divergence of vector function

1. Presentation on
Engineering Mathematics
Serajush Salekin
ID:141-15-3209
Sec- D

2. Topic
• Divergence of Vector function

3. Divergence of vector function
• If φ=φi+φj+φk is continuious and differentiable vector valued
function in a real field then the divergence of φ is denoted by div.
φ and difined as
• φ =(i
𝑑
𝑑𝑥
+
𝑑
𝑑𝑦
j+
𝑑
𝑑𝑧
k)(φ i+ φ j+ φ k)
=
𝑑
𝑑𝑥
φ1
+
𝑑
𝑑𝑦
φ2
+
𝑑
𝑑𝑧
φ3

4. Problem
• If φ=i𝑥2+j𝑦2+k𝑧2 then find divergence at the point (1,0,1)

5. Solution
Given that,
φ=i𝑥2+j𝑦2+k𝑧2
Now,
div. φ = φ
=(i
𝑑
𝑑𝑥
+
𝑑
𝑑𝑦
j+
𝑑
𝑑𝑧
k) (i𝑥2+j𝑦2+k𝑧2)
=i
𝑑𝑖𝑥2
𝑑𝑥
+j
𝑑𝑗𝑦2
𝑑𝑦
+k
𝑑𝑘𝑧2
𝑑𝑧
=2x+2y+2z
=2.1+0+2.1
=4
(Point: x=1,y=0,z=1)

6. Result
div. φ =4