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d-neighborhood
a set of a point (z) s.t. | z - z_0 | < d , d>
TERM 2
Limit Point
DEFINITION 2
if every d- nbdN_d(z_0) \ z_0contains a point of S
TERM 3
Closed
set
DEFINITION 3
contains all limit points
TERM 4
Bounded
set
DEFINITION 4
if there is a m > 0 s.t. if z is in s, then|z| < m
TERM 5
open
set
DEFINITION 5
only contain interior points
connected
set
if there is a linear piecewise path between any two points in
S that exists completely in S
TERM 7
compact
set
DEFINITION 7
closed, bounded set in the complex plane
TERM 8
interior
DEFINITION 8
if there is aN_d ( z_0) in S
TERM 9
Boundary
DEFINITION 9
every delta neighborhood of z_0 containg s and parts outside
of S
TERM 10
Exterior
DEFINITION 10
if not interior or boundary
subset
a set formed by choosing some , all, or no points in an S
TERM 17
limit
DEFINITION 17
L is limit of f(z) s.t.as z -> z_0, for every epsilon > 0, there is
a d > 0s.t.0 < | z - z_0 | < d then | f(z) - L | < epsilon
TERM 18
continuous
DEFINITION 18
if f(z0) is continuous for all z0 in D
TERM 19
uniformly continous
DEFINITION 19
when f(z) is continuous on a compact region
TERM 20
analytic
DEFINITION 20
when f '(z) exists (i.e. limit exists) for all points in D
poles
if there is a n > 0 s.t.lim z->z0 ( z - z0)^n f(z) = A 0
TERM 22
removable singularity
DEFINITION 22
where lim z -> z0 f(z) exists but f(z) lim z->z0 f(z)
TERM 23
essential singularity
DEFINITION 23
if not pole, branch point, or removable singularity
TERM 24
isolated singularity
DEFINITION 24
at z=a if f is differentiable in some annulus0 < | z - a | < R
TERM 25
Orthogonal
DEFINITION 25
In euclidian geometry, two vectors with 90 degrees between
each other. The dot products of the vectors must equal 0 and
the vectors cannot equal the 0 vector
Streamline
The direction something will go, i.e. a rock in a river. A
system of parametrized equations spawning fromdelta with
all components equaling each otherF(x,y,z)
TERM 32
Closed Curve
DEFINITION 32
If the initial and terminal points are the same.
TERM 33
Simple curve
DEFINITION 33
if for a < t1 < t2 < b< x(t1) , y(t1), z(t1) > < x(t2), y(t2),
z(t2) >
TERM 34
Smooth Curve
DEFINITION 34
continuous on function and first derivative
TERM 35
Piecewise smooth curve
DEFINITION 35
tangent vector is discontinous only at a finite number of
points
Positively oriented
when on a closed curve, a particle travels counterclockwise
as t increases
TERM 37
Path
DEFINITION 37
is a PW smooth curve
TERM 38
conservative vector field
DEFINITION 38
if there exists a potential scalar function/field theta s.t.F =
del * theta
TERM 39
Potential function
DEFINITION 39
a scalar function/field theta which in relation to F, the
following holds trueF = del * theta
TERM 40
Path Independence
DEFINITION 40
if the value for any path c between two points is the
sameintegral Fdr over c1 = integral Fdr over c
