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Unformatted text preview: Notes for Day : . : Direction Fie ds e direction eld (or slope eld ) is a tool we use to visualize the solutions to di erential equations. Because the direction eld is visual in nature, it doesnt give precise results and cant be used when a high degree of accuracy is called for. But it does give us an intuitive way of assessing the qualitative behavior of the solution. Examp e Sketch a direction eld for the di erential equation y = + ty in the square- t ,- y . t is on the horizontal axis, and y is on the vertical axis. Creating a direction eld by hand is a tedious and painstaking process, so we generally use so ware like Matlab or Maxima to create them for us. (We can even use a hand-held calculator like a TI- !) Here is a computer-generated direction eld for Example . e tiny line segments that form the direction eld are called eld laments . To plot a solution using the direction eld, start at the given initial position, and connect the arrows. e ner the...
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