MMDIFFEQ DIFFERENTIALEQUATIONSFINALPROJECT
NAME: DATE:
Objective
Thisprojectisthefinalassignmentforthiscourse. Thepurposeoftheprojectistoprovideyouwithanopportunitytoapply
whatyoulearnedallyear(i.e.,yourknowledgeofdifferentialequations)toareal-worldcontextthatwedidnotalreadyexplore
inthiscourseandhopefully,thatconnectstoafieldofinteresttoyou.
Guidelines
GeneralProjectGuidelines
• Real-WorldApplication: Thesubjectofyourprojectmustinvolveareal-worldapplicationofdifferentialequationsthat
wedidnotalreadyexploreinthiscourseandhopefully,thatconnectstoafieldofinteresttoyou.
• TopicSelection: Locatearesearcharticlethatutilizesdifferentialequations,decipheritscontent,andexplainit. Your
projectshouldaddressandclarifythemathematicalleapsmadeinthearticleusingtheconceptslearnedinclass.
• ReportandPresentation:Youarerequiredtowriteadetailedreportandpresentyourfindingstotheclass.Boththereport
andthepresentationshouldclearlyexplainthedifferentialequationstechniquesusedandexploredinyourproject.
• TechniqueUtilizationandExtension:Yourprojectmustutilizeandextendthedifferentialequationstechniqueslearned
duringthecourse.Thisincludesnotonlyapplyingfamiliarmethodsbutalsoadaptingandexpandinguponthemtosuit
novelcontextsormorecomplexscenarios.
PaperRequirements
• MathematicalExplanation:Provideadetailedwalk-throughoftheresearchpaper.Inparticular,highlightthedifferential
equationsusedinthepaper,explaininghowtheyarederivedandapplied.Thissectionshouldexplicitlyreferenceatleast
oneconceptormethodcoveredduringthecourse,showinghowitcanbedevelopedfurtherorappliedinanewcontext.
Youcanassumetheaudienceisstudentsthathavejustcompletedafirstyearordinarydifferentialequationscourse(i.e.,
yourcurrentclassmates).
• ExtensionofCourseConcepts:Includeaspecificsectioninyourpaperthatclearlyexplainstheextensionofoneormore
differentialequationstechniqueslearnedinclass.
• ClarityandProfessionalism:Yourpapermustbewell-organized,freeofgrammaticalerrors,andpreferably,typesetusing
LaTeX.
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MMDIFFEQ DIFFERENTIALEQUATIONSFINALPROJECT
PresentationRequirements
• ComprehensiveOverview: Presentaclearandconciseoverviewofyourproject,includingthekeymathematicaltech-
niquesandtheirapplications. Presentationsshouldprovidelistenerswithaglimpseintothefieldandtheuseofdiffer-
entialequationsinthefield. Presentersshouldassumetheaudienceismembersoftheclass,soonlythemathematics
shouldbeexplainedwiththatinmind.
• VisualandTechnicalSupport:Usevisualaidssuchasslidesordiagramstosupportyourexplanation. ToolslikeMatlab
orSimulinkforsimulationsandvisualizationsareencouraged.
• EngagementandDelivery: Ensurethatthepresentationisengaging,adherestothe15-minutetimelimit,anddemon-
stratesprofessionaldelivery.
Resources:
Therearelotsofgreatsourcesforpotentialprojects. Youarewelcometolookatothersimilarprojects,butmakesurethatthis
workisyourown.
• HarveyMuddCollegehascataloguedallarticlesintheCollegeMathematicsJournal(FormerlytheTwoYearCollegeMath-
ematicsJournal)andtheMathematicsMagazineoftheMAA.Asearchabledatabaseisavailableathttp://www.math.hmc.edu/journalsearch/.
• TheCODEEpageisalsoagreatplacetoexploreforpossiblemodelsofdifferentialequations.
• TheCollegeoftheRedwoodsdoesaverysimilarfinalproject. Hereisalinktosomeoftheirstudentprojectsfromprior
years:
https://mse.redwoods.edu/darnold/math55/DEProj/index.php
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MMDIFFEQ DIFFERENTIALEQUATIONSFINALPROJECT
RUBRIC:
CATEGORY EXPLANATION POINTS
Subject Theprojecttopicisaclear,real-worldapplicationofdifferentialequations 2points
that we have not already explored in this class. Topic chosen connects to
materialcoveredinthisclassandiscreativeandoriginal
Techniques The project utilizes differential equations techniques learned during the 5points
year.Thismathematicsisthoroughlyexplainedinthepaper.
Visualizations The project utilizes Matlab/Simulink to create visualizations that support 2points
theexplanationofkeyideas.
Paper
QualityandAccuracyofWriting Thewritingisclearandeffective,withnogrammaticalerrors. Thepaperis 5points
alsocompletelyfreeofmathematicalerrors,andallresultsarecorrect. The
paperistypesetusingLaTeX
DepthofAnalysis Thepapercontainsadeepandinsightfulanalysisofthemathematics,with 5points
clearandthoroughexplanations.Thepapercontainsmultipleoriginalideas
orinsights,whicharewell-developedandimpactful.
References Anyresourcesuseinwritingthepaper,includingtheoriginalarticleshould 1points
beproperlycitedinAPAformat.
Presentation
Presentation The presentation is clear, concise, and engaging. The speaker effectively 5points
usesvisualaidsandtechnologytoenhancethepresentation. Thepresen-
tationadherestothetimelimit.
UnderstandingoftheArticle Thepresenterdemonstratesadeepunderstandingofthearticle, correctly 5points
explainingallconcepts,theorems,andproofsinclear,conciselanguage.
OverallClarityandOrganization Thepresentationiswell-organizedandeasytofollowandunderstand,with 5points
gooduseoflanguageandappropriatepacing.Theprojectdemonstratesex-
ceptionaleffort,creativity,andunderstandingofdifferentialequationscon-
cepts.
Paper: DueonTuesday5/21
Presentations: DuringthefinaltwoclassmeetingsTuesday5/21andThursday5/23.
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