Tags: fitting

All Categories (1-17 of 17)

  1. 6-029-S-TumorGrowth

    04 Aug 2021 | | Contributor(s):: Allison Leigh Lewis

    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time. Students should have prior experience with solving ODEs using the separable...

  2. 2019-Hu,Yueqin and Raymond Treinen - A one-step method for modelling longitudinal data with differential equations.

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

    Hu,Yueqin and Raymond Treinen. 2019.  A one-step method for modelling longitudinal data with differential equations. British Journal of Mathematical and Statistical Psychology. 72: 38–60See https://bpspsychub.onlinelibrary.wiley.com/doi/abs/10.1111/bmsp.12135...

  3. 2018-Tatro, Dyjuan - The Mathematics of Cancer: Fitting the Gompertz Equation to Tumor Growth. Senior Project.

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

    Tatro, Dyjuan. 2018. The Mathematics of Cancer: Fitting the Gompertz Equation to Tumor Growth. Bard CollegeBard Digital Commons. Senior Projects Spring 2018 Bard Undergraduate Senior Projects. 23 pages.Abstract: Mathematical models are finding increased use in biology, and...

  4. 2018-McCarthy, C. - Newton's Law of Cooling.

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

    McCarthy, C. 2018.  Newton’s Law of Cooling.See  https://mccarthymat501.commons.gc.cuny.edu/newtonian-cooling/ .Active classroom scenario with step-by-step procedure, data, R code. Scenario: You have hot water (initial temperature ) in a container, say a cup....

  5. 1-084-S-GoingViral

    31 Aug 2019 | | Contributor(s):: Bill Skerbitz

    Students employ randomization in order to create a simulation of the spread of a viral disease in a population (the classroom).  Students then use qualitative analysis of the expected behavior of the virus to devise a logistic differential equation.  Finally, students solve the...

  6. 2019-Bukaita, Wisam Victor Yossif; Kelcey Meaney; and Angie Dimopulos - Ice Coverage in the Arctic Climate over time

    17 Aug 2019 | | Contributor(s):: Wisam Victor Yossif Bukaita, Kelcey Meaney, Angie Dimopulos

    In this paper, entitled Ice Coverage in the Arctic Climate, from two students, Angie Dimopulos and Kelcey Heaney, and their professor, Dr. Wisam Bukaita, ice coverage in the Arctic is modeled over time. We present their abstract here and include the paper itself.ABSTRACT The Arctic plays a...

  7. 1-054-S-GrowthInFarmland

    14 Aug 2018 | | Contributor(s):: Richard Spindler

    An enriching project developing a model from data with missing temporal information is described. Students fit functions to the data that leads to the creation of a differential equations model, which they then are required to analyze in multiple ways. Different fits, modeling approaches, and...

  8. 2017-Ramsay, Jim - From Data To Differential Equations

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

    Ramsay, Jim.  From Data To Differential Equations. Presentation. 52 slides. Themes: Differential equations are powerful tools for modeling data. There are new methods for estimating differential equations directly from data. Some examples are offered, drawn from...

  9. 2015-Enderling, Heiko - Integrating experimental data to calibrate quantitative cancer models. preprint.

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

    Enderling, Heiko. 2015. Integrating experimental data to calibrate quantitative cancer models. Preprint.  3 pp.See https://www.biorxiv.org/content/10.1101/032102v1.Abstract:  For quantitative cancer models to be meaningful and interpretable the number of unknown parameters...

  10. 1999-Allen, David M. 1999. Love and differential equations:  An Introduction to Modeling. PowerPoint Presentation.

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

    Allen, David M. 1999. Love and differential equations:  An Introduction to Modeling. PowerPoint Presentation. 44 slides. This is a set of slides with lots of topics touched upon briefly, but in the end there is an analysis of the Romeo and Juliet relationship. Keywords: differential...

  11. 2001-Motulsky, Harvey and Arthur Christopoulos - Curve fitting guide

    01 Mar 2017 | | Contributor(s):: Brian Winkel

    Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve FittingMotulsky, Harvey and Arthur Christopoulos. 2001. Fitting Models to Biological Data Using Linear and Nonlinear Regression: A Practical Guide to Curve Fitting. La Jolla CA: GraphPad...

  12. 2007-Graham, J. and Michael Lerch - Parameter Recovery for a Differential Equation Model

    25 Jun 2015 | | Contributor(s):: Jeff Graham, Michael Lerch

    Graham, J. and Michael Lerch. 2007. Parameter Recovery for a Differential Equation Model. PRIMUS-Problems, Resources, and Issues in Mathematics Undergraduate Studies. 17(2):...

  13. 2001-Motulsky, Harvey and Arthur Christopoulos - Fitting Models to Biological Data Using Linear and Nonlinear Regression:  A Practical Guide to Curve Fitting

    20 Jun 2015 | | Contributor(s):: Harvey Motulsky, Arthur Christopoulos

    Motulsky, Harvey and Arthur Christopoulos. 2001. Fitting Models to Biological Data Using Linear and Nonlinear Regression:  A Practical Guide to Curve Fitting. La Jolla CA:  GraphPad Software. 351 pp.Freely downloadable pdf text,...

  14. 1-011A-S-Kinetics

    06 Jun 2015 | | Contributor(s):: Karen Bliss

     Adapted from 1-11-Kinetics, SIMIODE modeling scenario.  We help students see the connection between college level chemistry course work and their differential equations coursework.  We do this through modeling kinetics, or rates of chemical reaction. We study zeroth, first, and...

  15. 1-019-S-RocksInTheHead

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

     We describe an experiment and offer data from a previously conducted experiment on the perception of the individual mass of a collection of rocks in comparison to a 100 g brass mass. We lead students to use the logistic differential equation as a reasonable model, estimate the parameters,...

  16. 1-011-S-Kinetics

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

    We help students see the connection between college level chemistry course work and their differential equations coursework. We do this through modeling kinetics, or rates of chemical reaction. We offer many opportunities to model these chemical reactions with data, some of which comes from...

  17. 1-002-S-Tossing

    11 May 2015 | | Contributor(s):: Brian Winkel

    We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.We add a Hand Out Working Version which can be used in class authored by Rachel ...