Vector Calculus: Solenoidal and Irrotational Vector Fields (Part 1 of 2)

multiple spectator x i Plus J Plus x square plus y Square in the vector f is equal to X by square plus y square into I plus y by foreign foreign foreign domain um [Music] [Music] B divided by V square e Pharma yield loading it absorb materials V under x square plus e y Square first y Square dou by dou X of p100 difference Square a data Plus 2B and Rhino x square plus y square is a dou by dou y of Y another one minus y 800 dou by dou y of x square plus y Square x square Y is 0 y square is divided by x square plus y Square whole Square then square plus y Square minus X into 2 x 0 2 x square divided by x square plus y Square whole Square Plus square plus y Square minus y into 2 y under 2 y Square to x square plus y Square whole Square okay [Applause] x square plus y Square minus 2 x square plus x square plus y squared minus 2 y Square whole divided by x square plus y Square whole Square meter x square x square 2x 2 x square 2 is equal to 2 y Square 2 y Square cancel out 0.0 [Music] therefore Divergence of effect are 0 1 right now foreign foreign [Music] foreign [Music] X to minus minus J into ethical multiplication zero minus zero plus K into you know dou by dou X [Music] is y by x square plus y Square minus x y square plus y Square negative zero minus zero under zero I mean 0 minus zero minus 0 foreign 0 minus X into ele with respect to Y under a x square is 0 y Square 2y 4 divided by x square plus y Square plus K into minus 2 X Y by square plus y Square whole square is D2 0 minus 2 x square 0 minus 2 X Y by x square plus y Square whole square is foreign

Channel: Mathematics Tutor

Views: 20,754

Keywords: engineering mathematics, vector differentiation, differentiation of vectors, vector calculus, gradient, curl, divergence, solenoidal, Irrotational, find the condition if vector is solenoidal and Irrotational, mathematics tutor, 18mat21, 21mat21, 15mat11, 17mat11

Id: QGsVveNktnk

Length: 9min 18sec (558 seconds)

Published: Wed Feb 08 2023