3) Graphical Methods for First Order ODEs Flashcards
1
Q
What is a directional field
A
The direction field associated with f,
d(x, y) = (1, f(x, y))
2
Q
What is the normalised directional field
A
3
Q
What is an integral curve
A
A single continuous line in the (x, y)-plane whose tangent lines coincide with the direction field
4
Q
Why is it impossible for intgeral curves to cross
A
- If f and ∂f/∂y are continuous then solutions to the ODE are unique by Picard’s Uniqueness Theorem
- It follows that it is impossible for integral curves to “cross”
5
Q
What is an Isocline
A
f(x, y) = K
6
Q
How do you derive Euler’s method
A
7
Q
What columns do you use when doing Euler’s method by hand
A
8
Q
What is the local truncation error of Euler’s method
A
9
Q
What is the local truncation error of Euler’s method of a IVP
A
10
Q
What is the global error of Euler’s method
A
11
Q
What is the global error of Euler’s method of a IVP
A
