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# CALCULUS III MA 242H

NCS

GPA 3.93

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This 3 page Study Guide was uploaded by Braeden Lind on Thursday October 15, 2015. The Study Guide belongs to MA 242H at North Carolina State University taught by Staff in Fall. Since its upload, it has received 43 views. For similar materials see /class/223728/ma-242h-north-carolina-state-university in Mathematics (M) at North Carolina State University.

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Date Created: 10/15/15

Study Guide for Test 4 MA 242 on campus MA 242601 and MA 242651 The test will cover the following sections of Chapter 13 1 2 3 5 and 6 In addition it will contain material from Chapter 10 section 5 on parametric surfaces material on pages 787 788 and Section 6 of Chapter 12 1 Chapter 13 section 1 Vector elds a You should know the general de nition of a vector eld and know the de nition of a conservative vector eld and potential function for a conservative vector eld 2 Chapter 13 section 2 Line Integrals a Be able to compute line integrals of the following type in which the parametrized curves will be speci ed in the problem so that you will NOT have to nd the parametrizations of the curves to work the problems i C fxyzds The line integral of a function with respect to arc length 1 ii 0 F dF The line integral of a vector eld along a curve The Work lntegral 3 Chapter 13 section 3 Fundamental Theorem for Line lntegrals a You should know and be able to use the Fundamental Theorem for Line lntegrals given on page 936 in your textbook b You should know how to a given vector eld to determine if it is conservative or not The information you need here is given in several places 1 For two dimensions see Theorem 5 page 939 2 For three dimensions see problem 27 page 944 3 Finally note that after we studied the curl of a vector eld section 135 we repackaged the preceding ideas in Theorem 4 page 954 c You should be able to nd all potential functions for a given conservative vector eld For a review see either the postscript or pdf version of the le 77Finding Potential Functions77 on my homepage at httpwwwmathncsuedu lknMA242009mainpagehtml 4 Chapter 12 section 5 Divergence and curl of vector elds a You should be able to compute the divergence V and the curl V gtlt F of a given vector eld b You should know the two identities V gtlt Vf 9 and V V gtlt 0 The rst of these is used in the test for a convervative vector eld and the second can be used to answer questions of type given in problems 17 and 18 on page 958 in your textbook Cf Chapter 10 section 5 Parametric Surfaces You should know the de ntion of a parametric surface and how to use them in the sections that follow I will not ask you parametrize any surfaces on this test since you have done this already in Maple HW 4 6 I 00 Pages 787 788 Be able to nd an equation for the tangent plane to a given parametric surface Chapter 127 section 6 Surface Area of Pararnetrized Surfaces You should be able to set up the Double lntegral ffD HF gtlt Full dA as a double iterated integral to compute the surface area of a pararneterized surface S7 given the pararnetrization for the surface You will NOT have to compute the iterated integral Chapter 137 section 6 Surface lntegrals Given the pararnetrization for a given surface you should be able to set up the following two types of surface integrals as double integrals and then as iterated integrals a 5 fxyzdS The surface integral of a function b f S F dS The surface integral of a vector eld 03 q 01 a 1 Test 1 study Guide MA 242601 and MA 242651 LK Norris NOTE The material in sections 96 and 97 will NOT be covered on this test Know the de nition of Cartesian coordinates in space VECTORS Know how to work with vectors This includes a adding and subtracting multiplying by a scalar dot and cross products and vector projections b Know and be able to use Theorem 932 and the theorem in the LAST box on page 668 of your textbook Lines and planes Section 95 Know the equations for lines and planes in space Be able to work problems like those worked out in the textbook and in lecture In particular you should be able to work problems like problems 2 28 on pages 683 684 Vector functions and space curves Section 101 a Know the de nition of a vector valued function Be able to determine the do main of a vector valued function b Know how to determine if a vector valued function of t has a limit at a point to and whether or not a vector valued function of t is continuous at a point to c NOTE You will NOT be asked to sketch any curves on the test Section 102 derivatives and integrals of vector functions a Be able to compute derivatives and integrals of vector valued functions b Know the properties in Theorem 3 on page 714 c Be able to compute the unit tangent vector T for a given curve Sectionsw 103 104 Arc length curvature of a curve and motion in space a Be able to compute the arc length of simple curves as in Example 1 page 718 and problems 1 4 on page 723 b Know the de nitions of curvature of a curve and unit normal vector of a curve and be able to compute both quantities for a given curve c Be able to compute The normal an and tangential aT components of accelera tion and the curvature using the following formulas 73yquot 4 d NOTE I will NOT ask you about the unit binormal B vector for a curve

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