Laplace Transforms and Coupled Differential Equations

  • Douglas J. Crawford-Brown


Chapter 3 considered systems in which the rate of flow between two compartments was described by zeroth or first order kinetics, and where flow was in one direction only. Solutions were obtained by solving for the amount in the first compartment of the chain, and then proceeding through the chain to the final compartment in the order in which compartments are encountered. This process of solution was effective because Bernoulli’s solution to any one compartment involved knowledge only of the functions describing compartments “higher” in the chain. At no time did the differential equation for a given compartment involve information on compartments “further down” the chain.


Differential Equation State Vector Couple System Environmental System Quadratic Formula 


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  1. 1.
    W. Schlesinger, Biogeochemistry: An Analysis of Global Change, Academic Press, New York, 1997.Google Scholar
  2. 2.
    A. Ford, Modeling the Environment: A n Introduction to System Dynamics Modeling of Environmental Systems, Island Press, Washington, DC, 1999.Google Scholar
  3. 3.
    M. Allaby, Basics of Environmental Science, Routledge, London, 1996.Google Scholar
  4. 4.
    M Spiegel, Laplace Transforms, Schaum Publishing Co., NY, 1965Google Scholar
  5. 5.
    D. Crawford-Brown, Theoretical and Mathematical Foundations of Human Health Risk Analysis, Kluwer Academic Publishers, 1997.CrossRefGoogle Scholar
  6. 6.
    F. Nixon, Handbook of Laplace Transformation, Prentice-Hall, Englewood Cliffs, NJ, 1960.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Douglas J. Crawford-Brown
    • 1
  1. 1.University of North CarolinaChapel HillUSA

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