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Unformatted text preview: Lecture VI Calculus of Vector Functions R d 2 R Recall that d denotes the first-order derivative of R ( t ), and that dt 2 de- dt notes the second-order derivative of R ( t ). We introduce new notations for these R R R ( t ) = a 1 ( t ) i + a 2 ( t ) + a 3 ( t ) functions: d = R ( t ) and d 2 = R ( t ). Let j k . dt dt 2 Then the following differentiation rules stand: j + a 3 ( t ) 1. R ( t ) = a 1 ( t ) i + a 2 ( t ) k . a 1 ( t ) i + j a 3 ( t ) 2. R ( t ) = a 2 ( t ) + k . A ( t ) and Let B ( t ) be differentiable vector functions, and let a ( t ) be a differentiable scalar function. The following differentiation rules stand: dt ( 3. d A ( t ) + B ( t )) = A + B . 4. d A ( t )) = a ( t ) A ( t ) + a ( t ) A ( t ). dt ( a ( t ) dt ( A B . 5. d A ( t ) B ( t )) = A B + 6. d A ( t ) B + B ( t )) = A A B ....
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