   Chapter 15.8, Problem 10E

Chapter
Section
Textbook Problem

Write the equation in spherical coordinates.10. (a) z = x2 + y2 (b) z = x2 – y2

(a)

To determine

To write: The given equation into spherical coordinates.

Explanation

Given:

The equation z=x2+y2 .

Formula used:

The rectangular coordinates (x,y,z) corresponding to the spherical coordinates (ρ,θ,ϕ) is,

x=ρsinϕcosθy=ρsinϕsinθz=ρcosϕ

Calculation:

From the formula mentioned above,

z=x2+y2ρcosϕ=(ρsinϕcosθ)2+(ρsinϕsinθ)2ρcosϕ=ρ2sin2ϕcos2θ+ρ2sin2ϕsin2θ

(b)

To determine

To write: The given equation into spherical coordinates.

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