MATH 2400 Lecture Notes - Lecture 13: Vector Field, Conservative Vector Field, Jansky
22 Apr 2019
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13. 1: math 2400 sec 006/011/ 013, fall 2018. Instructor: dr. xingzbou yang @ 2018 page 1 of 2. F < ~ -;. ,1: definition 1: let d be a set in jr2 (a plan region). A vector field on 1r2 is a function f. F {i -) l that assigns to each point (x, y) e d a vector. F(x , y) = p(x , y)i+q(x , y)j (p(x , y) , q(x, y)) or in short, f = (p, q). P , q are scalar func- tions of two variables, and are called scalar fields to distinguish them from vector fields. fl,4- ~ of ff, v~dqr (x,y) 0: definition 2: let e c jr3 . A vector field on jr3 is a function f that assigns to each point (x , y,z) ee a vector f(x,y, z) e 1r3: gradient vector field v f :
