Tags: first order

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  1. 1-092-S-DashItAll

    01 Sep 2019 | | Contributor(s):: Kurt Bryan

    This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. The model is driven by data from the world record race of Usain Bolt in the 2008 Beijing Olympic games. In particular, we derive the classic Hill-Keller model for a...

  2. 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...

  3. 5-005-Text-S-StiffDifferentialEquations

    05 Mar 2019 | | Contributor(s):: Kurt Bryan

    This material introduces the topic of ``stiffness'' for a system of ordinary differential equations (ODE's), through a series of examples.Stiffness is a property that a system of ODE's may possess that make it difficult to solve numerically with standard methods, and it is a...

  4. 1-003-S-Text-IntroNumericalMethods

    10 Jan 2019 | | Contributor(s):: Brian Winkel

    We ask students to develop two numerical methods for solving first order differential equations  geometrically and to compute numeric solutions and compare them to the analytic solutions for a number of different step sizes. 

  5. 6-006-T-ZombieGameHvZ

    09 Sep 2018 | | Contributor(s):: Jue Wang

    Invented in 2005, Humans vs. Zombies, or HvZ, is a game of tag, predominantly played at US college campuses. In this activity, students use systems of non-linear differential equations to model the HvZ game. Standard SIR and SIRS models are introduced to guide students as they set up the...

  6. 1-138-S-InnerEarDrugDelivery

    20 Aug 2018 | | Contributor(s):: Jue Wang

    Hearing loss is difficult to treat due to the inner ear location and structure. Drawing from this challenging case, this scenario guides students to transform a treatment protocol into a mathematical model. Students engage in pre-clinical studies to examine local drug delivery to the cochlea....

  7. 2-001-Text-S-NumericalMethodsComparisons

    18 Aug 2018 | | Contributor(s):: Swarn Singh

    It is not always possible to solve a differential equation analytically.This material makes an effort to teach the basics of numerical methods for first order differential equations by following graphical and numerical approaches. Here we also discuss the order of accuracy of the methods and...

  8. 1-081-S-TumorGrowth

    09 Jun 2018 | | Contributor(s):: Ryan Miller, Randy Boucher

    Students will transform, solve, and interpret a tumor growth scenario using non-linear differential equation models. Two population growth models (Gompertz and logistic) are applied to model tumor growth. Students use technology to solve the Gompertz model and answer a series of questions...

  9. FirstOrderModels

    03 Mar 2018 | | Contributor(s):: Unknown

    Modeling with First Order EquationsMathematical models characterize physical systems, often using differential equations.Model Construction: Translating physical situation into mathematical terms. Clearly state physical principlesbelieved to govern process. Differential equation is a...

  10. LeakingBucket: Differential Equations in Engineering

    03 Mar 2018 | | Contributor(s):: Unknown

    Differential Equations in Engineering: The Leaking Bucket. Laboratory Experiment. 4 pp.From the Text:7.1 Laboratory ObjectiveThe objective of this laboratory is to learn about first order differential equations and theirapplication to a leaking bucket. 7.2 Educational ObjectivesAfter...

  11. 2012-Levermore-OrdinaryDifferentialEquations-Graphical MethodsApplications

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

    Levermore. David. 21012. First-Order Ordinary Differential Equations II:  Graphical Methods and Applications. University of Maryland. Notes. 23 pp/5. First-Order Equations: General Theory5.1. Well-Posed Problems 25.2. Existence and Uniqueness 36. First-Order Equations: Graphical Methods6.1....

  12. 2015-Endale-ApplicationsOfODEsToRealWorldSystems

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

    2015. Endale, Mersha Amdie. Some application of first order differential equations to real world system. Masters Thesis. Haramaya University.We quote from the opening by the author,“The subject of differential equations is important part of mathematics for understanding the physical...

  13. 2009-MallettFetbrandt-Differential Equations Class Notes

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

    Mallett, Travis and Josh Fetbrandt. Differential Equations Class Notes. Washington State University.From the Dear Reader opening page of these notes,“These notes were written by two students (Travis Mallett and Josh Fetbrandt) at Washington State University in Fall 2009 and are intended to...

  14. 2012-Applied Differential Equations

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

    2012-Applied Differential Equations. Notes. 34 pp.Set of notes on solution strategies for first order differential equations with attention to detail in solutions and several models: tank mixing problems, mortgage, escape velocityKeywords: differential equation, model, first order, tank mixing,...

  15. Transient and Steady State response in RC or RL circuits

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

    Transient and Steady State response in RC or RL circuits . PowerPoint Slides. 54 Slides,This is a presentation to help understand the concepts of Transient and Steady State response in RC or RL circuits . There is detailed technical material and graphs to richly illustrate the clear...

  16. 2012-Bourne-Modeling fish stocks

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

    Bourne, Murray. 2012.  Bourne-Modeling fish stocks. https://www.intmath.com/blog/mathematics/modeling-fish-stocks-7377  . Accessed 10 September 2017.Discusses many models of harvesting and consequences.Keywords: logistic, harvest, differential equation, model, first order, fish, fish...

  17. 2013-Slavik-Mixing Problems with Many Tanks

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

    Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly.  120: 806-821.Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix representation of the linear mixing model of differential equations. Keywords: tank, circula,...

  18. Cengel-Differential Equations for Scientists and Engineers

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

    Cengel, Y. A.  Differential Equations for Scientists and Engineers. Chapters 1 and 2.This file contains the first two chapters of this book:  Introduction to Differential Equations and First Order Differential Equations. There are reasonable introduction and derivation of models and...

  19. 2005-Howard-Modeling with Differential Equations

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

    Howard P. 2005. Modeling with ODE. Notes. 48 pp.Great exposition and lots of Modeling Scenarios almost laid out completely as exercises.From the textOverviewA wide variety of natural phenomena such as projectile motion, the flow of electric current, and the progression of chemical reactions are...

  20. 2010-Clementi-DelCiello-Hart Modeling Disease

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

    Del Ciello, Sarah, Jack Clementi, and Nailah Hart. 2010. Modeling Disease – FinalReport. http://educ.jmu.edu/~strawbem/math_201/final_reports/Clementi_DelCiello_Hart_Final.pdf . Acessed 8 September 2017.Abstract: This paper models the progression of a disease through a set population...