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Unformatted text preview: 1 tom.h.wilson tom.wilson@mail.wvu.edu Tom Wilson, Department of Geology and Geography Dept. Geology and Geography West Virginia University Simultaneous Equations A kD A 1) 1490 (19.75) 2) 10510 (407) k A k A Two unknowns k and A To determine these two unknowns you need at least two sets of observations Tom Wilson, Department of Geology and Geography 2) 10510 (407) k A These are simultaneous equations 2 1) 1490 (19.75) k A Simultaneous Equations 2) 10510 (407) k A From observation 1 express A o as 1) 1490 (19.75) A k Which you can then substitute into 2) to solve for k Tom Wilson, Department of Geology and Geography Which you can then substitute into 2) to solve for k 2) 10510 (407) 1490 19.75 10510 1490 (407 19.75) k k k (10510 1490 ) (407 19.75 ) yrs yrs k cm cm Simultaneous Equations 23.29 A yrs k D c m Then take observation 1) or 2 and solve for A Tom Wilson, Department of Geology and Geography 3 2000 150 Estimating the rate of change of functions with variable slope y = x 3 500 1000 1500 y = x 2 50 100 Slope Tom Wilson, Department of Geology and Geography X 2 4 6 8 10 12 14 X 5 10 15 20 X2 X1 del x del y slope 7 5 2 2 4 1 2 8 4 4 4 8 1 2 10 2 8 96 12 X2 X1 del x del y slope 7 5 2 218 109 8 4 4 448 112 10 2 8 992 124 Derivatives > The process of taking a derivative (computing the tangent at a point on a curve) results in a set of rules that vary with the type and complexity of function you are trying to differentiate. It is best to memorize these rules so you can make ready use of them. Tom Wilson, Department of Geology and Geography Memory helps put them into practice and makes them more concrete to manage 4 Rules Rules Rules Tom Wilson, Department of Geology and Geography The book works through the differentiation of y = x 2 so differentiation of y = x 2 , so lets try y =x 4 . 4 ) ( dx x dy y multiplying that out  you get ... Tom Wilson, Department of Geology and Geography 4 3 2 2 3 4 ) ( ) ( 4 ) ( 6 4 dx dx x dx x dx x x dy y 5 Tom Wilson, Department of Geology and Geography 4 3 2 2 3 4 ) ( ) ( 4 ) ( 6 4 dx dx x dx x dx x x dy y 4 3 2 2 3 4 ) ( ) ( 4 ) ( 6 4 dx dx x dx x dx x x dy y Remember the idea of the dy and dx is that they represent differential changes that are infinitesimal  very small....
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This document was uploaded on 02/29/2012.
 Spring '09
 Geography, Geology

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