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Mathematical and Experimental Modeling of Physical and Biological Processes

H. T. Banks and H. T. Tran
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Hardcover with CDROM
Textbooks in Mathematics
We do not plan to review this book.

Introduction: The Iterative Modeling Process


Modeling and Inverse Problems

Mechanical Vibrations

Inverse Problems

Mathematical and Statistical Aspects of Inverse Problems

Probability and Statistics Overview

Parameter Estimation or Inverse Problems

Computation of sigman, Standard Errors, and Confidence Intervals

Investigation of Statistical Assumptions

Statistically Based Model Comparison Techniques

Mass Balance and Mass Transport


Compartmental Concepts

Compartment Modeling

General Mass Transport Equations

Heat Conduction

Motivating Problems

Mathematical Modeling of Heat Transfer

Experimental Modeling of Heat Transfer

Structural Modeling: Force/Moments Balance

Motivation: Control of Acoustics/Structural Interactions

Introduction to Mechanics of Elastic Solids

Deformations of Beams

Separation of Variables: Modes and Mode Shapes

Numerical Approximations: Galerkin’s Method

Energy Functional Formulation

The Finite Element Method

Experimental Beam Vibration Analysis

Beam Vibrational Control and Real-Time Implementation


Controllability and Observability of Linear Systems

Design of State Feedback Control Systems and State Estimators

Pole Placement (Relocation) Problem

Linear Quadratic Regulator Theory

Beam Vibrational Control: Real-Time Feedback Control Implementation

Wave Propagation

Fluid Dynamics

Fluid Waves

Experimental Modeling of the Wave Equation

Size-Structured Population Models

Introduction: A Motivating Application

A Single Species Model (Malthusian Law)

The Logistic Model

A Predator/Prey Model

A Size-Structured Population Model

The Sinko–Streifer Model and Inverse Problems

Size Structure and Mosquitofish Populations

Appendix A: An Introduction to Fourier Techniques

Fourier Series

Fourier Transforms

Appendix B: Review of Vector Calculus

References appear at the end of each chapter.