138 Course Outline W19.pdf - University of Waterloo MATH...

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University of Waterloo MATH 138 Calculus II for Honours Mathematics Winter 2019 Course objectives. The goal of this course is to further expand your knowledge of calculus and its applications for one-variable functions. The course can broadly be split into three parts. First, we will explore areas under curves and the Fundamental Theorem of Calculus, integration techniques, and applications of integration including finding the area between two curves, volumes of solids of revolution, and the average value of a function. Secondly, we will examine differential equations. We will study how to solve separable differential equations and linear differential equations as well as their applications to population growth and Newton’s Law of Cooling. Finally, we investigate infinite series. Various tests of convergence will be introduced for series of numbers. Then, we study power series with a focus on Taylor series and look at their applications. Tentative Course Schedule Week Dates Text Sections Topics Events 1 Jan 7–11 1.2–1.4 Riemann Sums, Definite Integrals, Average Value 2 Jan 14–18 1.5–1.7 FTC I, FTC II, Change of Variable Quiz 1 3 Jan 21–25* 2.1–2.3 Trig. Sub., Integration By Parts, Partial Fractions Quiz 2 4 Jan 28–Feb 1 2.4, 3.1 Improper Integrals, Areas Between Curves Quiz 3 5 Feb 4–8 3.2, 3.3, 4.1, 4.5.1 Volumes, Intro to DEs, Direction Fields Quiz 4 MT Feb 11–15** 4.2, 4.3, 4.5–4.8 Separable DEs, Linear DEs, Applications Quiz 5 RW Feb 18–22 READING WEEK 6 Feb 25 –Mar 1 5.1–5.4 Intro to Series, Geo. Series, Div. Test midterm 7 Mar 4–8 5.5–5.7 Positive Series, Integral Test, Alternating Series Quiz 6 8 Mar 11–15 5.8–5.10 Types of Convergence, Ratio & Root Tests Quiz 7 9 Mar 18–22 6.1, 6.2, 6.3 Intro. to Power Series, Functions, Differentiation Quiz 8 10 Mar 25–29 6.4, 6.5, 6.6, 6.7 Integration, Review of Taylor Polys., Taylor Series Quiz 9 FE Apr 1–5 6.8, 6.9, 6.10 Convergence, Binomial Series, Applications Quiz 10 * 100% tuition refund deadline Jan 25 th ** 50% tuition refund deadline Feb 15 th Drop, penalty 1 period ends March 22 nd

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