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MATH 118: Calculus II for Mechanical EngineersPeter StechlinskiUniversity of Waterloo(Credit to Alex Shum for slides)May 6, 2014Lecture 1Peter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20141 / 12
Important InformationOutline Posted Online on D2L (LEARN), Important ItemsGrading Scheme:Finalmark= max{A,B}A= 10Asst/25Midterm/65Final,B= 7.5Asst/2.5MyMathLab/25Midterm/65FinalCheating/Academic IntegrityMidterm: Monday June 16, 8:30 AMMay 19th Tutorial Cancelled, (Wed May 21 follows May 19 schedule)Assignments Due Fridays in class (starting next week)MyMathLab assts due same day (as written assts) at noonIrrelevant Laptop Use: Sides and Back of the Room PleaseOH: MC6127 Tuesday 12:30 - 1:30 pm, Thursday 12:30 - 1:30 pm, oryou can e-mail me for an appointment.Peter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20142 / 12
Topics OutlineFour Broad Concepts:IntegrationDifferentialEquationsSequences andSeriesy=exPolar Co-ordinatesPeter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20143 / 12
Integration: Recap and ReviewOpposite of Differentiation:E.g.ddxx2= 2xZ2xdx=x2+CE.g.ddxcos(x2) sin(x) =-2xsin(x2) sin(x) + cos(x2) cos(x)Z(-2xsin(x2) sin(x) + cos(x2) cos(x))dx= cos(x2) sin(x) +CFundamental Theorem of Calculus 1: (FTC 1)Zbaf(x)dx=F(b)-F(a) whereF0(x) =f(x);Fundamental Theorem of Calculus 2: (FTC 2)ddxZxaf(t)dt=f(x)Peter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20144 / 12
Recap and ReviewDefinite Integral: Area (above x-axis: +ve, below x-axis: -ve)Adding rectangles height defined by function.Zbaf(x)dxNXi=1f(xi)4xiInfinite rectangles:Rbaf(x)dx= Sum fromatob,f(x) is height,dxwidth.Peter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20145 / 12
Recap and ReviewDefinite Integral: Area (above x-axis: +ve, below x-axis: -ve)Adding rectangles height defined by function.Zbaf(x)dxNXi=1f(xi)4xiRbPeter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20145 / 12
Integration Techniques: SubstitutionNew stuff, time to pay attention. Take notes!Integration is way harder than differentiation.f(x) =ecos(x)arctan(11+x2)ln(sin(sin(x))) + csc(1x)Next 3 weeks: Techniques of IntegrationSubstitution -Substitute the variable of integration with another thatyou chooseIdea: Rewrite all thex’s inRf(x)dxin terms ofu=g(x)anddu.Remember the notationdudx=u0(x), ordu=u0(x)dx=g0(x)dxPeter Stechlinski (University of Waterloo(Credit to Alex Shum for slides))MATH 118: Calculus II for Mechanical EngineersMay 6, 20146 / 12
Example 1Letu(x) = sin(x).