
Theorems in Multivariable Calculus

Interactive Video
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Mathematics
•
University
•
Hard

Thomas White
FREE Resource
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8 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What was the speaker's initial challenge with multivariable calculus?
Understanding individual theorems
Seeing the connections between theorems
Solving complex equations
Memorizing formulas
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which theorem is a special case of Stokes's theorem?
Fundamental theorem of line integrals
Fundamental theorem of single variable calculus
Divergence theorem
Green's theorem
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the fundamental theorem of single variable calculus relate?
The integral of a function to its derivative
The derivative of a function to its integral
The sum of function values to the integral of its derivative
The difference between function values to the integral of its derivative
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of line integrals, what is a vector field?
A function that outputs a scalar at each point in space
A function that outputs a vector at each point in space
A function that outputs a matrix at each point in space
A function that outputs a tensor at each point in space
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does Green's theorem help to measure in a vector field?
The gradient of the field
The curl of the field
The flux of the field
The divergence of the field
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the curl in Stokes's theorem?
A scalar function
A vector field
A matrix
A tensor
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the Divergence Theorem relate?
The integral over a line to the integral over a surface
The integral over a surface to the integral over a volume
The integral over a curve to the integral over a line
The integral over a volume to the integral over a surface
8.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the generalized Stokes's theorem?
It is only relevant for physicists
It only applies to two-dimensional calculus
It generalizes calculus to any number of dimensions
It simplifies all calculus to a single dimension
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