Math Exam 2

0.0(0)
Studied by 0 people
call kaiCall Kai
learnLearn
examPractice Test
spaced repetitionSpaced Repetition
heart puzzleMatch
flashcardsFlashcards
GameKnowt Play
Card Sorting

1/14

encourage image

There's no tags or description

Looks like no tags are added yet.

15 Terms

1
New cards
Proper Nodal Source: Conditions?
Repeated positive real eigenvalue with 2 independent eigenvectors; straight lines outward.
Repeated positive real eigenvalue with 2 independent eigenvectors; straight lines outward.
2
New cards
Proper Nodal Sink: Conditions?
Repeated negative real eigenvalue with 2 independent eigenvectors; straight lines inward.
Repeated negative real eigenvalue with 2 independent eigenvectors; straight lines inward.
3
New cards
Saddle Point: Conditions?
Real eigenvalues of opposite signs; trajectories approach in one direction and leave in another.
Real eigenvalues of opposite signs; trajectories approach in one direction and leave in another.
4
New cards
Center: Conditions?
Purely imaginary eigenvalues ±bi; closed elliptical trajectories.
Purely imaginary eigenvalues ±bi; closed elliptical trajectories.
5
New cards
Spiral Source: Conditions?
Complex eigenvalues a±bi with a>0; spirals outward.
Complex eigenvalues a±bi with a>0; spirals outward.
6
New cards
Spiral Sink: Conditions?
Complex eigenvalues a±bi with a<0; spirals inward.
Complex eigenvalues a±bi with a<0; spirals inward.
7
New cards
Parallel Lines: One zero eigenvalue?
One eigenvalue is 0; negative nonzero eigenvalue means flow toward an equilibrium line, positive means away.
One eigenvalue is 0; negative nonzero eigenvalue means flow toward an equilibrium line, positive means away.
8
New cards
Parallel Lines: Repeated zero eigenvalue?
Repeated zero eigenvalue with 1 independent eigenvector; parallel straight-line trajectories.
Repeated zero eigenvalue with 1 independent eigenvector; parallel straight-line trajectories.
9
New cards
Variation of Parameters (ODE): Formula for u1'?
u1' = -y2*g(x)/W
10
New cards
Variation of Parameters (ODE): Formula for u2'?
u2' = y1*g(x)/W
11
New cards
Variation of Parameters (systems): Full general solution from 0 to t?
x(t) = e^(At)[xc + ∫_0^t e^(-As)f(s) ds]
12
New cards
Improper Nodal Source: Distinct eigenvalues case?
Two distinct positive real eigenvalues; trajectories move outward and tend to align with the dominant eigenvector.
Two distinct positive real eigenvalues; trajectories move outward and tend to align with the dominant eigenvector.
13
New cards
Improper Nodal Source: Repeated eigenvalue case?
Repeated positive real eigenvalue with only 1 independent eigenvector; trajectories move outward.
Repeated positive real eigenvalue with only 1 independent eigenvector; trajectories move outward.
14
New cards
Improper Nodal Sink: Distinct eigenvalues case?
Two distinct negative real eigenvalues; trajectories move inward and tend to align with the dominant eigenvector.
Two distinct negative real eigenvalues; trajectories move inward and tend to align with the dominant eigenvector.
15
New cards
Improper Nodal Sink: Repeated eigenvalue case?
Repeated negative real eigenvalue with only 1 independent eigenvector; trajectories move inward.
Repeated negative real eigenvalue with only 1 independent eigenvector; trajectories move inward.