Differential Equations Flashcards
Writing limits of multivariable functions
Lim(x,y)→(a,b) for f
Boundry point
Any point that exists on the border of a set of points that meet a multivariable equation
Interior point
Point that exists within the set of points that fit the multivariable equation
Open set
A set of only interior points
Closed sets
A set of points that include all boundary points for a multivariable equation
2 path test
If there are two paths to the (x,y) point, the limit does not exist
Partial derivatives for x-value
Lim(h→0) [f(a+h,b)-f(a,b)]/h
Partial derivatives for y-value
Lim(h→0) [f(a+h,b)-f(a,b)]/h
Higher order Derivatives
J
Differentiable points on a region
Of a function is differentiable at one point, its differentiable at all points
Chain Rule (One independent Variable)
H
Chain Rule (Two independent Variables)
S
Implicit Differentiation
dy/dx=-F(x)/F(y)
Directional Derivative
Lim(h→0) (f(a+hcosθ,b+hsinθ)-f(a,b))/h
Check for extrema in surfaces using differtial equations
P