Calculus Volume 3 · 免费预览
散度与旋度
散度度量场的单位体积局部流出量，旋度度量其局部旋转；这两个导数是向量场的基本微分算子，而接下来各节中的定理就是它们相应的积分恒等式。
1. Divergence
Divergence
2. Curl
Curl
3. The vector identities
The vector identities
4. The Helmholtz decomposition
The Helmholtz decomposition
5. Divergence definition
The divergence of F = (P, Q, R) equals which expression?
6. Curl definition
The curl of F = (P, Q, R) has which z component?
7. Divergence of curl
The divergence of the curl of any smooth field equals what?
8. Curl of gradient
The curl of the gradient of a scalar function equals what?
9. Irrotational meaning
A field with zero curl everywhere is called irrotational. What does this imply for its flow?
10. Divergence radial
The divergence of (x, y, z) is 3. As a number, what is it? Answer with a number.
11. Curl rotation z
The curl of (-y, x, 0) is (0, 0, 2). As a number, what is the z component? Answer with a number.
12. Incompressible meaning
A zero divergence field is called incompressible, conserving which quantity? Answer with one word.
13. Nabla symbol
The operator symbol for divergence and curl is the inverted delta, nabla. The curl is nabla cross F. As an operation symbol between nabla and F, what is the divergence? Answer with the single word.
14. Laplacian name
The divergence of the gradient is the Laplacian. As a surname, whose? Answer in lowercase.