CalculusIIfortheMathematicalandPhysicalSciences–640:152(Sections30,31,and32)

2016FallSemester

I.COURSEWEBPAGE: http://www.math.rutgers.edu/courses/152/

II.SEMESTER: Tuesday,September6th–Friday,December23rd,2016 http://nbregistrar.rutgers.edu/undergrad/f16ugcal.htm

https://scheduling.rutgers.edu/scheduling/academic-calendar

III.LECTURES: Tuesday/Friday 10:20AM-11:40AMBRR-3071 LIV

IV.RECITATIONS: Section30: Wednesday 8:40AM-10:00AM TIL-103B LIVSection31: Wednesday 10:20AM-11:40AM TIL-103B LIVSection32: Wednesday 12:00PM-1:20PM TIL-103B LIV

V.EXAMS: MidtermExam1: Friday,October14thMidtermExam2: Friday,November18thFinalExam: Monday,December19th

VI.INSTRUCTORINFORMATION• Instructor: Dr.EvgeniNikolaev• Officehour: Thursdays,7:00PM–8:00PM• Office: 273HillCenter,Busch• Email: evgeni@math.rutgers.edu• Availability: Pleasefeelfreetocontactmeviaemail

VII.TEACHINGASSISTANTINFORMATION• RecitationInstructor: MatthewHohertz• Officehours: Wednesdays,4:00PM–5:00PM• Office: 622HillCenter,Busch• Email: mrh163@math.rutgers.edu• Availability: Pleasefeelfreetocontactmeviaemail

VIII.PEERMENTORSSection 30: Anushka Desai email: ad1055@scarletmail.rutgers.edu Section 31: Tyler Volpe email: Tyler.volpe@rutgers.edu Section 32: Tyler Volpe email: Tyler.volpe@rutgers.edu

VIX.TEXTBOOKJonRogawski&ColinAdams,Calculus,EarlyTrancendentals,3rdedition,plusWebAssignPurchaseoptions:

• Hardcovercustom3rdeditionandWebAssignpremiumaccesscode(forthedurationofthe3rdedition).ISBN978-1-319-04853-2NJBooks:$125.00.

• E-bookcustom3rdeditionandWebAssignpremiumaccesscode(forthedurationofthe3rdedition)ISBN978-1-319-04911-9NJBooks:$107.50

The3rdeditionispurchasedwithaWebAssignaccesscode,whichwillbeusedthroughoutthesequence151-152-251.Thepublisherisunabletoreplacethiscodeifitislost,sobecarefultoretainit.

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X.CALCULATORAgraphingcalculatorisrequiredforthiscourse.WehavetraditionallyusedtheTI-83or83+andrecommendeitherofthem,butanycalculatorwithequivalentcapacitiescanbeused,suchasthepopularTI-85or86.Calculatorswillnotbepermittedduringexams.Formulasheetswillnotbepermittedduringexams.XI.GRADESANDCOURSEPOLICIES

• WebAssign: 10%• Workshops: 10%• MidtermExam1: 20%• MidtermExam2: 20%• Finalexam: 40%

Total: 100%XII.CORECURRICULUMLEARNINGGOALS(ratified5/08)

TheCORECurriculumSummaryofLearningOutcomesThe SAS Core Curriculum focuses on the learning goalsthat formthecoreofamodern liberalartseducationataleading comprehensive 21st century public researchuniversity. Student progress in the Core is measured bythe breadth of goals achieved, and a single course canfulfillmultiple goals. Students exercisemeaningful choiceamong courses from across disciplines specificallycertifiedasmeetingthesegoals.

UponcompletionoftheSASCoreCurriculumSTUDENTSWILLBEABLETO:QuantitativeandFormalReasoning (6 creditsor3plusplacementoutof3)Studentsmustmeet2goals.[QQ;QRorplacementoutof]

• Formulate,evaluate,andcommunicateconclusionsandinferencesfromquantitativeinformation.[QQ] (includesvariousquantitativemethodscoursesaswellas640courses)

• Applyeffectiveandefficientmathematicalorotherformalprocessestoreasonandtosolveproblems.

[QR](includes640coursesandformalreasoningcourses–orplacementoutof) A SINGLE COURSEMAY BE USED TOMEETMULTIPLE GOALS. ALL COURSESMUST BE CREDIT-BEARING,GRADEDCOURSESCERTIFIEDBYTHESASFACULTYASMEETINGCOREGOALS(e.g.Ecreditcoursescannotbeusedtomeetgoals,norcanPass/NoCreditcourses).Generally,studentswillneedtotake10–14coursestocompletetheCore,someofwhichmayalsofulfillmajororminorrequirements.

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XIII.MATHEMATICSPROGRAMS: DisciplinaryLearningGoalsThegeneralliberalartsstudentwillbeabletoemployalgebraanddiscussbringingabstractmathematicstobear on areaswith no obviousmathematical content to the layman, such as political science, aesthetics, orcreditcardsecurity.Studentswhosemajorsrequiremoreadvancedmathematicswillbeadequatelyprepared.Students aiming toward careers in elementary school education will be able to pass state-mandatedexaminationsbeforecertification,andtosatisfytheUniversity’scourserequirementsrelatedtocertification.MAJORS will be able to employ problem-solving skills in a wide range of modern mathematics; analyzequantitative information and apply advance mathematic techniques and concepts where appropriate;communicaterigorousmathematicalideasandreasoningeffectively;appropriatelyusesupportingtechnologyandworkcooperativelyaspartofateamtosolvemathematicalproblems;andtopstudentswilldemonstrateexperienceinresearch.Studentsincombinedmath/educationprogramswillbeabletodemonstrateabroadperspective onmathematics, including the history of the subject, and an understanding of the connectionsbetween collegemathematics and the state's curriculum framework. Students in the B.S. program (HonorsTrack)willbeabletoengageingraduatelevelworktowardthedoctorate.MINORSwillbeabletodemonstrateanunderstandingofthespecialnatureofmathematicalthinking;createand communicate mathematical arguments; apply mathematical knowledge and techniques in advancedcoursesintheirmajordiscipline.STATISTICS/MATHEMATICS JOINTMINOR: the jointmajor provides a stronger preparation for graduatestudy in statistics; the Statisticsmajor is best for studentswho are interested in statistical applications inindustry,government,orappliedareasofgraduatestudy.XIV.COURSELEARNINGGOALSANDDESCRIPTION

01:640:152CalculusIIfortheMathematicalandPhysicalSciences–640:152(4)Math 152 is the introductory year course in the calculus sequence in New Brunswick for majors in themathematicalsciences,thephysicalsciences,andengineering.Thesecondsemester,Math152,continuesthestudy of the integral calculus, with applications, and covers the theory of infinite series and power series,touchingondifferentialequationsandafewothertopicsaswell.XV.CURRENTACADEMICINTEGRITYSTATEMENT

AllstudentsenrolledinRutgerscoursesareexpectedtobefamiliarwithandabidebytheacademicintegritypolicy(http://academicintegrity.rutgers.edu/policy-on-academic-integrity).Violationsofthispolicyaretakenvery seriously.Violations include: cheating, fabrication, plagiarism,denyingothers access to informationormaterial,andfacilitatingviolationsofacademicintegrity.(http://academicintegrity.rutgers.edu/files/documents/AI_Policy_9_01_2011.pdf).AnHonorPledge:"Onmyhonor,IpledgethatIhaveneithergivennorreceivedanyunauthorizedaidonthis(exam,test,paper)."XVI.CHEATINGANDPLAGIARISM

Shortversion:Don’tcheat.Don’tplagiarize.

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Longerversion: Cheatingon testsorplagiarizingmaterials inyourpapersdeprivesyouof theeducationalbenefitsofpreparingthesematerialsappropriately.Itispersonallydishonesttocheatonatestortohandinapaperbasedonunacknowledgedwordsorideasthatsomeoneelseoriginated.Itisalsounfair,sinceitgivesyouanundeservedadvantageoveryourfellowstudentswhoaregradedonthebasisoftheirownwork. Inthis class we will take cheating very seriously. All suspected cases of cheating and plagiarism will beautomatically referred to theOffice of JudicialAffairs, andwewill recommendpenalties appropriate to thegravityoftheinfraction.Theuniversity'spolicyonAcademicIntegrityisavailableathttp://academicintegrity.rutgers.edu/files/documents/AI_Policy_9_01_2011.pdf1Istronglyadviseyoutofamiliarizeyourselfwiththisdocument,bothforthisclassandforyourotherclassesandfuturework.Sincewhatcountsasplagiarismisnotalwaysclear,IquotethedefinitiongiveninRutgers'policy:Plagiarism

Plagiarism is the use of another person’s words, ideas, or results without giving that personappropriatecredit.Toavoidplagiarism,everydirectquotationmustbeidentifiedbyquotationmarksor appropriate indentation and both direct quotation and paraphrasing must be cited properlyaccording to the accepted format for the particular discipline or as required by the instructor in acourse.Somecommonexamplesofplagiarismare:• Copying word for word (i.e. quoting directly) from an oral, printed, or electronic source withoutproperattribution.• Paraphrasing without proper attribution, i.e., presenting in one’s own words another person’swrittenwordsorideasasiftheywereone’sown.• Submitting a purchased or downloaded term paper or other materials to satisfy a courserequirement.• Incorporating into one’s work graphs, drawings, photographs, diagrams, tables, spreadsheets,computerprograms,orothernontextualmaterialfromothersourceswithoutproperattribution.2A SPECIAL NOTE: Students often assume that because information is available on the Web it is publicinformation,doesnotneedtobeformallyreferenced,andcanbeusedwithoutattribution.Thisisamistake.Allinformationandideasthatyouderivefromothersources,whetherwritten,spoken,orelectronic,mustbeattributedto theiroriginalsource. Suchsources includenot justwrittenorelectronicmaterials,butpeoplewithwhomyoumaydiscussyour ideas,suchasyourroommate, friends,or familymembers. Theydeservecreditfortheircontributionstoo!Judgmentsaboutplagiarismcanbesubtle.Ifyouhaveanyquestions,pleasefeelfreetoaskforguidancefromyourTA.XVII.DISABILITYSTATEMENT

RutgersUniversitywelcomes studentswithdisabilities into all of theUniversity's educational programs. Inorder to receiveconsideration for reasonableaccommodations, a studentwithadisabilitymust contact the 1 ThisweblinkwascorrectedonJuly13,2012.S.Lawrence2http://academicintegrity.rutgers.edu/files/documents/AI_Policy_9_01_2011.pdfUpdatedwiththeUniversity’scurrentlanguageonJuly13,2012.S.Lawrence

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appropriatedisabilityservicesofficeatthecampuswhereyouareofficiallyenrolled,participateinanintakeinterview, and provide documentation: https://ods.rutgers.edu/students/documentation-guidelines. If thedocumentation supports your request for reasonable accommodations, your campus’s disability servicesofficewill provide youwith a Letter ofAccommodations. Please share this letterwith your instructors anddiscuss the accommodationswith them as early in your courses as possible. To begin this process, pleasecompletetheRegistrationformontheODSwebsiteat:https://ods.rutgers.edu/students/registration-form.

• Fulldisabilitypoliciesandproceduresareathttp://disabilityservices.rutgers.edu/

• Students with disabilities requesting accommodations must follow the procedures outlined athttp://disabilityservices.rutgers.edu/request.html

XVIII.ATTENDANCEANDABSENCE

TheUniversityiscommittedtoacultureofacademicengagementbetweenstudentsandfaculty. Partofthiscommitment involves taking responsibility for attending your classes, labs, and exams, and informing yourinstructorswhenyoucannotattend.Rutgersstudentsareexpectedtoattendallscheduledcoursemeetings.UniversitypolicyexcusesabsencesduetoreligiousobservanceorparticipationinRutgers-approvedactivities,andpermitsstudentstomakeupworkmissedforthesecircumstances.Students are expected to attend all classes; if you expect tomiss one or two classes, please use theUniversityabsencereportingwebsitehttps://sims.rutgers.edu/ssra/to indicatethedateandreason foryourabsence. Anemailisautomaticallysenttome.XIX.EXAMS

Therewillbetwoacademicone-hour(80minutes)midtermexamsandacumulativefinalexam.Allexamswillbewrittenbythelecturer.Thelocationofthefinalexamwillbeannouncedlaterintheterm.Nocalculatororcomputerwillbepermittedonexams.Mypolicyformissedexamswithoutanyexcuseisthattheexamisassignedan“F”withoutgivinganopportunityforamakeupexam.XX.HOMEWORKSANDWRITEUPS

HomeworkassignmentswillbeadministeredviatheWebAccessavailablethroughtheCourseSakaiWebSiteInordertokeepupwiththepaceofthecourse,itishighlysuggestedthatyoucomplete5-8DAILYWriteupswillbecollectedinthebeginningofeachworkshop.Nolatesubmissionisallowed,andtwoworst-scorewriteupswillbedropped.

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XXI.WEEKLYCOURSESCHEDULE

Date

Readings(Sections)

Topics

Lecture#1Tue.9/6

5.7and6.1 Substitutionmethodandareasbetweentwocurves

Lecture#2Fri.9/9

6.2 Settingupintegrals,volume,density,averagevalue

Lecture#3Tue.9/13

6.3 Volumesofrevolution

Lecture#4Fri.9/16

6.4 Themethodofcylindricalshells

Lecture#5Tue.9/20

7.1 Integrationbyparts

Lecture#6Fri.9/23

7.2 Trigonometricintegrals

Lecture#7Tue.9/27

7.3 Trigonometricsubstitution

Lecture#9Tue.2/17

5.6 IntroductiontoDifferentialEquations 5.6:1,5*,7,9,11*,17,20,21,23*,25,27,29*,45,47,57**

Lecture#8Fri.9/30

7.4 Integralsinvolvinghyperbolicandinversehyperbolicfunctions

Lecture#9Tue.10/4

7.5 Themethodofpartialfractions

Lecture#10Fri.10/7

7.6 Strategiesforintegration

Lecture#11Tue.10/11

Review Sections:5.7,6.1–6.4,7.1–7.6

Lecture#12Fri.10/14

Exam1 Sections:5.7,6.1–6.4,7.1–7.6Examtobegiveninthelectureroomduringthelectureperiod

Lecture#13Tue.10/18

7.7 Improperintegrals

7.9 Numericalintegration

Lecture#14Fri.10/21

8.1 Arclengthandsurfacearea

Lecture#15Tue.10/25

10.1 Sequences

Lecture#16Fri.10/28

10.2 Summinganinfiniteseries

Lecture#17Tue.11/1

10.3

Convergenceofserieswithpositiveterms

Lecture#18Fri.11/4

10.4 Absoluteandconditionalconvergence

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WEEKLYCOURSESCHEDULE(continued)

Date

Readings(Sections)

Topics

Lecture#19Tue.11/8

10.5 Theratioandroottest.Strategiesforchoosingtests

Lecture#20Fri.11/11

10.6 Powerseries

Lecture#21Tue.11/15

Review Sections:7.7,7.9,8.1,10.3–10.6

Lecture#22Fri.11/18

Exam2 Sections:7.7,7.9,8.1,10.1–10.6Examtobegiveninthelectureroomduringthelectureperiod

Lecture#23Wed.11/23

8.4and10.7

TaylorpolynomialsandTaylorseries

Lecture#24Tue.11/29

11.1 ParametricEquations11.2 Parametricarclengthandspeed

Lecture#25Fri.12/2

11.3 Polarcoordinates11.4 Areaandarclengthinpolarcoordinates

Lecture#9Tue.2/17

5.6 IntroductiontoDifferentialEquations 5.6:1,5*,7,9,11*,17,20,21,23*,25,27,29*,45,47,57**

Lecture#26Tue.12/6

9.1and5.9 Solvingdifferentialequations.Exponentialgrowthanddecay

Lecture#27Fri.12/9

9.2and9.3 Modelsinvolvingy'=k(y-b).Graphicalandnumericalmethods

Lecture#28Tue.12/13

Review Sections:allsectionsfromthesyllabus

Mon.12/19 FINALEXAM