Abstract
Mathematical modeling plays useful roles towards sustainable development in arriving at the understanding, prediction and control of developmental processes. For long term prediction ordinary differential equation models are used. We have described exponential and logistic equation models as used in studies of growth of population, water quality, fishery and economy. Equilibrium solutions and their stability have been illustrated. For controlling developmental process, the relevant utility function is maximized with the equation of growth as constraint. This methodology is illustrated from an example of economic growth model. It is concluded that for sustainable development, it is necessary to build comprehensive mathematical models of human-environmental systems.
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References
Beltrami E (1987) Mathematics for dynamic modeling. Academic, Boston, p 277
Chapra S (1975) Comment on ‘An empirical method of estimating the retention of phosphorus in lakes’ by W.B. Kirchner and P.J. Dillon. Water Resour Res 11:1033–1034
Dasgupta P (2008) Mathematics and economic reasoning. In: Gowers WT, Barrow-Green J (eds) The Princeton companion to mathematics. Princeton University Press, Princeton
Gershenfield N (1999) The nature of mathematical modeling. Cambridge University Press, Cambridge, p 344
Kapur JN (1985) Mathematical models in biology and medicine. Affiliated East–West Press, New Delhi, p 520
May RM (1976) Simple mathematical models with very complicated dynamics. Nature (Lond) 261: 459–467
Meerschaert MM (2007) Mathematical modeling. Elsevier, Amsterdam, p 335
Modis T (2012) Long-Term GDP forecasts and the prospects for growth. http://www.growth-dynamics.com/articles/GDP_long_term_TFSC.pdf
Schaefer MB (1954) Some aspects of the dynamics of populations, important for the management of the commercial marine fisheries. Inter Am Trop Tuna Comm Bull 1:27–56
Acknowledgements
The author is grateful to the Indian National Science Academy for award of a INSA Senior Scientist scheme. He is also grateful to the Director of CSIR-NGRI for his kind support.
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Singh, R.N. (2014). Mathematical Models in Sustainable Development. In: Fulekar, M., Pathak, B., Kale, R. (eds) Environment and Sustainable Development. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1166-2_14
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DOI: https://doi.org/10.1007/978-81-322-1166-2_14
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