
1118SSolowEconomicGrowth
22 Aug 2018  Modeling Scenarios  Contributor(s):: Yuri Yatsenko

7040STankInterruptMixing
22 Aug 2018  Modeling Scenarios  Contributor(s):: Norman Loney
We present a differential equation model for the interrupted mixing of a tank with salt water. We offer two solution strategies (1) two step approach and (2) Laplace Transforms.

7020SThermometerInVaryingTempStream
22 Aug 2018  Modeling Scenarios  Contributor(s):: Norman Loney
We present a differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.

1138SInnerEarDrugDelivery
20 Aug 2018  Modeling Scenarios  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 preclinical studies to examine local drug delivery to the cochlea....

4055SShatterWineGlass
20 Aug 2018  Modeling Scenarios  Contributor(s):: Jue Wang
This module takes students through real life scenarios to examine resonance and its destructive power using differential equation models. What is resonance? How does it happen? Why is it important? Three cases are presented: shattering a wine glass, collapse of a suspension bridge, and crash of...

2001TextSNumericalMethodsComparisons
18 Aug 2018  Technique Narratives  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...

9001TextSSkinBurnModelNumericalMethods
18 Aug 2018  Technique Narratives  Contributor(s):: Suruchi Singh
The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Here we learn to solve a heat equation numerically. It is difficult to study the behavior of temperature in problems with interfaces analytically so...

1067SModelingWithSigmoidCurves
18 Aug 2018  Modeling Scenarios  Contributor(s):: Natali Hritonenko
The assignment considers two wellknown models of population growth, VerhulstPearl and Gompertz models, for which qualitative and quantitative analyses are provided. The graphs of the corresponding functions have a sigmoidal or Sshape. The assignment contains two opposite, but related tasks:...

1032SDigoxinElimination
17 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``firstorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This activity can be used to introduce compartmentalized...

1131SCaffeineElimination
15 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the concentration of caffeine eliminated from the human body at a rate proportional to the concentration. This is a reaction in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations, and it can...

1130SAspirinAbsorption
15 Aug 2018  Modeling Scenarios  Contributor(s):: Therese Shelton
We model the amount of aspirin absorbed by the human body at a constant rate. This is a ``zeroorder reaction'' in the language of pharmacokinetics  the study of how drugs move in the body. This simple activity can be used to introduce differential equations and it can be used to...

1089SSpreadOfDisease
15 Aug 2018  Modeling Scenarios  Contributor(s):: Shinemin Lin
In this project we use the algebra based concept “difference quotient” to solve differential equations models with the help of Excel.

1054SGrowthInFarmland
14 Aug 2018  Modeling Scenarios  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...

6007SFunctionsAndDerivativesInSIRModels
12 Aug 2018  Modeling Scenarios  Contributor(s):: Meredith Greer

5026SEvictions
12 Aug 2018  Modeling Scenarios  Contributor(s):: Mary Vanderschoot

1102SCancerGrowth
29 Jul 2018  Modeling Scenarios  Contributor(s):: Jue Wang
This scenario guides students in the use of differential equation models to predict cancer growth and optimize treatment outcomes. Several classical models for cancer growth are studied, including exponential, power law, Bertalanffy, logistic, and Gompertz. They examine the behaviors of the...

Kaabar, Mohammed2018A First Course in Linear Algebra: Study Guide for the Undergraduate Linear Algebra Course
29 Jul 2018  Free Online Texts  Contributor(s):: Mohammed K A Kaabar
There are five chapters: Systems of Linear Equations, Vector Spaces, Homogeneous Systems, Characteristic Equation of Matrix, and Matrix Dot Product. It has also exercises at the end of each chapter above to let students practice additional sets of problems other than examples, and they can also...

Kaabar, Mohammed2018A Friendly Introduction to Differential Equations
29 Jul 2018  Free Online Texts  Contributor(s):: Mohammed K A Kaabar
In this book, there are five chapters: The Laplace Transform, Systems of Homogeneous Linear Differential Equations (HLDE), Methods of First and Higher Orders Differential Equations, Extended Methods of First and Higher Orders Differential Equations, and Applications of Differential Equations. In...

Modeling in Differential Equations Courses – SIMIODE Resources and Community
13 Jul 2018  Presentations  Contributor(s):: Brian Winkel
Talk presented SIAM ED18 Minisymposium, Portland OR USA, 911 July 2018, by Brian Winkel, Director SIMIODE concerning the community and features of SIMIODE.

SIMIODE / SCUDEMAssessment/Evaluation Plans and Results
13 Jul 2018  Presentations  Contributor(s):: Jennifer Czocher, Barbara Edwards
Results of assessment and evaluation of SIMIODE workshops 2015 and projected workshop 2018 as well as SCUDEM I 2017 and SCUDEM II 2018 by BARBARA EDWARDS (Oregon State University, Corvallis) JENNIFER CZOCHER (Texas State University, San Marcos) are presented.