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University of WaterlooMATH 138Calculus II for Honours MathematicsWinter 2018Course objectives.The goal of this course is to further expand your knowledge of calculus and its applicationsfor one-variable functions. The course can broadly be split into four parts. First, we will explore areas under curvesand the Fundamental Theorem of Calculus, integration techniques, and applications of integration including findingthe area between two curves, volumes of solids of revolution, and the average value of a function. Secondly, we willexamine differential equations.We will study how to solve separable differential equations and linear differentialequations as well as their applications to population growth. Thirdly, we investigate infinite series. Various tests ofconvergence will be introduced for series of numbers. Then, we study power series with a focus on Taylor series andlook at their applications.Finally, the course will conclude with the study of vector-valued functions, parametriccurves, and polar coordinates.Tentative Course ScheduleWeekDatesText SectionsTopicsEvents1Jan 3–51.1, 1.2, 1.3Areas Under Curves, Riemann Sums, Definite Integrals2Jan 8–121.3, 1.4, 1.5, 1.6Definite Integrals, Average Value, FTC I, FTC IIA1 due3Jan 15–191.7, 2.1, 2.2Change of Variable, Trig. Sub., Integration By PartsA2 due4Jan 22–26*2.3, 2.4Partial Fractions, Improper IntegralsA3 due5Jan 29–Feb 23.1, 3.2, 3.3, 3.4Areas, Volumes, ArclengthA4 due6Feb 5–94.1, 4.2, 4.3, 4.4Intro to DEs, Separable DEs, Linear DEs, IVPsA5 due7Feb 12•–164.5, 4.6, 4.7, 4.8Qualitative Solutions, Applications of DEsmidterm•8Feb 19–23**READING WEEK9Feb 26–Mar 25.1–5.4, 5.5, 5.6Review of Seq. and Series, Positive Series, Integral TestA6 due10Mar 5–95.7, 5.8, 5.9Alternating Series, Types of Convergence, Ratio TestA7 due11Mar 12–166.1, 6.2, 6.3Intro. to Power Series, Functions, DifferentiationA8 due12Mar 19–23†6.4, 6.5, 6.6, 6.7Integration, Review of Taylor Polys., Taylor SeriesA9 due13Mar 26–30♠6.8, 6.9, 6.10Convergence, Binomial Series, ApplicationsA10 due14Apr 2–4Chapter 7Curves* 100% tuition refund deadline Jan 23rd** 50% tuition refund deadline Feb 20th†Drop, penalty 1 period ends March 20th(note that drop, penalty 2 period ends April 8th)•Midterm Test: