Transcription of Vector Calculus - Whitman College
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Vector Calculus - Whitman College
16 Vector torFieldsThis chapter is concerned with applying Calculus in the context ofvector fields. Atwo-dimensional Vector field is a functionfthat maps each point (x, y) inR2to a two-dimensional vectorhu, vi, and similarly a three-dimensional Vector field maps (x, y, z) tohu, v, wi. Since a Vector has no position, we typically indicate a Vector field in graphicalform by placing the vectorf(x, y) with its tail at (x, y). Figure shows a represen-tation of the Vector fieldf(x, y) =h x/ x2+y2+ 4, y/ x2+y2+ 4i. For such a graphto be readable, the vectors must be fairly short, which is accomplished by using a differentscale for the vectors than for the axes.
Vector Calculus 16.1 Vector Fields This chapter is concerned with applying calculus in the context of vector fields. A two-dimensional vector field is a function f that maps each point (x,y) in R2 to a two-dimensional vector hu,vi, and similarly a three-dimensional vector field maps (x,y,z) to hu,v,wi.
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