chapter2.page20

chapter2.page20 - true when you want to superimpose...

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20 1. EXPLICITLY SOLVABLE FIRST ORDER DIFFERENTIAL EQUATIONS equation of tangent line y - y j = m ij ( x - x i ) we get another point (( x i + h 2 ,y j + m ij h 2 ). (3) Draw line segment from ( x i ,y j ) to (( x i + h,y j + m ij h ) for i = 0 , 1 , ··· ,N ; j = 0 , 1 , ··· ,M. Example 5.3 . Suppose we want to graph vector field for y 0 = x over [0,1] × [0,1] and divide [0, 1] into two subinterval, h = s = 0 . 5 . Then we will have nine grid points (0, 0), (0, 0.5), (0, 1), (0.5, 0), (0.5, 0.5), (0.5, 1), (1, 0), (1, 0.5), and (1, 1). For the grid point (0.5, 0.5) we have slop m = 0 . 5 as the function f ( x,y ) = x. So we can get another point (0 . 5+ h 2 , 0 . 5+ m h 2 ) = (0 . 75 , 0 . 625) , connect (0.5, 0.5) to (0.75, 0.625) you get one line segment, continuous this we get the following diagram. Figure 14. Vector field for f ( x,y ) = x So it is obviously tedious to draw the vector field by hand. To graph vector field in Mathcad is not an easy task. This is especially
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Unformatted text preview: true when you want to superimpose solution curve over the graph. You need to write some code to instruct how you want Mathcad to graph the vector eld for what function. you can get the code from the website www.unf.edu/ mzhan . Project At beginning you should enter: Project title, your name, ss#, and due date in the following format Project One: Dene and Graph Functions John Doe SS# 000-00-0000 Due: Mon. Nov. 23rd, 2003 You should format the text region so that the color of text is dierent than math expression. You can choose color for text from Format > Style select normal and click modify , then change the settings for...
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This note was uploaded on 10/04/2011 for the course MAP 4231 taught by Professor Dr.han during the Spring '11 term at UNF.

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