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</center><p>Calculus: The study of real functions f, and their derivatives f0 and integrals R f. Of course there is a go o d deal of explanation, and annotation as w e go along. R be  By \elementary formula", we mean a formula that can be written down in terms of constants, polynomials, rational functions, exponentials, trigonometric functions, and logarithms  with calculus: it turns out that calculus operations are “easier” when dealing with natural exponentials and logarithms rather than exponentials and logarithms with bases other  Calculusfor Honours Mathematics Instructor: Barbara Forrest Access to the course notes and online lectures are available according to the following terms of use. We can also do this with the product rule, which says that if f;gare di erentiable functions, then d dx If you miss anything, the complete notes will be Area of a Surface of Revolution Calculus with Parametric Curves III Part Three: Sequences and SeriesInfinite Sequences and Series Sequences SeriesThe Integral Test and Estimates of Sums The Comparison Test Alternating Series CALCULUS II (Math) Text: Essential Calculus 2/e by James Stewart Calculus: The study of real functions f, and their derivatives f0and integrals R f. Let f: [a; b]! Note: xis a \dummy" variable Math Foundations of Calculus II Course Notes Barbara A. Forrest and Brian E. Forresty = f(x) aaaan a k n1 nk1 k f(2) f(3) These notes are an exact cop y of the slides used in lectures. The ideal w ay to use these notes is to read ahead and b e prepared for the lecture. The narro w 2 =LectureIntegration by parts Stewart x, Spivak ChA consequence of the product rule We found the substitution rule for integrals by looking at the chain rule for derivatives, and exploring its consequences for integrals. De nition Thede nite integral of ffrom ato bis Z b a f = Z b a f(x)dx:= lim n!1 Xn i=1 f(x i) x where x= (b a)=nand x i = a+ i x. CALCULUS II (Math) Text: Essential Calculus 2/e by James Stewart. Let f: [a;b]!R be continuous. The  Print out the skeleton notes before class and bring them to class so that you don't have to write down everything said in class. But these notes should sa ve you some writing during the class and giv e you more time to listen.</p></translate>
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