
2001TextSNumericalMethodsComparisons
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...

1054SGrowthInFarmland
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...

1081STumorGrowth
09 Jun 2018   Contributor(s):: Randy Boucher, Ryan Edmund Miller
Students will transform, solve, and interpret a tumor growth scenario using nonlinear 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...

6070SBeerBubbles
24 Apr 2018   Contributor(s):: Michael Karls
The goal of this project is to set up and numerically solve a firstorder nonlinear ordinary differential equation (ODE) system of three equations in three unknowns that models beer bubbles that form at the bottom of a glass and rise to the top. The system solution is then used to verify...

2012Levermore. David  FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications
01 Dec 2017   Contributor(s):: Brian Winkel
Levermore. David. 21012. FirstOrder Ordinary Differential Equations II: Graphical Methods and Applications. University of Maryland. Notes. 23 pp.5. FirstOrder Equations: General Theory5.1. WellPosed Problems 25.2. Existence and Uniqueness 36. FirstOrder Equations:...

2015Endale, Mersha Amdie  Some application of first order differential equations to real world system. Masters Thesis.
26 Nov 2017   Contributor(s):: Brian Winkel
Endale, Mersha Amdie. 2015. 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...

2009Mallett, Travis and Josh Fetbrandt  Differential Equations Class Notes.
11 Sep 2017   Contributor(s):: Brian Winkel
Mallett, Travis and Josh Fetbrandt. 2009. 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...

2012Unknown  Applied Differential Equations. Notes
11 Sep 2017   Contributor(s):: Brian Winkel
2012Applied 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...

2012Bourne, Murray  Modeling fish stocks.
10 Sep 2017   Contributor(s):: Brian Winkel
Bourne, Murray. 2012. BourneModeling fish stocks.https://www.intmath.com/blog/mathematics/modelingfishstocks7377 . Accessed 10 September 2017.Discusses many models of harvesting and consequences.Keywords: logistic, harvest, differential equation, model, first order,...

2013Slavik, Antonin  Mixing Problems with Many Tanks.
10 Sep 2017   Contributor(s):: Brian Winkel
Slavik, Antonin. 2013. Mixing Problems with Many Tanks. Mathematics Monthly. 120: 806821.See https://www.tandfonline.com/doi/abs/10.4169/amer.math.monthly.120.09.806 .Discusses many tank configurations, circular, cascading, in a row, etc. and the attendant matrix...

2005Howard P.  Modeling with ODE. Notes.
10 Sep 2017   Contributor(s):: Brian Winkel
Howard P. 2005. Modeling with ODE. Notes. 48 pp.See https://www.math.tamu.edu/~phoward/m412/modode.pdf .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,...

2010Del Ciello, Sarah, Jack Clementi, and Nailah Hart  Modeling Disease
10 Sep 2017   Contributor(s):: Brian Winkel
Del Ciello, Sarah, Jack Clementi, and Nailah Hart. 2010. Modeling Disease – FinalReport. See 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...

2017Bialek, William  Boxes and Arrows To Differential Equations
09 Sep 2017   Contributor(s):: Brian Winkel
Bialek, William. Boxes and Arrow to Differential Equation. https://www.princeton.edu/~wbialek/intsci_web/dynamics1.2.pdf From An Integrated, Quantitative Introduction to the Natural SciencesPart 1: Dynamical Models at...

2017AccessPharmacy  Pharmacokinetics Of Drug Absorption
09 Sep 2017   Contributor(s):: Brian Winkel
AccessPharmacy (McGraw Ill). Applied Biopharmaceutics & Pharmacokinetics. Chapter 7. Pharmacokinetics of Oral.See https://accesspharmacy.mhmedical.com/book.aspx?bookID=1592 . Accessed 7 September 2017.From the web page.“The pharmacokinetics of drugs...

2017Peletier, L. A.  Ordinary Differential Equations in Pharmacodynamics. Notes.
09 Sep 2017   Contributor(s):: Brian Winkel
Peletier, L. A. 2018 Ordinary Differential Equations in Pharmacodynamics. Notes. 23 pp.See http://www.math.leidenuniv.nl/~peletier/azcourse04.pdf . Accessed 8 September 2017.Good mix of theory, application, solution technique in a number of areas of applications of...

1967Israelsson, D. and A. Johnsson  Circumnutations In Helianthus Annuus
08 Sep 2017   Contributor(s):: Brian Winkel
Israelsson, D. and A. Johnsson. 1967. A Theory for Circumnutations in Helianthus annuus. Physiologia Plantarum. 20: 957976.https://onlinelibrary.wiley.com/doi/10.1111/j.13993054.1967.tb08383.x Abstract:“A theory is given for circumnutations in plants,...

1969Israelsson, D. and A. Johnsson  Phase Shift In Geotropical Oscillations
08 Sep 2017   Contributor(s):: Brian Winkel
Israelsson, D. and A. Johnsson. 1969. Phaseshift in Geotropic Oscillations a Theoretical and Experimental Study. Physiologia Plantarum. 22: 12261237.See https://pubmed.ncbi.nlm.nih.gov/20925673/ .The paper studies geotropical induced phaseshifts in circumnutations (turning)...

2017Domokos , Andras  Differential Equations  Theory and Applications – Notes
07 Sep 2017   Contributor(s):: Andras Domokos
Domokos , Andras. 2017. Differential Equations  Theory and Applications – Notes. 126 pp. California State University, Sacramento. See http://www.csus.edu/indiv/d/domokos/diffeq.pdf . Accessed 6 September 2017.The author says in the...

2010Liakos, Kelly  A lion chases down an antelope
06 Sep 2017   Contributor(s):: Brian Winkel
Liakos, Kelly. A lion chases down an antelope. http://calculus7.com/id9.html Accessed 4 September 2017.This material comes the site, Calculus Animations, Graphics and Lecture Notes, which is dedicated to a very creative teacher, Kelly Liakos. The opening says, “In...

1115SModelingWithFirstOrderODEs
04 Sep 2017   Contributor(s):: Michael Grayling
Several models using first order differential equations are offered with some questions on formulating a differential equations model