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If your browser does not support Java 1.1 then download Netscape Communicator 4.08 or download the HotJava Browser. ... This program uses an altered version of the parser written by Darius Bacon which is available at his web site. Please see his file on copying the parser code.
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Slope field - Wikipedia, the free encyclopedia
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So, back to the direction field for our differential equation. Suppose that we want to know what the solution that has the value v(0) = 30 looks like. We can go to our direction field and start at 30 on the vertical axis.
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The vector at a point [t,y(t)] is given by <t,f(t,y)> with the field being represented in the applet as a "direction field" of arrows. The arrow at a given point points in the direction of the vector at that point, but the length of the vector is not represented.
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This applet draws solution curves in the phase plane of a 2x2 autonomous system of Ordinary Differential Equations over the systems direction field. The system is of the form:
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Direction Field of First Order Differential Equations ... For each point (x,y), the differential equation defines a line segment with slope f(x,y). We say that the differential equation defines the direction field of the differential equation.
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dfield and pplane ... the java versions ... If you do not see the applet buttons above, it means that your browser is not Java 1.1.6 enabled. There are several possible reasons for this, including the following.
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The direction field ; Suppose we draw a collection of tangent lines as shown in the picture below. This collection is often called a direction field since it seems to give us a sense of direction in the plane. ... Notice that the curve has an overall shape and direction "guided by" the direction field. Indeed,
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This applet plots direction fields, (approximate) solution curves, and isoclines. You should be able to use this either in the lab or at home, ...
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Slope fields (also called vector fields or direction fields) are a tool to graphically obtain the solutions to a first order differential equation. Consider the following example: ... Here is the same slope field again. What is special about the points on the red parabola?
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