Parametric Equations

Parametric Equations - Parameterization Study Guide Charlie...

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Parameterization Study Guide Charlie Egedy April 3, 2009 1 Parametric Equations A parameterization is a vector valued function c ( t )= ° f ( t ) ,g ( t ) ,h ( t ) ± .I f h ( t ) = 0, then we can talk about a parameterization of a path in R 2 ; otherwise, we have a path in R 3 . In R 2 , we can parameterize a line through the point ( a, b ) having slope m ,by c ( t )= ° a + t, b + mt, 0 ± . A standard way to parameterize a cirle in R 2 having center at ( a, b ) and radius R is c ( t )= ° a + R cos θ,b + R sin θ, 0 ± , thereby giving the circle a counter-clockwise orientation. The cycloid in R 2 has parameterization c ( t )= ° Rt R sin( t ) ,R R cos( t ) ± . Given a parameterization c ( t ), we can facilitate the construct of a graph by computing the fol- lowing quantities. Set the Frst coorinate equal to zero to Fnd y -intercepts; set the second coorinate equal to zero to Fnd x -intercepts. Compute derivatives using the equations dy dx = dy dt dx dt and d 2 y dx 2 = d dt ( dy dx ) dx dt .
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This note was uploaded on 03/20/2012 for the course MATH 1552 taught by Professor Staff during the Spring '08 term at LSU.

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Parametric Equations - Parameterization Study Guide Charlie...

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