othercoordinates

othercoordinates - POLAR,CYLINDRICAL,SPHERICAL COORDINATES...

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POLAR,CYLINDRICAL,SPHERICAL COORDINATES Math21a, O. Knill HOMEWORK: 14.8: 4,10,19. Problem A) invent a surface ρ = f ( φ, θ ), simple enough to draw, but not in the book. Problem B) invent a surface r = g ( θ, z ),, simple enough to draw but not appear in the book. You can use technology like online applets or graphing software like Grapher if you like. POLAR COORDINATES. A point ( x, y ) in the plane has the polar coordinates r = r x 2 + y 2 , θ = arctg( y/x ). We have ( x, y )( r cos( θ ) , r sin( θ )) Footnote: Note that θ = arctg( y/x ) defnes the angle θ only up to an addition o± π . The points ( x, y ) and ( - x, - y ) would have the same θ . In order to get the correct θ , one could take arctan( y/x ) in ( - π/ 2 , π/ 2] as Mathematica does, where π/ 2 is the value when y/x = , and add π x < 0 or x = 0 , y < 0. In Mathematica, you can get the polar coordinates with ( r, θ ) = (Abs[ x + Iy ] , Arg[ x + Iy ]). x
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This note was uploaded on 03/29/2008 for the course MATH 251 taught by Professor Skrypka during the Spring '08 term at Texas A&M.

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