Tags: system

All Categories (1-20 of 113)

  1. 1-027-S-StochasticProcesses

    04 Jun 2015 | | Contributor(s):: Brian Winkel

    We build the infinite set of first order differential equations for modeling a stochastic process, the so-called birth and death equations. We will only need to use integrating factor solution strategy or DSolve in Mathematica for success.  We work to build our model of random events which...

  2. 1-029-S-ConeToCubeFlow

    02 Mar 2016 | | Contributor(s):: Sania Qureshi

    We consider a configuration of two containers. An inverted right circular cone with a hole in point at the bottom  is suspended above an open-topped cube which also has a hole in the center of the bottom. The cone is filled with water and we wish to model the water flow from cone to cube and...

  3. 1-108-S-PoissonProcess

    27 Aug 2018 | | Contributor(s):: Mehdi Hakim-Hashemi

    In this project students learn to derive the probability density function (pdf) of the Poisson distribution and the cumulative distribution (cdf) of the waiting time. They will use them to solve problems in stochastic processes.

  4. 1966-Intriligator, Michael D.  and Dagobert L. Brito - Predator-Prey Model of Guerrilla Warfare

    20 Jun 2015 | | Contributor(s):: Michael D. Intriligator, Dagobert L. Brito

    Article Review and AnnotationIntriligator, Michael D.  and Dagobert L. Brito. 1988.  A Predator-Prey Model of Guerrilla Warfare. Synthese . 76(2): 235-244. Special issue: Formal Analysis in International Relations.Excerpt from Article Abstract: “The purpose of this paper...

  5. 1968-Wagner, J. G.,G. K. Aghajanian, and O. H. L. Bing - Correlation of performance test scores with tissue concentration of lysergic acid diethylamide.

    26 Jun 2015 | | Contributor(s):: J. G. Wagner, G. K. Aghajanian, O. H. L. Bing

    Wagner, J. G.,G. K. Aghajanian, and O. H. L. Bing. 1968. Correlation of performance test scores with tissue concentration of lysergic acid diethylamide. Clinical Pharmacology and Therapeutics. 9(5): 635-638.See https://ascpt.onlinelibrary.wiley.com/doi/10.1002/cpt196895635 .This...

  6. 1977-Freedman, H. I. and Paul Waltman - Mathematical models of population interactions with dispersal. I Stability of two habitats with and without a predator

    01 Apr 2020 | | Contributor(s):: Brian Winkel

    FREEDMAN, H. I. AND PAUL WALTMAN, 1977. MATHEMATICAL MODELS OF POPULATION INTERACTIONS WITHDISPERSAL. I: STABILITY OF TWO HABITATS WITH AND WITHOUTA PREDATOR.  SIAM J. APPL. MATH. 32(3): 631-648,See https://epubs.siam.org/doi/abs/10.1137/0132052?mobileUi=0&...

  7. 1988-Strogatz, Steven H. - Love Affairs and Differential Equations.

    26 Nov 2017 | | Contributor(s):: Brian Winkel

    Strogatz, Steven H. 1988. Love Affairs and Differential Equations. Mathematics Magazine. 61(7):  35.See http://ai.stanford.edu/~rajatr/articles/SS_love_dEq.pdf .This is a system of differential equations to describe the love between Shakespeare’s Romeo and...

  8. 1991-Chicone, Carmine - Ordinary Differential Equations with Applications. Textbook.

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Chicone, Carmine. 1991. Ordinary Differential Equations with Applications. New York: Springer. 571 pp.See http://math.ecnu.edu.cn/~zmwang/teaching/Advanced_ODE-2014-2015/1-Textbook_and_Reference_book/2-Ordinary%20Differential%20Equations%20with%20Applications.pdf . Accessed 6 September...

  9. 1991-Watson, Jane M. - Building probability models in a differential equations course

    26 Jun 2015 | | Contributor(s):: Jane M. Watson

    Watson, Jane M. 1991. Building probability models in a differential equations course. International Journal of Mathematical Education in Science and Technology. 22(4): 507-517.See https://www.tandfonline.com/doi/abs/10.1080/0020739910220402 .Article Abstract: An application is...

  10. 1994-McDill, J. M.  and Bjorn Felsager - The Lighter Side of Differential Equations

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    McDill, J. M.  and Bjorn Felsager.  1994. The Lighter Side of Differential Equations. The College Mathematics Journal. 25(2): 448-452.See https://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/the-lighter-side-of-differential-equations .First...

  11. 2000-Erdman, Donald  and Maurice M. Morelock - A Study of Kinetics: The Estimation and Simulation of Systems of First-Order Differential Equations. Notes.

    25 Mar 2020 | | Contributor(s):: Brian Winkel

    Erdman, Donald  and Maurice M. Morelock. 2000. A Study of Kinetics: The Estimation and Simulation of Systems of First-Order Differential Equations. Notes. 8...

  12. 2001-Edwards, David A. and Ron Buckmire - A differential equation model of North American cinematic box-office dynamics.

    20 Jun 2015 | | Contributor(s):: David A. Edwards, Ron Buckmire

    Edwards, David A. and Ron Buckmire. 2001. A differential equation model of North American cinematic box-office dynamics. IMA Journal of Management Mathematics. 12: 41-74.See https://academic.oup.com/imaman/article-abstract/12/1/41/664476?redirectedFrom=fulltext .Article Abstract: A...

  13. 2002-de Pillis, L. G. and A. E. Radunskaya - Parameter Estimation for Tumor-Immune ODE System. Slides.

    21 Sep 2017 | | Contributor(s):: Brian Winkel

    de Pillis, L. G. and A. E. Radunskaya. 2002. Parameter Estimation for Tumor-Immune ODE System, 24 slides. See https://pages.pomona.edu/~aer04747/TumorModule/parameter_estimation.pdf . This is a very thorough and complete introduction to estimating parameters for a simple differential...

  14. 2003-Fay, T.H. and S. D. Graham - Coupled spring equations. 

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Fay, T.H. and S. D. Graham. 2003. Coupled spring equations.  Int.J. Math. Educ. Sci. Technol. 34(1): 65-79.  See https://www.tandfonline.com/doi/abs/10.1080/0020739021000029258 . ABSTRACT Coupled spring equations for modelling the motion of two springs with...

  15. 2003-Rasmussen, Chris and  Michael Keynes - Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations

    03 Mar 2018 | | Contributor(s):: Chris Rasmussen, Michael Keynes

    Rasmussen, Chris and  Michael Keynes. 2003. Lines of Eigenvectors and Solutions to Systems of Linear Differential Equations.  PRIMUS. 13(4): 308-320.See - https://www.tandfonline.com/doi/abs/10.1080/10511970308984065 .Abstract: The purpose of this paper is to describe an...

  16. 2003-Yildirim, Necmettin and Michael C. Mackey - Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data.

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Yildirim, Necmettin and Michael C. Mackey. 2003.  Feedback Regulation in the Lactose Operon: A Mathematical Modeling Study and Comparison with Experimental Data. Biophysical Journal. 84:  2841–2851.   See https://pubmed.ncbi.nlm.nih.gov/12719218/...

  17. 2004-Jones, M. and D. Thomas - Controlling wound healing through debridement.  Preprint.

    08 Sep 2017 | | Contributor(s):: Brian Winkel

    Jones, M. and D. Thomas. Controlling wound healing through debridement.  Preprint.See https://digitalcommons.montclair.edu/appliedmath-stats-facpubs/33/. Abstract. The formation of slough (dead tissue) on a wound is widely accepted as an inhibitor to natural wound healing....

  18. 2005-Sprott, J. C. - Dynamical Models of Happiness.

    28 Nov 2017 | | Contributor(s):: Brian Winkel

    Sprott, J. C. 2005. Dynamical Models of Happiness. Nonlinear Dynamics, Psychology, and Life Sciences. 9(1): 23-35.See https://sprott.physics.wisc.edu/pubs/paper281.pdf.Abstract: A sequence of models for the time evolution of one’s happiness in response to external events is...

  19. 2005-Wedenberg, Minna - Pharmacokinetic modeling of gastric emptying and small intestinal transit time in dogs using paracetamol and sulfasalazine as markers

    09 Sep 2017 | | Contributor(s):: Brian Winkel

    Wedenberg, Minna. 2005. Pharmacokinetic modeling of gastric emptying and small intestinal transit time in dogs using paracetamol and sulfasalazine as markers. Master’s Degree Project.  Uppsala Universitet. 41...

  20. 2006-Coleman, Michael J. - Population Modeling with Ordinary Differential Equations - Notes. 

    13 Mar 2020 | | Contributor(s):: Brian Winkel

    Coleman, Michael J.  2006. Population Modeling with Ordinary Differential Equations - Notes. See https://www2.gwu.edu/~mathgss/old_site/Slides/MikeC_Seminar.pdfAbstract: Population modeling is a common application of ordinary differential equations and can be studied...