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Calculus II - 13
1.
9.2 Direction Fields
and Euler’s Method Most differential equation cannot be solved explicitly. We can study the solution through a graphical approach (direction fields) or a numerical approach (Euler’s method).
2.
Direction fields.
= +
3.
Direction fields.
= +
4.
Direction fields.
= + , ( )=
5.
Direction fields.
= + , ( )=
6.
Direction fields.
= + , ( )=
7.
Direction fields.
= + , ( )=
8.
Direction fields.
= + , ( )=
9.
Direction fields.
= + , ( )=
10.
Direction fields.
= + , ( )=
11.
Direction fields.
= +
12.
Direction fields.
= +
13.
Direction fields.
= + , ( )= , , , ,
14.
Direction fields.
= + , ( )= , , , ,
15.
Direction fields.
= + , ( )= , , , ,
16.
Direction fields.
= + , ( )= , , , ,
17.
Euler’s method
= ( , ), ( )=
18.
Euler’s method
= ( , ), ( )= Let be a small step size.
19.
Euler’s method
= ( , ), ( )= Let be a small step size. = + = + = + ······
20.
Euler’s method
= ( , ), ( )= Let be a small step size. = + = + = + ······ = + · ( , ) = + · ( , ) = + · ( , ) ······
21.
Euler’s method
= + , ( )= Let be a small step size. = + = + = + ······ = + · ( , ) = + · ( , ) = + · ( , ) ······
22.
Euler’s method
= + , ( )= Let be a small step size. = . = + = + = + ······ = + · ( , ) = + · ( , ) = + · ( , ) ······
23.
Euler’s method
= + , ( )= Let be a small step size. = . = + = + = . = + = + = . = + = + = . ······ ······ = + · ( , ) = + · ( , ) = + · ( , ) ······
24.
Euler’s method
= + , ( )= Let be a small step size. = . = + = + = . = + = + = . = + = + = . ······ ······ = + · ( , ) = + ·( + )= . = + · ( , ) = + ·( + )= . = + · ( , ) = + ·( + )= . ······ ······
25.
Euler’s method
= + , ( )=
26.
Euler’s method
= + , ( )=
27.
Euler’s method
= + , ( )= =
28.
Euler’s method
= + , ( )= = .
29.
Euler’s method
= + , ( )= = .
30.
Euler’s method
= + , ( )= = .
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