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# 09.22 - [Take formal attendance Demboske,Michael J...

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[Take formal attendance] Demboske,Michael J DeWitt,Stephen John Amon Frey,Samuel B Kennedy,Dean Leger,Christopher James Natti,Elias Henry Pflanz,Timothy R Pham,CiCi Polcari,Matteo Joseph Skinner,Brie Lynn Smith,Christopher William-Devereaux Wall,Bradley David [Announce office hours; return homeworks] Section 10.7: Vector functions and space curves Main ideas of pp. 559–563? ..?.. The connection between space curves and ranges of vector functions Matching vector equations with the curves they determine Parametrizations of curves in space are not unique Visualization of curves in three dimensions 2-D plane curves: r ( t ) = x ( t ), y ( t ) = the vector with tail at (0,0) and head at ( x ( t ), y ( t )). This is the vector-function [ O P ( t )] that at time t points from the origin O to the moving point P ( t ) = ( x ( t ), y ( t )).

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Example: r ( t ) = t 2 , t 4 . What curve does the head of this vector trace out as t goes from –1 to 1? ..?.. The part of the parabola y = x 2 with 0 x 1. On to three dimensions! r ( t ) = x ( t ), y ( t ), z ( t ) Example: cos t , sin t , t Show “Vector Functions and Space Curves” (curve 2)
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09.22 - [Take formal attendance Demboske,Michael J...

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