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34 - Lecture 5 References Marsden and Tromba Vector...

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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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