HH_Sec_11_2

HH_Sec_11_2 - (9/1/08) Math 10B. Lecture Examples. Section...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 4

HH_Sec_11_2 - (9/1/08) Math 10B. Lecture Examples. Section...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online