ch13sec2 - 13.2 Derivatives and Integrals of Vector...

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13.2 Derivatives and Integrals of Vector Functions The derivative of a vector function () , () tf t g t h t = r is ' ' , ' , ' t g t h t = r . Note that you differentiate each component separately. For example, look at the 2-dimensional space curve defined by 4s in , 2cos tt =− t r . If r is the position function of a particle, then r is the velocity function, like the velocity function in one dimension. t '( ) t Let's look at a geometric description of the derivative r . The derivative r is tangent to the space curve r . t t t -2 -1 1 2 -0.5 0.5 1 The figure shown above is the curve 2s ,cos r t with the derivative vector 2 cos( ),
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This note was uploaded on 01/20/2012 for the course MATH 2057 taught by Professor Estrada during the Fall '08 term at LSU.

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