2224-Sec13_1-HWT

2224-Sec13_1-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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Math 2224 Multivariable Calculus – Chapter 13 Multiple Integrals Sec. 13.1: Double and Iterated Integrals over Rectangles I. Review from math 1205 A. Riemann Sums Def n : Given y=f(x) : 1. Let f be defined on a closed interval [ a,b ]. 2. Partition [ a,b ] into n subintervals[ x ki-1) ,x k ] of length Δ x k = x k -x (k-1) . Let P denote the partition a = x 0 , x 1 , x 2 ,..., x n = b . 3. Let P be the length of the longest subinterval. ( P - norm of the partition P.) 4. Choose a number c k in each subinterval ( c k may be an endpoint). 5. Form the Riemann Sum: S n = f c k ( ) ! " # $ % x k ( ) { } k = 1 n B. Definite Integral 1. Def n : If f is a continuous function defined for a ! x ! b , we divide the interval [ a,b ] into n subintervals of equal width ! x = b " a n . We let a = x 0 , x 1 , x 2 ,..., x n = b be the endpoints of these subintervals and we choose sample points c 1 , c 2 , c 3 ,..., c n in these subintervals, so c k lies in the k th subinterval [ x k-1
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2224-Sec13_1-HWT - Mat h 22 24 Multiva ri a ble C alc ul us...

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