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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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