Unformatted text preview: x = f ( t,x ) is to draw a segment of tangent line to many chosen points ( t ,x ) with slope x ( t ) = f ( t ,x ) . When we draw enough such line segments, patterns shall emerge and we shall have a clear idea(with some training) of the behavior of solutions to the equation. The following diagram shows the vector ﬁeld of x = sin ( t ) . Clearly we see the wave pattern of typical solution x ( t ) =cos ( t ) + C. Here two diagrams are shown, the right one is provided for novel eyes, which has solutions curves superimposed on the vector ﬁeld. For complicated vector ﬁeld only trained eyes will see the subtle patterns...
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 Spring '11
 Dr.Han
 Derivative, Vector Space, Vector field

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