Sample Course Syllabus

Sample Course Syllabus

Brian Winkel, Director, SIMIODE 

This is a sample syllabus for a 15 week, 3 credit hour course using experimentation, modeling, and technology to lead students through a traditional sequence of differential equations topics.  This is ONLY a set of suggestions for SIMIODE materials and is by no means complete in its listing. Nor do we suggest using ALL the resources listed. Rather pick and choose and please look up even more resources added over the years by Searching on topics in SIMIODE.

All these resources listed and MANY more resources are available at www.simiode.org.  Included here are hyperlinks to Student Versions of all materials which are publicly available. To gain access to the Teacher Version of all materials colleagues should register and request membership in the Teacher Group.  All is FREE in SIMIODE.  

The syllabus does not have material from SIMIODE for every topic, nor is every topic of interest in such a course listed.  SIMIODE offerings are increasing all the time through author submissions.  Please consider contributing your own materials.                                                 

This syllabus can be tailored for different semester lengths, credit hours, topical foci, flow level. Amount of emphasis on technology, emphasis on areas of application, newer resources, and emphases on theory by selecting alternative learning activities, including many more that are available on www.simiode.org.  All materials can be downloaded, modified, and excerpted according to the most generous Creative Commons license.                                                   

At every opportunity a modeling activity is used to introduce and support the study of differential equations.

Numbered resources are hyperlinked and available for use now.  The numbering system indicates Week(Day) so 3(7) means the 7th day in the 3rd week.

Each entry contains the following information: Week(Day), Topic, Description, Activity,  Main Resource,  Extra Resources                                                                                                                        

1(1)        First order ODE  - Intro to Modeling - collecting data, modeling

1-001-S-MandMDeathAndImmigration     1-002-S-Tossing      1-007-S-AntTunnelBuilding

1-034-FishMixing     1-130-AspirinAbsorption     1-140-LeakyBucket 

1(2)        First order ODE  -  Modeling using collected data            

1-012-S-Sublimation     1-040-S-OutcomeSavings     1-016-S-DogDrugs

1(3)        First order ODE - separation of variables - Kinetics data motivating form

1-011-S-Kinetics     1-045-S-TimeOfDeath     1-019-S-RocksInTheHead

2(4)       First order ODE - separation of variables   Newton's Law of

1-031-S-CoolIt     3-008-S-HangTime     1-013-S-Sleuthing

1-030-S-IntraocularGasBubbles     1-079-S-HomeHeating

2(5)        First order ODE - integrating factor - Discover natural need for integrating factor

1-002-S-Text-Integrating Factor     1-020-S-IceMelt

1-006-FinancingSavingsAndLoans     1-138-S-InnerEarDrugDelivery

2(6)        First order ODE - Modeling growth of oil slick - problem with poor data

1-005-S-OilSlick     1-005a-S-ChemDataCollection     1-025-S-MixingItUp

1-026-S-Evaporation     1-020-IceMelt

3(7)        Exam 1                                              

3(8)        First order ODE - nonlinear   - Torricelli's Law and confirming with video

1-015-S-Torricelli     1-058-S-WaterClocks     1-029-S-ConeToCubeFlow

YouTube Data Collection Video

3(9)        First order ODE – nonlinear - Logistic equation modeling

1-018-S-LogisticPopModeling      1-009-S-ICUSpread

1-060-S-SalesMarketing     1-017-S-DiseaseSpread

4(10)      Second order ODE - homogeneous  Modeling a spring mass damper system

3-030-SecondOrderIntro      3-001-S-SpringMassDataAnalysis

3-060-S-DataToDifferentialEquation

4(11)      Second order ODE – homogeneous - Modeling falling objects using  experimental data       

3-013-S-WhiffleBallFall     3-016-S-FallingCoffeeFilters      3-019-S-ShuttlecockFall

 

4(12)      Second order ODE – nonhomogeneous - Modeling mystery RLC circuit

4-023-S-MysteryCircuit     4-060-S-CircuitTuner

5(13)      Second order ODE - nonhomogeneous   Modeling spring mass damper and driver

3-001-S-SpringMassDataAnalysis       3-002-S-ModelsMotivatingSecondOrder

3-030-SecondOrderIntro     3-040-S-FirstPassageTime      3-102-S-SpringMassDamped

3-110-S-MilitarySpringMassApplication

4-055-S-ShatterWineGlass      4-050-S-ResonanceBeats

5(14)      Second order ODE - nonhomogeneous   Tuned Mass

5-040-S-TunedMassDampers-Part I     5-040-S-TunedMassDampers-Part II

5(15)      Second order ODE - nonhomogeneous Projectile Motion  

3-044-S-DeepWell     3-042-S-CatapultLaunch     3-045-S-BallBounce

3-035-S-StadiumDesign     3-054-S-Relay      3-020-S-ChordPathTime

6(16)      Student Project Sharing and Presentations                           

               Opportunity to briefly present work done on activities.                             

6(17)      Exam 2                                             

6(18)      System - Linear homogenous

7(19)      System - Linear nonhomogeneous

7(20)      System - Linear nonhomogeneous Dialysis - counter or concurrent         

5-005-S-Dialysis         5-012-S-LipoproteinMetabolism        5-026-S-Evictions

 5-025-S-SaltCompartments      5-030-S-AirshedSulphur

7(21)      System - Linear nonhomogeneous  - LSD levels in human subjects  

1-010-S-LSDAndProblemSolving

8(21)      Systems - Linear  -  Modeling a two spring mass damper system         

5-14-S-TwoSpringMass     5-080-S-SpaceFlightRecolonize

8(22)      Systems – Linear – Chemical reactions for profitable yield and evictions                  

5-007-S-ChemOpt-StudentVersion      5-026-S-Evictions         

8(23)      Systems - Linear  - Infinite system of differential equations for stochastic processes  

1-027-S-StochasticProcesses      1-108-S-PoissonProcess

9(24)      System – Nonlinear -  Flu in English Boarding School              

6-001-S-Epidemic     6-035-S-Shampoo     6-030-S-SaltTorricelli

9(25)      First Order ODE - Bifurcation - a break in the action          

1-009-S-Text-Bifurcation

9(26)      System - Nonlinear  - Modeling an optimal insect colony                 

6-005-S-InsectColonySurvivalOpt      6-025-S-WhalesAndKrill

10(27)    System – Nonlinear - Pursuit models                 

6-008-S-PursuitModels     6-012-S-RiverCrossing

6-026-S-IsleRoyaleModeling     6-023-S-DroneHeadingHome

10(28)    System – Nonlinear - Classical ecology modeling          

6-020-S-AlgaePopulationSelf-Replenishment      6-040-S-StruggleForExistence

6-015-S-CombatingEbolaEpidemic     6-018-S-ExploringSIRModel

10(29)    System - Nonlinear  - Equilibrium and stability analysis

6-010-S-SocialCampaigns        6-065-S-InternetPlatformUsers

11(3)      Exam 3                                              

11(31)    Project Selection Class    Everything!        

               Students come to class prepared to discuss their project interest and share.                         

11(32)  Laplace Transforms - Changing venue from time to frequency domain                  

9-005-S-LaplaceTransformOverview

12(33)   Laplace Transforms - Modeling with discontinuous functions                                       

7-040-S-TankInterrupt Mixing 

12(34)    Laplace Transforms – Convolution, spike, and jump issues

7-008-S-MachineReplacement-LaplaceTransform

7-020-S-ThermometerInVaryingTempStream

12(35)    Laplace Transforms -  Applied to revisited problems 

13(36)    Fourier series     Sums of trigonometric functions represent many phenomena 

8-002-S-Text-TrigSumRepresentation

13(37)    Spectrum - Spectral analysis using Fourier series        

13(38)    Partial differential equation - Modeling a Guitar string - example of wave.         

9-012-S-GuitarTuning

14(39)    Partial differential equation - Heat equation

14(40)    Partial differential equation - nonhomogeneous

14(41)   Exam 4                                                                                                                                  

15(42)    Project Development Time                                                        

15(43)    Class Project Presentations                                                       

15(44)    Class Project Presentations

15(45)    Class Project Presentations                                                       

FINAL EXAM