.1. State Estimator (Luenberger Observer)
  • 7.4.2. Dynamic Output Feedback Compensator
  • 7.5. Linear Quadratic Regulator Theory
  • 7.6. Beam Vibrational Control: Real-Time Feedback Control Implementation
  • References
  • 8. Wave Propagation
  • 8.1. Fluid Dynamics
  • 8.1.1. Newton's Law of Viscosity
  • 8.1.2. Derivative in Fluid Flows
  • 8.1.3. Equations of Fluid Motion
  • 8.2. Fluid Waves
  • 8.2.1. Terminology
  • 8.2.2. Sound Waves
  • 8.2.2.1. Euler's Equation
  • 8.2.2.2. Equation of Continuity
  • 8.2.2.3. Equation of State
  • 8.2.3. Wave Equations
  • 8.3. Experimental Modeling of the Wave Equation
  • References
  • 9. Size-Structured Population Models
  • 9.1. Introduction: A Motivating Application
  • 9.2. A Single Species Model (Malthusian Law)
  • 9.3. The Logistic Model
  • 9.4. A Predator/Prey Model
  • 9.5. A Size-Structured Population Model
  • 9.6. The Sinko-Streifer Model and Inverse Problems
  • 9.7. Size Structure and Mosquitofish Populations
  • References
  • A. An Introduction to Fourier Techniques
  • A.1. Fourier Series
  • A.2. Fourier Transforms
  • B. Review of Vector Calculus
  • References
  • Index