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MATH 2413Fall2012, Lectures1-3 QingwenHu DepartmentofMathematicalSciences TheUniversityofTexasatDallas Richardson, Texas [email protected] August, 2012 . QingwenHu (UTD) Lecture1-3 . . . . August, 2012 . 1/4 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: . . 3. 4. 5. 6. 1 2 13gradedhomeworkpostedate-Learning, 10% 14digitalhomeworkpostedatWebAssign, 10% 13classnotes, 5% 11quizzes, 15% 2exams, 20%+15% 1Finalexam, 25% . QingwenHu (UTD) Lecture1-3 . . . . August, 2012 . 1/4 Sometipsonlearningcalculus . Keepitaroutinetoworkonthehomework; Thefastestwaytoget intotroubleincalculusisnottodothehomework; 2. Listeningtothelectures, weunderstandthegeneralphilosophy; 1 doingthehomework, weacquiretheskills. .3 Mostimportant: Alwayskeepcurioustoaskwhy? Whatisthemotivation? Insucha way, wecandevelopabilitiestoworkindependentlyandactively. . QingwenHu (UTD) Lecture1-3 . . . . August, 2012 . 2/4 Outlineofthetopics . Functionanditsdefinition; 2. Graphoffunctions; Theverticallinetest; 1 . Domainconvention; 4. Symmetryofthegraphofafunction; even/oddfunctions; 3 . Monotonicfunctionsandtheirdefinitions; 6. Absolutevaluefunctionanditssimplifiednotation; 5 . Polynomials; 8. Powerfunctions; 7 . Rationalfunctions; Algebraicfunctions; . Trigonometricfunctions; 10 9 . Exponentialfunctions; Lawsofexponents, thenumber e; . Logarithmicfunction. 12 11 . QingwenHu (UTD) Lecture1-3 . . . . August, 2012 . 3/4 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. . QingwenHu (UTD) Lecture1-3 . . . . August, 2012 . 4/4