Mathematical and experimental modeling of physical and biological processes /
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Author / Creator: | Banks, H. T. (Harvey Thomas), 1940- |
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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 |
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