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Unformatted text preview: (9/1/08) Math 10B. Lecture Examples. Section 11.2. Slope fields Example 1 (a) Draw the slope lines for the differential equation dy dx = 1 2 ( x- y ) at the twenty points with coordinates x = 0 , 1 , 2 , 3 , 4 and y = 0 , 1 , 2 , 3 in Figure 1. (b) Describe the patterns of the slope lines and explain how they are determined by the differential equation. x 1 2 3 4 y 1 2 3 FIGURE 1 Answer: (a) Figure A1 (b) One description and explanation: the slope lines are horizontal on the line y = x where 1 2 ( x- y ) is zero, point up to the right under the line y = x where y < x and 1 2 ( x- y ) is positive, point down to the right above the line y = x where y > x and 1 2 ( x- y ) is negative, and become steeper as they move away from the line y = x . x y 4 3 2 1 1 2 3 y = x Figure A1 Lecture notes to accompany Section 11.2 of Calculus by Hughes-Hallett et al 1 Math 10B. Lecture Examples. (9/1/08) Section 11.2, p. 2 Example 2 Figure 3 shows the slope field for dy dx = 1 which consists of line segments of slope 1. Figure 2 shows the graphs of seven solutionswhich consists of line segments of slope 1....
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