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Mathematical and Experimental Modeling of Physical and Biological Processes

H.T. Banks, H.T. Tran
Publication Date:
January 12, 2009
Content Details:
298 pages

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  • About the Book

    Book Summary

    Through several case study problems from industrial and scientific research laboratory applications, Mathematical and Experimental Modeling of Physical and Biological Processes provides students with a fundamental understanding of how mathematics is applied to problems in science and engineering. For each case study problem, the authors discuss why a model is needed and what goals can be achieved with the model.

    Exploring what mathematics can reveal about applications, the book focuses on the design of appropriate experiments to validate the development of mathematical models. It guides students through the modeling process, from empirical observations and formalization of properties to model analysis and interpretation of results. The authors also describe the hardware and software tools used to design the experiments so faculty/students can duplicate them.

    Integrating real-world applications into the traditional mathematics curriculum, this textbook deals with the formulation and analysis of mathematical models in science and engineering. It gives students an appreciation of the use of mathematics and encourages them to further study the applied topics. Real experimental data for projects can be downloaded from CRC Press Online.


      • Discusses mathematical modeling in the context of case study problems that arise in industry and government laboratories
      • Covers thermal imaging and detection, dynamic properties of beams, acoustics and fluid transport, and size-structured population dynamics for marine populations
      • Explains physical and biological relationships and mechanisms through a first principles-based fundamental modeling approach
      • Emphasizes model validation through specific laboratory experiments as well as data collection and analysis
      • Includes several application-oriented projects—all developed by the authors—to enhance learning 
      • Offers real experimental data for projects at CRC Press Online


      …would I buy this textbook? Again, absolutely yes! The concise and clear style in which the background is written for each chapter will be invaluable as a quick, ‘before the lecture is given’ refresher. … Most of the topics covered are those which have arisen out of the research projects that the authors have conducted themselves. This is the kind of hands-on experience that a lecturer would need in order to make the laboratory experiences for the students enjoyable and rewarding. … the true value of this textbook, namely, [is that] it provides a stimulus package to provoke the reader to adopt a similar teaching philosophy.
      Mathematical Reviews, Issue 2010f

      The aim of this book is twofold: to develop some standard models of physical and biological processes (the transport equation, heat conduction, the beam equation, fluid dynamics, and structured population models) in mathematical language, and probably more importantly, to show how and why to design concrete engineering experiments for comparing numerical results of models with specific experimental data. … The book can be recommended to advanced undergraduate students for whom mathematics is a bit more than just proving theorems. Teachers can find suggestions for motivations for introductory parts of lectures on ordinary differential equations and partial differential equations.
      EMS Newsletter, September 2009

  • Contents

    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.