Calculus Volume 3 · free preview
Vector Fields
Vector fields assign a vector to each point of the plane or space, modeling fluid flow, forces, and gradients, with flow lines threading the field and the gradient fields the conservative special case.
1. Vector fields and their models
Vector fields and their models
2. Flow lines
Flow lines
3. Gradient and conservative fields
Gradient and conservative fields
4. Fields in physics
Fields in physics
5. Vector field definition
A vector field on the plane is which kind of function?
6. Flow line condition
A flow line of the field F satisfies which equation?
7. Conservative field definition
A vector field is conservative when it is which special form?
8. Rotation field flow lines
The flow lines of the rotation field F = (-y, x) are which curves?
9. Source and sink
A point where vector field arrows point outward is called a source, and inward a what? Answer with one word.
10. Scalar field contrast
A function assigning a number to each point is called which kind of field? Answer with two words.
11. Flow line alternate name
Flow lines are also called streamlines or integral what? Answer with one word.
12. Radial field formula
The radial field pointing outward from the origin is (x, y) times which constant for the unit version? Answer with a number.
13. Gradient field example
The gradient field of f(x, y) = x^2 + y^2 is which vector field?
14. Potential level relation
A conservative field's potential has level curves which relation to the field's flow lines? Answer with one word.
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