MAT\t330:\tApplication\tAssignment\tGuidelines\tand\tGrading\tGuide Overview The\tpurpose\tof\tthis\tassignment\tis\tto\tguide\tyou\tthrough\tthe\tprocess\tof\tdeveloping\ta\tdifferential\tequation\tmodel,\tsolving\tthe\tresulting\tinitial\tvalue problem,\tand\tinterpreting\tthe\tsolution\tin\tthe\tcontext\tof\ta\treal-world\tapplication.\tCompleting\tthe\tassignment\twill\tenable\tyou\tto\tmake\ta\tconnection between\twhat\tyou\tare\tlearning\tabout\tdifferential\tequations\tand\tthe\tworld\tin\twhich\twe\tlive.\tEconomists,\tengineers,\tlinguists,\tbiologists,\tand\tmany other\tprofessionals\tuse\tmodels\tbased\ton\tdifferential\tequations,\tand\tthis\tactivity\twill\tgive\tyou\ta\tglimpse\tof\thow\tdifferential\tequations\tapply\tto every-day\tlife. The\tassignment\tsubmission\tprocess\tis\torganized\tinto\ttwo\tmilestones\tand\ta\tfinal\tsubmission.\tAt\teach\tmilestone,\tyou\twill\tsubmit\ta\tportion\tof\tthe overall\tassignment\tto\tscaffold\tlearning\tand\tto\tensure\tquality\tfinal\tsubmissions.\tThese\tmilestone\tsubmissions\twill\tbe\tmade\tat\tthe\tconclusion\tof Module\tTwo\tand\tModule\tFive.\tThe\tfinal\tsubmission\twill\tbe\tdue\tin\tModule\tSeven. Assignment\tRequirements Submit\ta\treport\tin\twhich\tyou\tdescribe\tand\tanalyze\ta\treal-world\tscenario\tfor\twhich\tordinary\tdifferential\tequations\tapply.\tResearch\tapplications\tfor ordinary\tdifferential\tequations\tand\tsubmit\tthe\tfollowing\treports\tat\teach\tmilestone.\tYour\tfinal\tsubmission\tshould\tinclude\tthe\tfollowing\tcritical elements: 1. Select\ta\ttopic\tthat\tcan\tbe\tmodeled\tby\ta\tfirst-order\tordinary\tdifferential\tequation.\tNote\tthat\tyour\ttopic\tshould\tgenerate\ta\tdifferential equation\tthat\tcan\tbe\tsolved\tby\tthe\ttechniques\tin\tthis\tcourse.\tChapter\t3\tof\tour\ttext\tintroduces\tthe\tmodeling\tprocess\tand\texamples\tof applications\tthat\tcan\tbe\tfound\tthroughout\tthe\ttext.\tAdditionally,\tit\tis\tnot\thard\tto\tfind\tinteresting\tapplications\tby\tsearching\tthe\tinternet. Example\ttopics: Crime\tscene\tinvestigation\tusing\tNewton's\tlaw\tof\tcooling Population\tgrowth\tmodels,\twith\teither\tunconstrained\tor\tconstrained\tgrowth Simple\tdynamic\tmodels\tof\tmathematical\teconomics,\tsuch\tas\tthe\tchange\tin\tthe\tprice\tof\ta\tproduct\trelated\tto\tstock\tlevels\tof\tthat product Interest\trate\tmodels\tinvolving\tloans\tor\tinvestments,\tsuch\tas\tdetermining\tthe\tlargest\tloan\taffordable\tthat\tcan\tbe\tpaid\toff\tin\ta\tgiven time\tperiod\twhen\tconsidering\ta\tfixed-rate\tmortgage\twith\tmonthly\tpayments Modeling\tthe\tvelocity\tof\ta\tsprinter Carbon\tdating 2. 3. 4. 5. Drug\tconcentration\tin\tthe\thuman\tbody Model\tthe\ttopic\tusing\ta\tdifferential\tequation. a) Draw\tany\tvisuals\t(diagrams)\tthat\texemplify\tthe\tmodel\tand\tfacilitate\tunderstanding\tof\tthe\tmodeling\tprocess.\tYour\tvisuals\tshould represent\tthe\ttopic\tand\thelp\tdevelop\tthe\tdifferential\tequation. b) Write\tthe\tdifferential\tequation\tthat\tmodels\tyour\ttopic\tof\tchoice.\tDefine\tall\tthe\tvariables\tused\tin\tthe\tmodel,\tand\tbe\tsure\tto\tinclude initial\tconditions. c) Classify\tthe\tdifferential\tequation,\tincluding\tthe\torder\tand\tif\tit\tis\tlinear\tor\tnonlinear. Solve\tthe\tdifferential\tequation\tusing\tthe\ttechniques\tfrom\tthis\tcourse. a) Provide\ta\tvalid\tsolution\tto\tthe\tdifferential\tequation.\tBe\tsure\tto\tapply\tthe\tinitial\tconditions\tthat\tyou\tdeveloped. b) Discuss\tthe\tmethod\tused\tto\tsolve\tthe\tdifferential\tequation.\tExplain\tall\tsteps\tin\tarriving\tat\tthe\tsolution,\twriting\tin\tparagraph\tform\tand in\tcomplete\tsentences. Discuss\tthe\tsolution\tin\tcontext\tof\tthe\tinitial\ttopic.\tWrite\tthe\tsolution\tof\tthe\tdifferential\tequation\tin\tterms\tof\tthe\tinitial\ttopic\tyou\tchose\tin Part\t1.\tDescribe\thow\tthis\tcould\tbe\tuseful\tfor\tsomeone\tin\tthe\tfield\tfrom\twhich\tthe\tmodel\twas\tobtained.\tInclude\tsolution\tvalues\tor\tgraphics to\tillustrate\tthe\tutility\tand\tapplicability\tof\tthe\tsolution\tin\tthe\tcontext\tof\tthe\ttopic\tyou\tchose. Discuss\twhat\tyou\tlearned\tfrom\tthe\tmodeling\tprocess.\tWrite\tone\tto\ttwo\tparagraphs\tpertaining\tto\twhat\tyou\tcan\ttake\taway\tfrom\tthe modeling\tprocess\tin\tgeneral. Deliverable\tMilestones Milestone 1 2 Deliverables Module Due Determine\tthe\ttopic\tof\tyour\tchoice.\tSubmit\tthe Two topic\tonly\tto\tyour\tinstructor\t(Part\t1).\tYour instructor\tmust\tapprove\tbefore\tyou\tcan\tmove forward. Develop\tthe\tmodel\tand\tsolve\tthe\tdifferential Five equation.\tYou\tshould\tinclude\tonly\tthe differential\tequation,\tvariables\tand\tinitial conditions,\tand\tsolution\t(Part\t2b\tand\tPart\t3a only). You\tcan\tchoose\tto\tinclude\tthe\tclassification\tof the\tdifferential\tequation,\tany\tvisuals,\tand method\tused\tto\tsolve,\tbut\tthat\tis\tnot required\tin\tthis\tmilestone. Parts\t1-5:\tFinal\tSubmission Seven Grading Ungraded\tbut\trequired.\tYour\ttopic\tmust\tbe\tapproved\tby\tthe\tinstructor before\tyou\tcan\tmove\tforward. Graded\tat\t50\tpoints\tfor\tsubmission. Graded\tseparately\tat\t200\tpoints;\tFinal\tProduct\tRubric Final\tProduct\tRubric Requirements\tof\tsubmission:\tWritten\tcomponents\tof\tproject\tmust\tfollow\tthese\tformatting\tguidelines\twhen\tapplicable:\tdouble\tspacing,\t12-point\tTimes\tNew Roman\tfont,\t1-inch\tmargins,\tand\tdiscipline-appropriate\tcitations.\tAn\tequation\ttool\tmust\tbe\tused\tfor\tall\tmathematical\tformulas\tand\tequations. Critical\tElements Topic\tSelection Model\tVisuals Differential\tEquation Classification\tof Differential\tEquation Solution\tto Differential\tEquation Exemplary Submission\tmeets\t\"Proficient\" criteria\tand\teffectively describes\tthe\tinterest\tin\tthe topic\tof\tchoice (5) Submission\tmeets\t\"Proficient\" criteria\tand\tdescribes\teach component\tof\tthe\tvisual\tand\tits connection\tto\tthe\ttopic\tof choice (14-15) Submission\tmeets\t\"Proficient\" criteria\tand\tincludes\texplicit variable\tdefinitions\tand\tinitial conditions (18-20) Submission\tmeets\t\"Proficient\" criteria\tand\tdescribes\twhy\tit\tis classified\tas\tsuch (9-10) Submission\tmeets\t\"Proficient\" criteria\tand\tsolution\tis\twritten using\tclear\tdisplayed\tmath (14-15) Proficient Submission\tcontains\ta\trealworld\ttopic\tthat\tcan\tbe modeled\tby\ta\tfirst-order differential\tequation (4) Submission\tcontains\ta\tvisual representation\tof\tthe\tmodel\tin order\tto\tfacilitate\tthe\tmodeling process (12-13) Differential\tequation\taccurately describes\tthe\tmodel (16-17) Submission\tincludes\tthe classification\tof\tthe\tdifferential equation (8) Solution\tis\tcorrect\tand\tinitial conditions\tare\tapplied (12-13) Needs\tImprovement Submission\tcontains\ta\ttopic that\tcan\tbe\tmodeled\tby differential\tequation,\tbut\tdoes not\thave\ta\treal-world application\tor\tit\tcannot\tbe modeled\tby\ta\tdifferential equation\tin\tthe\tscope\tof\tthis course (3) Submission\tcontains\tsome visual\trepresentation\tof\tthe model,\tbut\tit\tdoes\tnot\tfully represent\tthe\treality\tof\tthe topic (11) Differential\tequation\tdoes\tnot accurately\tdescribe\tthe\tmodel (14-15) Submission\tincludes\tpartial\tor incorrect\tclassification\tof differential\tequation (7) Solution\tis\tincorrect\tor submission\tdoes\tnot\tinclude the\tcorrect\tapplication\tof\tthe initial\tconditions (11) Not\tEvident Submission\tdoes\tnot\tinclude\ta real-world\ttopic\tmodeled\tby\ta first-order\tdifferential\tequation (0-2) Submission\tdoes\tnot\tcontain any\tvisual\trepresentation\tto describe\tthe\tmodel (0-10) Submission\tdoes\tnot\tcontain\ta differential\tequation\tto\tsolve (0-13) Do\tattempt\tto\tclassify\tthe differential\tequation (0-6) No\tattempt\tto\tsolve\tthe differential\tequation (0-10) Value 5 15 20 10 15 Method\tto\tSolve Submission\tmeets\t\"Proficient\" criteria\tand\tfurther\textends\tthe explanation\tto\twhy\tthat method\twas\tchosen (9-10) Solution\tin\tContext\tto Submission\tmeets\t\"Proficient\" Initial\tTopic criteria\tand\tfurther\tillustrates the\tapplicability\tin\tthe\tcontext of\tthe\ttopic (14-15) Lessons\tLearned Submission\tdescribes\tin\twords the\tmethod\tused\tto\tsolve\tthe differential\tequation (8) Submission\tincludes\tthe solution\tin\tterms\tof\tthe\ttopic and\tincludes\thow\tit\tcould\tbe useful\tin\tthe\tfield (12-13) Submission\tincludes\ta\tsummary of\twhat\twas\tlearned\tfrom\tthe differential\tequation\tmodeling process (9-10) Comments: Submission\tdescribes\tthe method\tfrom\tthe\tcourse\tused to\tsolve\tthe\tdifferential equation,\tbut\tthe\tdescription\tis incomplete\tor\tnot\tin\tparagraph form (7) Submission\tdoes\tnot\tinclude how\tthe\tmodel\tand\tsolution\tare used\tin\tthe\tfield (11) Summary\tof\tthe\tmodeling process\tis\tlacking\tin\tpersonal tone\tor\tis\tnot\tappropriate\tto the\ttopic (7-8) Submission\tdoes\tnot\tinclude the\tmethod\tused\tto\tsolve\tthe differential\tequation (0-6) No\tsolution\tin\tterms\tof\tthe topic\tof\tchoice\tis\tprovided (0-10) Submission\tdoes\tnot\tinclude lessons\tlearned\tfrom\tthe modeling\tprocess (0-6) Total 10 15 10 100%