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Unformatted text preview: Lecture 5 January 10, 2012 References: Marsden and Tromba, Vector Calculus , E.B. Wilson, Vector Analysis , Courant and John, Introduction to Calculus and Analysis 1 3D coordinate systems We live in a three dimensional world, hence it is helpful to be able to represent points, surfaces and volumes in three dimensional space. We have denoted a point in cartesian coordinates in two dimensions by ( x,y ) R 2 ADD PICTURE The extension to three dimensions is easy, we denote a point by ( x,y,z ) R 3 . ADD PICTURE Note that the convection for howe we order our coordinate system can be im- portant in applications. It is good to be consistent, and in most applications a right-handed coordinate system is assumed. In this setting if the thumb on our right hand points up, then if we curve our fingers around, they go from the x- axis to the y- axis. As an example the point (1 , 3 , 4) has x- coordinate 1, y- coordinate 3 and x- coordinate 4....
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This note was uploaded on 01/18/2012 for the course MATH 255 taught by Professor Jackwaddell during the Winter '08 term at University of Michigan.
- Winter '08
- Vector Calculus