Download Lectures 1 to 3

MATH 2413Fall2012, Lectures1-3
QingwenHu
DepartmentofMathematicalSciences
TheUniversityofTexasatDallas
Richardson, Texas
[email protected]
August, 2012
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QingwenHu (UTD)
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Courseinformation
1. Instructor: QingwenHu
2. Timeandlocation: M &W &F
2:00pm–2:50pmforMATH2413.004FO 2.208
3. Formoredetails, seethecoursewebsiteate-Learningandthe
syllabus
4. Text: Calculus, EarlyTranscendentals, Stewart, 7/6thedition
5. Gradepolicy:
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13gradedhomeworkpostedate-Learning, 10%
14digitalhomeworkpostedatWebAssign, 10%
13classnotes, 5%
11quizzes, 15%
2exams, 20%+15%
1Finalexam, 25%
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Sometipsonlearningcalculus
. Keepitaroutinetoworkonthehomework; Thefastestwaytoget
intotroubleincalculusisnottodothehomework;
2. Listeningtothelectures, weunderstandthegeneralphilosophy;
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doingthehomework, weacquiretheskills.
.3 Mostimportant:
Alwayskeepcurioustoaskwhy? Whatisthemotivation? Insucha
way, wecandevelopabilitiestoworkindependentlyandactively.
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Outlineofthetopics
. Functionanditsdefinition;
2. Graphoffunctions; Theverticallinetest;
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. Domainconvention;
4. Symmetryofthegraphofafunction; even/oddfunctions;
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. Monotonicfunctionsandtheirdefinitions;
6. Absolutevaluefunctionanditssimplifiednotation;
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. Polynomials;
8. Powerfunctions;
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. Rationalfunctions; Algebraicfunctions;
. Trigonometricfunctions;
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. Exponentialfunctions; Lawsofexponents, thenumber e;
. Logarithmicfunction.
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Exercises
Dropinmyofficeifyouareinterestedtosolvethem.
x
3
1. Solvetheequation x−1
− x−2
= 1 for x ∈ R.
2. Solvetheinequalitiesfor x ∈ R. a) |2x + 3| > 7, b) |3x − 2| < 7.
3. Showthatthefunction y = x2 isdecreasingontheinterval (−∞, 0].
Howabout y = x3 ?
4. Let f beafunctiondefinedin R whichsatisfies
( )
f
1
x
=
1
forevery x ∈ R, x ̸= 0.
x+1
Findtheexpressionof f anddetermineitsdomain.
5. Let a beaconstant. Supposethattheset {x|ax2 + 2x + 1 = 0} ⊆ R
hasauniqueelement. Findallthevalue(s)of a. Justifyyouranswer.
6. Let f beanoddfunctiondefinedin R. If f (0) isdefined, canyou
determinethevalueof f (0)? Justifyyouranswer.
7. Isittruethateverydecreasing(increasing)function f : R → R is
one-to-one? Istheconversetrue? Justifyyouranswers.
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