Course Outline Math 203 Winter 2019 PDF
| Title | Course Outline Math 203 Winter 2019 |
|---|---|
| Course | Math |
| Institution | Concord University |
| Pages | 7 |
| File Size | 392.3 KB |
| File Type | |
| Total Downloads | 78 |
| Total Views | 143 |
Summary
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Description
Department of Mathematics & Statistics Concordia University
MATH 203 Differential & Integral Calculus I Winter 2019
Instructor*: Office/TelNo.: OfficeHours:
*Students should get the above information from their instructor during class time. The instructor is the person to contact should there be any questions about the course.
Textbook: Prerequisite: Pre‐test:
OfficeHours:
Tutorials:
MathHelpCentre:
WeBWorK:
ThomasʹCalculus:EarlyTranscendentals,SingleVariable,(ed.14) Booksala Carteedition plus MyLabMath,(Pearson). Math201oranequivalentFunctionscourse. A pre‐test is posted on the Meta Moodle site of this course to help students determine whethertheirprerequisitemathematical backgroundis strong enoughtotakethiscourse. StudentsareencouragedtogototheMetasite,clickon“README:AboutthePre‐test”link, readit,andthentakethetest. Theresultsofthetestmaybeusedbythecoursecoordinators toadvisestudentsonwhatremedialactionstheycantakeiftheyperformpoorlyonthispre‐ test. Yourprofessorwillannounceher/hisofficehoursduringwhichshe/hewillbealsoavailable to give a reasonable amount of help. Note, however, that if you missed a class it is not reasonabletoexpectyourprofessortocoverthemissedmaterialforyou. Thematerialinthiscourserequiresalotofpractice.Thereisnotenoughclasstimetodoall theexamplesandproblemsneededto learn the material thoroughly.The Departmenthas therefore organized special tutorial sessions conducted every week to provide additional supporttostudentsoutsidethelectureroomenvironment.Thesesessionsareconductedby tutorswhowillhelpwith solvingproblemsonthetopicslearned inclassthatweek,with particularemphasisonthematerialthat studentsmayhavedifficultieswithinthiscourse. Studentsmayattendanyofthescheduled tutorials,notnecessarilythe oneforwhichthey areregistered,and arestrongly encouragedtoparticipateandbeactive attheseproblem‐ solvingsessions.Tutorialsareanimportantresourcetohelpstudentssucceedinthiscourse. In addition to Tutorials, a Math Help Centre staffedbygraduatestudentsisavailable.The schedule of its operation and its location will be posted in the Department and on the Department webpage (https://www.concordia.ca/artsci/math‐stats/services/math‐help‐ centre.html). Every student will be given access to an online system called WeBWorK. The system providesyouwithmanyexercises.Studentswillusethissystemto doonlineassignments Departmentalwebsite:http://www.mathstat.concordia.ca
MATH 203 – Winter 2019 Page 2
(seeAssignmentsbelow).Inaddition,beforethemidtermtestandbeforethefinalexam,a numberofpracticeproblemswillbepostedinWeBWorKtohelpyoureviewthematerialof thecourse. MyLabMath:
Assignments:
Calculators:
MidtermTest:
Everystudentwho purchasestheloose‐leafversionof thetextbookwillbegivenaccessto one more online system called MyLab Math. This system contains an e‐version of the textbook, as well as a large number of various resources, like practice exercises, typical examplesondifferenttopics,oftenwithsolutions,videomaterials,etc.,thathelpyoumaster thecoursematerial. StudentsareexpectedtosubmitassignmentsonlineusingWeBWorK.Lateassignmentswill notbeaccepted.Assignments contribute10%to thefinalgrade.Workingregularlyonthe assignmentsisessentialforsuccessinthis course.Studentsarealsostronglyadvisedto do asmanyproblemsastheirtimepermitsfromthelistofrecommendedproblemsincludedin thisoutline,aswellasworkonthepracticeexercisesopenedinWeBWorKandinMyLab. Only calculators approved by the Department (with a sticker attached as a proof of approval), such as Sharp EL 531 or the Casio FX 300MS, available at the Concordia Bookstore, are permitted for the class test and final examination. For a list of Approved calculators see www.concordia.ca/artsci/math‐stats/services.html Therewillbeonemidtermtest,basedonthematerialofweeks1‐6,whichwillcontributeup to25%toyourfinalgrade(seetheGradingSchemebelow).Thetestwillbecommonforall sectionsofthiscourseand will be heldonSundayMarch 10,2019, at 10:00 A.M.Students whowillnotbeabletowritethetestthatdayforavalidreason,e.g.religious(tobereported tothesection’sinstructorinadvance)orillness(avalidmedicalnoterequired),maywrite analternatemidtermtestonSaturdayMarch16,2019,at10:00A.M.
NOTE: It is the Departmentʹs policy that tests missed for any reason, including illness, cannotbemadeup.If you missboththemidtermandalternatetestbecause ofillnessthe finalexam will count for 90% of yourfinal grade, and the Assignments will count for the remaining10%. FinalExam:
Thefinalexaminationwillbethreehourslongandwillcoverallthematerialinthecourse. NOTE:Studentsare responsible forfindingoutthedateandtimeofthefinalexamsonce thescheduleispostedbytheExaminationsOffice.Conflictsorproblemswiththescheduling of the final exam must be reported directly to the Examinations Office, not to your instructor.ItistheDepartmentʹspolicyandtheExaminationsOfficeʹspolicythatstudents aretobeavailableuntilthe endof thefinalexamperiod.Conflictsduetotravelplans willnotbeaccommodated.
GradingScheme: IMPORTANT:
Thefinalgradewillbebasedonthehigherof(a)or(b)below: a) 10%fortheassignments,25%forthemidtermtest,65%forthefinalexam. b)10%fortheassignments,10%forthemidtermtest,80%forthefinalexam. PLEASENOTETHATTHEREISNOʺ100%FINALEXAMʺOPTIONINTHISCOURSE.
AcademicIntegrityandtheAcademicCodeofConduct This course is governed by Concordia Universityʹs policies on Academic Integrity and the Academic Code of Conduct as set forth inthe Undergraduate Calendar and the Graduate Calendar. Students are expected tofamiliarize themselves with these policies andconduct themselvesaccordingly.ʺConcordiaUniversityhasseveralresourcesavailabletostudentstobetterunderstandandupholdacademicintegrity. Concordia’swebsiteonacademicintegritycanbefound at the following address, which also includes linksto eachFaculty and the School of GraduateStudies:concordia.ca/students/academic‐integrity.ʺ[UndergraduateCalendar,Sec17.10.2]
MATH 203 – Winter 2019 Page 3
CONTENTS
Note:
Weeks 1
All of Chapter 1 is a review of material that is covered in prerequisite courses, and is important for this course. The material that is skipped in this review will be introduced briefly later in the course when needed. If you don’t know this preliminary material thoroughly,itisparticularlyimportantthat youlearnit throughthe assignmentquestions andrecommendedproblems.Ifyoustillfeel you don’t know it well enoughafterthefirst classorso(youshouldalsotrythequizattheveryendofthisdocument)youmaywantto considerdroppingthecourseandtakingMATH201instead. Topics 1.1RepresentationsofFunctions
p.11:
Recommended Problems 3,5,7,9,13,21,23,27,49,51
1.2 CombiningFunctions;Shifting& ScalingGraphs
p.18:
1,3,5,7,9,15,17,19,21,23,25
1.3 TrigonometricFunctions
p.27:
7,9,11,15,19,25,29,37,41,47,49
2
1.5 ExponentialFunctions
p.37:
3,7,9,11,13,15,21,25,27,33
1.6 InverseFunctionsandLogarithms
p.49:
9,17,21,29,31,41,47,53,61,63,71
3
2.1 RatesofchangeandTangentLines
p.61:
1,3,5,23,25
2.2 LimitofaFunctionandLimitLaws
p.71:
3,5,13,15,19,25,27,35,37,55,65
2.4 One‐SidedLimits 2.6 LimitsInvolvingInfinity;Asymptotes
p.88: p.112:
3,7,9,15,17,19,33,37 1,9,11,21,27,35,41,69,71,87,89
4
2.5 Continuity
p.100:
5,13,19,29,31,41,45,49,61
3.1 TangentLinesandtheDerivatives 3.2 TheDerivativeasaFunction
p.123: p.130:
5,11,17,21,25,31,33 3,9,11,17,23,25,55,59
5
3.3 Differentiationrules
p.142:
5,7,11,15,21,23,29,43,47,61
3.4 TheDerivativeasaRateofChange
p.150:
5,7,9,13,15,19,23
3.5 DerivativesofTrigonometricFunctions 3.6 TheChainRule
p.158: p.166:
3,7,11,13,19,23,31,37 5,7,13,21,23,31,35,37,45,63,77
p.172:
1,5,11,15,25,27,37,39,41
6
Pre‐MidtermReview(timepermitting)
7
3.7 Implicitdifferentiation
3.8 DerivativesofInverseFunctionsandLogs p.183:
7,11,27,31,33,37,39,51,53,89,95
8
3.9 InverseTrigonometricFunctions(startwithp.189: thereviewofinversesin&cos,§1.6)
5,9,11,17,25,29,39,43,45
3.10 Relatedrates
p.196:
7,11,13,15,17,21,23,27,31,33,39
9
3.11 LinearizationandDifferentials 4.1 ExtremeValuesofFunctionsonIntervals
p.209: p.227:
5,11,17,19,23,33,39,45,49,55,59 5,17,23,31,37,39,53,63,69,89
10
4.2 MeanValueTheorem
p.235:
5,11,13,21,25,27,29,61,63,65
4.5 IndeterminateformsandLʹHôpitalʹsRule
p.262:
9,11,15,17,21,43,47,51,53,61,63
11
4.3 MonotonicFunctions
p.241:
5,7,19,27,29,54,57,61
4.4 ConcavityandCurveSketching
p.251:
5,9,13,17,31,37,43,63,81,85,99
12
4.6 AppliedOptimization
p.269:
3,5,7,9,11,13,15,19,29,37,39,41
13
REVIEW
MATH 203 – Winter 2019 Page 4
Choosing Between Math 201 and Math 203
Ifthelastmathcourseyoutookwasat thehigh schoollevel (Quebec),andmorethanfiveyears have passedsince,youshouldprobablyregisterforMath200.Ifyouarestillunsureofyourlevel,readon.
Math Courses at Concordia
Math200 BasicAlgebra
Math206 Algebra/Functions
Math209 CalI/Commerce
Math208
Algebra/Commerce
Math201 Functions&Trigonometry
Math202 Interm.Algebra/
Math203 CalI/Science
Math204 LinearAlgebra
Science
Math205 CalII/Science
B.A.;SocialScience,Commerce,etc. Non‐ScienceMathematics
B.Sc.;Engineering,ComputerScience,etc.Science Mathematics
Aself‐administeredtesttohelpyoudecidebetweenMath201andMath203follows.Giveyourselfabout 30minutestocompletethetest.Behonestwithyourself,sinceregisteringinthewrongcoursemaycost youmoneyandresultinapoorgrade.Rememberthatalluniversity‐levelcoursesusuallydemandquite abitofyourtime.StudentsinMath203willfindtheywillnothavetimeoncethecoursebeginstoreview materialthattheyareexpectedtoknowbeforetheyenterthecourse.
MATH 203 – Winter 2019 Page 5
Scoring:10orless=Math201;11‐14=seeanadvisor;15orbetter=Math203.Answersareonthelast page. MATH 203 Qualifying Test 1) What is the equation, in slope intercept form, of the line whose slope is 7 and whose y intercept is 3? a) y = 3x + 7 c) y = 7x + 21 e) y = 7x + 3
b) y = 7x 3 d) y = 7x 21
2) What is the slope of any line parallel to the line 5x + 6y= 30? a)
6 5
b)
5 6
c) 0
d)
5 6
e)
6 5
3) The lines 4x + 5y = 10 and 5x + ky = 12 are perpendicular. What is the value of k? a) 5
b) 4
c) 4
d) 5
e) 10
4) Find the coordinates of the midpoint M, and the length L of the line segment joining the points (3, 2) and (4, 1). Answer in simple radical form. 3 7 a) M , , L 2 2 2 1 1 d) M , , L 2 2 2
7 3 b) M , , L 3 2 2
1 1 c) M , , L 2 2 2
1 1 e) M , , L 3 2 2
5) What is the equation of the line having a slope of 0 and passing through the point (6, 1)? a) x = 6 d) y = 1
b) x = 1 1 e) y = 6
c) y = 6
b) (x+3)(x+5) e) (2x+1)(x+15)
c) (2x+15)(x+1)
6) Factor: 2x2 + 11x + 15 a) (2x+3)(x+5) d) (2x+5)(x+3)
7) The expression x2 10kx + R is a perfect square. Find the value of R. a) 25 d) 100k2
b) 5k2 e) 25k2x2
c) 25k2
8) Consider solving x2 + 12x + 5 = 0 by completing the square: x2 + 12x + ____ = 5 + ____ What is the number that goes in the blanks? a) 144 b) 36 c) 16 d) 16 e) 36
MATH 203 – Winter 2019 Page 6
9) Solve 3x2 5x 1 = 0 using the Quadratic Formula. a)
d)
10 101 3 10
b)
101
e)
9
5 37 6 10
c)
5
37 6
101 3
10) The graph of the parabola y = x2 + 6x + 13 is symmetric about a line. What is the equation of that line? a) x = 3 d) y = 0
b) x = 0 e) y = 3
c) x = 3
11) What is the equation of the circle centered at (4, 5) with a radius of 16? a) (x + 4)2 + (y 5)2 = 16 c) (x + 4)2 + (y 5)2 = 256 e) (x + 4)2 + (y 5)2 = 4
b) (x 4)2 + (y + 5)2 = 4 d) (x 4)2 + (y + 5)2 = 256
12) Determine which of the following triangles are right triangles if the sides’ lengths are: I) 8, 15, 17 II) 4, 5, 6 III) 2, 2, 3 IV) 9, 12, 15 a) I only
b) II only
c) III only
d) I and IV only
e) I, II and IV
13) A triangle ABC has right angle B. Sides AB and BC have the lengths 3 and 4 respectively. Determine the cosine of angle A (cos A). a)
3 5
b)
3 4
c)
4 5
d)
4 3
e)
5 3
c)
adjacent hypotenuse
14) Which of the following ratios is the tangent of an angle? hypotenuse adjacent
a)
opposite hypotenuse
b)
d)
hypotenuse opposite
e)
opposite adjacent
c)
3 2
15) What is the value of sin
a)
1 2
2 ? 3
b)
1 2
d)
3 2
d)
2 2
e)
2 2
16) What is the value of cot a) 0
3 ? 2
b) 1
c) 1
e) does not exist
MATH 203 – Winter 2019 Page 7
17) What is the value of log2 64? a) 6
b) 8
c) 16
18) Which of the following is equal to log k A A
a) k 3 A
3 b) k 2
c)
d) 128
e) 4096
3 ? 2 3 k A 2
d) A k
3 2
3 e) A k
19) Write as a single logarithm: log 8 5 2 log 8 6 a) log 8
5 36
b) log 8
20) What is the result when log
a) log A +
5 12
d) log 8 41
e) log 8 180
AB is expanded? C
1 (log B log C) 2
c) log A + log B – 2 log C e) log A + log B
c) log 8 11
b)
1 (log A + log B – log C) 2
d)
1 (log A log B – log C) 2
1 log C 2
ANSWERS:
1.b);2.b);3.c);4.a);5.d);6.d);7.c);8.b);9.c);10.a);11.d);12.d);13.a);14.e);15.c);16.a);17.a);18.e); 19. a); 20. e)...
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