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

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University of Waterloo MATH 138 Calculus II for Honours Mathematics Winter 2018 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 four 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. Thirdly, 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. Finally, the course will conclude with the study of vector-valued functions, parametric curves, and polar coordinates. Tentative Course Schedule Week Dates Text Sections Topics Events 1 Jan 3–5 1.1, 1.2, 1.3 Areas Under Curves, Riemann Sums, Definite Integrals 2 Jan 8–12 1.3, 1.4, 1.5, 1.6 Definite Integrals, Average Value, FTC I, FTC II A1 due 3 Jan 15–19 1.7, 2.1, 2.2 Change of Variable, Trig. Sub., Integration By Parts A2 due 4 Jan 22–26* 2.3, 2.4 Partial Fractions, Improper Integrals A3 due 5 Jan 29–Feb 2 3.1, 3.2, 3.3, 3.4 Areas, Volumes, Arclength A4 due 6 Feb 5–9 4.1, 4.2, 4.3, 4.4 Intro to DEs, Separable DEs, Linear DEs, IVPs A5 due 7 Feb 12 –16 4.5, 4.6, 4.7, 4.8 Qualitative Solutions, Applications of DEs midterm 8 Feb 19–23** READING WEEK 9 Feb 26–Mar 2 5.1–5.4, 5.5, 5.6 Review of Seq. and Series, Positive Series, Integral Test A6 due 10 Mar 5–9 5.7, 5.8, 5.9 Alternating Series, Types of Convergence, Ratio Test A7 due 11 Mar 12–16 6.1, 6.2, 6.3 Intro. to Power Series, Functions, Differentiation A8 due 12 Mar 19–23 6.4, 6.5, 6.6, 6.7 Integration, Review of Taylor Polys., Taylor Series A9 due 13 Mar 26–30 6.8, 6.9, 6.10 Convergence, Binomial Series, Applications A10 due 14 Apr 2–4 Chapter 7 Curves * 100% tuition refund deadline Jan 23 rd ** 50% tuition refund deadline Feb 20 th Drop, penalty 1 period ends March 20 th (note that drop, penalty 2 period ends April 8 th ) Midterm Test:

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