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# Calculus III MA 113

RHIT

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This 3 page Class Notes was uploaded by Eldon Trantow on Monday October 19, 2015. The Class Notes belongs to MA 113 at Rose-Hulman Institute of Technology taught by Staff in Fall. Since its upload, it has received 12 views. For similar materials see /class/225078/ma-113-rose-hulman-institute-of-technology in Mathematics (M) at Rose-Hulman Institute of Technology.

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Date Created: 10/19/15

MA 113 Calculus lll Worksheet 4 Parametric Surface Plots Professor Broughton 7 Winter 03 04 Name Box 1 Cartesian parametric surface plots 0 Download 3Dpotsmws do this worksheet 0 You will have to look over section 106 0 You will need to review material on hyperbolic sins and cosines A Cartesian parametric surface is given by 3 functions of two variables Note that this generalizes the notion of a space curve A parametric plot is an explicit representation of a surface whereas an implicit representation of a surface is given by an equation such as 2 2 2 5 1 i 1 11 4 9 16 which is the equation of an ellipsoid Very often we will want to nd a paramedic representation of a surface to graph the surface or to do some sort of computation For instance smooth 3D modeling often results required nd in certain good tting parametric plots 1 Now consider a speci c parametric plot given by z 2sins cost 12 y 3sins sint z 4coss Plot the surface for 0 S s S 7r2 and 0 S t S 27139 2 Plot the top half of the ellipsoid above by either solving for Z 07quot using implicit plot 3 What is the relationship between the two plots above Substitute the formulas in 2 into 1 and simplify What happens Now consider the surface 2 yz 22 i i 7 i 1 13 4 9 16 4 Repeat Problem 1 for this parametrization7 you will need to come up with a good interval for s z 2 coshs cost 14 y 3coshs sint z 4sinhs 5 Repeat problem 2 for the surface given by 13 and the parametrization given by 14 6 Find a parametrization of the top half of a hyperboloid of one sheet 2 Cylindircal parametric plots A cylindrical parametric surface is given by 3 functions of two variables where 7 t9 2 are the cylindr4ical coordinates of a point in space 7 Suppose that we look at particular type of cylindrical parametric plots of the form with 0 t S 27139 Sketch the following plots f 8 718 1 52 s 71 S s S 1 32coss 3sins 0 s 2W 3COS25 sin3s 0 s 2W 8 Find a parametrization of a torus and plot it

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