Calculus Volume 3 · 免费预览
柱坐标与球坐标
柱坐标把极坐标推广到三维空间并加上高度，球坐标则使用径向距离和两个角；每种坐标系统都能简化对称区域上的三重积分。
1. Cylindrical coordinates
Cylindrical coordinates
2. Spherical coordinates
Spherical coordinates
3. Choosing the system
Choosing the system
4. The Jacobian preview
The Jacobian preview
5. Cylindrical definition
Cylindrical coordinates are which combination?
6. Spherical phi meaning
In spherical coordinates, the angle phi measures what?
7. Volume element Jacobian
The spherical volume element is which expression?
8. Conversion example
The point (1, 1, 0) in Cartesian has cylindrical coordinates which triple?
9. When spherical wins
A triple integral over a solid ball is simplest in which coordinate system?
10. Cylinder surface constant
In cylindrical coordinates, the surface r = 2 is which solid's boundary? Answer with one word.
11. Rho constant surface
In spherical coordinates, the surface rho = 3 is a sphere. As a single word, what surface? Answer with one word.
12. Phi constant surface
The surface phi = pi/4 is a cone about the z axis. As a single word, what surface? Answer with one word.
13. Theta range uniqueness
The spherical and cylindrical systems share the azimuthal angle theta. Over what range does a full turn run? Answer like 0 to 2 pi.
14. Z conversion cylindrical
Cylindrical coordinates leave which coordinate unchanged from Cartesian? Answer with one lowercase letter.