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Differential Equations

In: Mathematics and Methodology for Economics

Author

Listed:
  • Wolfgang Eichhorn

    (Karlsruhe Institute of Technology (KIT))

  • Winfried Gleißner

    (University of Applied Sciences Landshut)

Abstract

In this chapter we deal with differential equations. After defining differential equations we proceed with first order linear differential equations but we also discuss some nonlinear important examples: the Bernoulli and the Riccati equations. The latter is used to investigate the saturation of markets, the logistic growth. As linear differential equations of second order are very important in mathematical modelling they are discussed in full detail. At last we deal with a ubiquitous model in economics and biology the predator-prey model and the Lotka-Volterra differential equations, whose solutions are based on the Poincaré-Bendixson theorem.

Suggested Citation

  • Wolfgang Eichhorn & Winfried Gleißner, 2016. "Differential Equations," Springer Texts in Business and Economics, in: Mathematics and Methodology for Economics, edition 1, chapter 11, pages 535-563, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-23353-6_11
    DOI: 10.1007/978-3-319-23353-6_11
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