Triple integrals in cylindrical and spherical coordinates
Triple integrals in cylindrical and spherical coordinates
Triple integrals in cylindrical and spherical coordinates
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MATH 209—<br />
Calculus,<br />
III<br />
Volker Runde<br />
<strong>Triple</strong><br />
<strong><strong>in</strong>tegrals</strong> <strong>in</strong><br />
cyl<strong>in</strong>drical<br />
coord<strong>in</strong>ates<br />
<strong>Triple</strong><br />
<strong><strong>in</strong>tegrals</strong> <strong>in</strong><br />
<strong>spherical</strong><br />
coord<strong>in</strong>ates<br />
Spherical coord<strong>in</strong>ates coord<strong>in</strong>ates<br />
Rectangular versus <strong>spherical</strong> coord<strong>in</strong>ates<br />
x = ρ s<strong>in</strong> φ cos θ,<br />
y = ρ s<strong>in</strong> φ s<strong>in</strong> θ,<br />
z = ρ cos φ,<br />
ρ 2 = x 2 + y 2 + z 2 .
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