HH_Sec_11_3

HH_Sec_11_3 - an approximate solution of dy dx = (1-x ) y x...

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(9/1/08) Math 10B. Lecture Examples. Section 11.3. Euler’s method Example 1 Figure 1 shows the slope feld ±or the di²erential equation, dy dx = (1 - x ) y. Draw the graph o± approximate solution y = y E ( x ) ±or 0 x 4 with the initial value y (0) = 1 that is obtained by Euler’s method with the partition, 0 < 1 < 2 < 3 < 4. x 1 2 3 4 y 1 2 Slope feld For dy dx = (1 - x ) y ±IGURE 1 Answer: ±igure A1a (±igure A1b shows the graph oF the exact solution y = y ( x ) with the Euler approximation.) x 1 2 3 4 y 1 2 x 1 2 3 4 y 1 2 ±igure A1a ±igure A1b Lecture notes to accompany Section 11.3 oF Calculus by Hughes-Hallett et al. 1
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Math 10B. Lecture Examples. (9/1/08) Section 11.3, p. 2 Example 2 Use Euler’s method with four subintervals to Fnd the values at the partition points of
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Unformatted text preview: an approximate solution of dy dx = (1-x ) y x , y (1) = 3 , 1 x 5. Then draw its graph Answer: y E (1) = 3 y E (2) = 1 . 5 y E (4) = 0 . 5 y E (5) = 0 . 125 Figure A2 x 1 2 3 4 5 y 1 2 3 Figure A2 Interactive Examples Work the following Interactive Examples on Shenks web page, http//www.math.ucsd.edu/ashenk/: Section 9.4: Example 1 The chapter and section numbers on Shenks web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course....
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HH_Sec_11_3 - an approximate solution of dy dx = (1-x ) y x...

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