Vector Fields (16.1)
A vector field F is conservative if it has this
What is a potential function f ?
int_C 1 dS
What is the length of curve C ?
If F is a conservative vector field, oint F cdot dr =
What is 0 ?
int int_D || N(u, v) || du dv =
What is the area of surface S ?
How do you write 2024 in Roman numerals?
What is MMXXIV ?
For a conservative vector field F, what is known about curl(F)
What is curl(F) = 0?
Formula to compute the scalar line integral of f(r(t))
What is
int_a^b f(r(t)) || r'(t) || dt ?
A potential function f for F = y overset(rightarrow)(i) + x overset(rightarrow)(j)
What is f = xy ?
Formula for a scalar surface integral of f(G(u, v))
What is
int int_D f(G(u, v)) || N(u, v) || du dv ?
At what temperature are Celsius and Fahrenheit equal?
What is -40 ?
div(F) = grad cdot F =
What is
(del F_1)/(del x)+(del F_2)/(del y)+(del F_3)/(del z) ?
Formula to compute the vector line integral of F(r(t))
What is
int_a^b F(r(t)) cdot r'(t) dt ?
Fundamental Theorem for Conservative Vector Fields: If r is a path along a curve C from P to Q, then int_C F cdot dr =
What is f(Q) - f(P) ?
If a fluid has velocity vector field v, the flow rate across S (volume per unit time) =
What is
int int_S v cdot dS ?
What is the depth of the deepest part of an ocean on Earth? (in miles, within 1)
What is 7 miles ? (Mariana Trench)
overset(rightarrow)(e_r) = <x/r, y/r, z/r> is known as _____
What is the unit radial vector?
Formula to compute the work performed by F
What is
int_C F cdot dr = int_C F cdot r'(t) dt ?
The total energy E of a particle moving under the influence of a conservative force field F ______________
What is "is constant" ?
The normal vector in the standard parametrization of the sphere of radius R
What is
R^2 sin phi < cos theta sin phi, sin theta sin phi, cos phi > ?
How many rooms are there in the entirety of the Palace of Versailles ? (within 50%)
What is 2300 ?
The relationship between a conservative vector field F and the level curves of the potential function f
What is orthogonal?
Formula to compute the flux of F across a curve
What is int_a^b F(r(t)) cdot N(t) dt ?
A potential function f for F = < z sec^2x, z, y + tan x >
What is f = z tan x + zy ?
Formula for the vector surface integral of F(G(u, v))
What is
int int_D f(G(u, v)) cdot N(u, v) du dv ?
How many moons would fit inside the Earth? (within 10)
What is 49 ?