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PRIMUS
Problems, Resources, and Issues in Mathematics Undergraduate Studies
Volume 21, 2011 - Issue 2: A Tribute to Brian J. Winkel
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Original Articles

Parameter Estimates in Differential Equation Models for Population Growth

Pages 101-129 | Published online: 13 Feb 2011

REFERENCES

  • Banks , H. T. and Kunisch , K. 1989 . Estimation Techniques for Distributed Parameter Systems , Boston : Birkhauser .
  • Banks , H. T. and Tran , H. T. 2009 . Mathematical and Experimental Modeling of Physical and Biological Processes , Boca Raton, FL : CRC Press .
  • Winkel, B. J. 1996. Complex, technology-based, problem-solving in calculus http://www.rosehulman.edu/Class/CalculusProbs/ (http://www.rosehulman.edu/Class/CalculusProbs/) (Accessed: 28 January 2010 ).
  • Fletcher , R. 1987 . Practical Methods of Optimization , 3rd , New York : John Wiley & Sons .
  • Gause , G. F. and Alpatov , W. W. 1931 . Die logistische kurve von Verhulst-Pearl und ihre anwendung im gebiet der quantitativen biologie . Biologisches Zentralblatt. , 51 : 1 – 14 .
  • Gause, G. F. 1932. Experimental studies on the struggle for existence. Journal of Experimental Biology. 9(4): 389–402. Available on-line http://jeb.biologists.org/cgi/reprint/9/4/389.pdf (http://jeb.biologists.org/cgi/reprint/9/4/389.pdf) (Accessed: 3 January 2010 ).
  • Gause, G. F. 1971. The Struggle for Existence. New York: Dover Publications, Inc. First published in 1934 by the Williams & Wilkins Company and available completely on the internet http://www.ggause.com/Contgau.htm (http://www.ggause.com/Contgau.htm) (Accessed: 31 March 2008 ).
  • Gause , G. F. , Nastukova , O. K. and Alpatov , W. W. 1934 . The influence of biologically conditioned media on the growth of a mixed population of Paramecium cadatum and P. aureliax . Journal of Animal Ecology. , 3 ( 2 ) : 222 – 230 .
  • Gordon , S. P. 2009 . Modeling population growth and extinction . PRIMUS. , 19 ( 6 ) : 548 – 560 .
  • Graham , J. and Lerch , M. 2007 . Parameter recovery for a differential equation model . PRIMUS. , 17 ( 2 ) : 148 – 156 .
  • Groetsch , C. W. 1999 . Inverse Problems in the Mathematical Sciences , Washington, DC : The Mathematical Association of America .
  • Groetsch , C. W. 1999 . Inverse Problems: Activities for Undergraduates , Braunschweig/Weisbaden, , Germany : Vieweg .
  • Hutchinson , G. E. 1978. Introduction to Population Ecology , New Haven, CT : Yale University Press .
  • Kingsland , S. 1982 . The Refractory Model: The logistic curve and the history of population ecology . The Quarterly Review of Biology. , 57 : 29 – 52 .
  • Klebanoff , A. and Winkel , B. J. Technology-based problems in calculus from science and engineering . Proceedings of the 1996 ASEE Conference, June 1996. Session 1265: Applications in the Mathematics Classroom, Paper 126503. Conference CD-ROM. Washington, DC: ASEE .
  • knol: A Unit of Knowledge. Competitive Exclusion (Gause's Principle) and Limiting Similarity http://knol.google.com/k/competitive-exclusion-gause-s-principle-and-limiting-similarity# (http://knol.google.com/k/competitive-exclusion-gause-s-principle-and-limiting-similarity#) (Accessed: 3 January 2010 ).
  • Lomen , D. and Lovelock , D. 1998 . Differential Equations: Graphics, Models, Data , New York : John Wiley & Sons .
  • Ledder , G. 2008 . An experimental approach to mathematical modeling in biology . PRIMUS. , 18 ( 1 ) : 119 – 138 .
  • Winkel , B. J. and Myers , J. 2007 . Mystery circuit in mathematics class . The UMAP Journal. , 28 ( 1 ) : 15 – 25 .
  • Winkel , B. J. and Landry , K. 2008 . Peak frequency responses and tuned mass dampers — Exciting applications of systems of differential equations . The UMAP Journal. , 29 ( 1 ) : 15 – 30 .
  • Winkel , B. J. 2009 . Parameter estimates in differential equation models for free fall with resistance . In preparation. ,
  • Winkel , B. J. 2009 . Population modeling with M&Ms . International Journal of Mathematical Education in Science and Technology. , 40 ( 4 ) : 554 – 558 .
  • Winkel, B. J. 2010. Ranting for CAS — Longing for the world to be fully in post computer algebra system emergence. Mathematica Militaris. 18(1): 23–2819 February 2010 http://www.dean.usma.edu/math/pubs/mathmil/default.htm (http://www.dean.usma.edu/math/pubs/mathmil/default.htm)
  • Winkel , B. J. 2011 . Parameter estimates in differential equation models for chemical kinetics . International Journal of Mathematical Education in Science and Technology. , 42 ( 1 ) : 37 – 51 .

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