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Linear Difference Equations of Higher Order

  • Saber N. Elaydi
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In this chapter we examine linear difference equations of high order, namely, those involving a single dependent variable1. Those equations arise in almost every field of scientific inquiry, from population dynamics (the study of a single species) to economics (the study of a single commodity) to physics (the study of the motion of a single body). We will be acquainted with some of these applications in this chapter. We start this chapter by introducing some rudiments of difference calculus which are essential in the study of linear equations.

Keywords

General Solution Difference Equation National Income Characteristic Root Fibonacci Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    L. Edelstein-Keshet, Mathematical Models in Biology, Random House, New York, 1988.zbMATHGoogle Scholar
  2. [2]
    S. Goldberg, Introduction to Difference Equations, Dover, New York, 1986.Google Scholar
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    P.A. Samuelson, “Interactions Between the Multiplier Analysis and the Principle of Acceleration,” Rev. Econom. Stat., 21 (1939), 75–78CrossRefGoogle Scholar
  4. P.A. Samuelson, Readings in Business Cycle Theory, Blakiston Co., Philadelphia, 1944.Google Scholar
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    C.E. Shannon and W. Weaver, The Mathematical Theory of Communication, University of Illinois, Urbana, 1949, pp. 7–8.zbMATHGoogle Scholar

Bibliography

  1. R.P. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.zbMATHGoogle Scholar
  2. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Academic, New York, 1988.zbMATHGoogle Scholar
  3. R. Mickens, Difference Equations, Van Nostrand, Reinhold, New York, 1990.zbMATHGoogle Scholar
  4. K.S. Miller, Linear Difference Equations, W.A. Benjamin, New York, 1968.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • Saber N. Elaydi
    • 1
  1. 1.Department of MathematicsTrinity UniversitySan AntonioUSA

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