Differential Equations Flashcards

1
Q

Writing limits of multivariable functions

A

Lim(x,y)→(a,b) for f

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2
Q

Boundry point

A

Any point that exists on the border of a set of points that meet a multivariable equation

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3
Q

Interior point

A

Point that exists within the set of points that fit the multivariable equation

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4
Q

Open set

A

A set of only interior points

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5
Q

Closed sets

A

A set of points that include all boundary points for a multivariable equation

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6
Q

2 path test

A

If there are two paths to the (x,y) point, the limit does not exist

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7
Q

Partial derivatives for x-value

A

Lim(h→0) [f(a+h,b)-f(a,b)]/h

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8
Q

Partial derivatives for y-value

A

Lim(h→0) [f(a+h,b)-f(a,b)]/h

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9
Q

Higher order Derivatives

A

J

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10
Q

Differentiable points on a region

A

Of a function is differentiable at one point, its differentiable at all points

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11
Q

Chain Rule (One independent Variable)

A

H

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12
Q

Chain Rule (Two independent Variables)

A

S

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13
Q

Implicit Differentiation

A

dy/dx=-F(x)/F(y)

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14
Q

Directional Derivative

A

Lim(h→0) (f(a+hcosθ,b+hsinθ)-f(a,b))/h

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15
Q

Check for extrema in surfaces using differtial equations

A

P

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16
Q

Euler’s method for differential equations

A

D