Chapter 2 FirstOrder Differential Equations 2 3 FIGURE 211 A solution curve is tangent to lineal element at 2 3 4 FIGURE 212 Solution curves following flow of a direction field 5 FIGURE 213 ID: 771620
Download Presentation The PPT/PDF document "Chapter 2 First-Order" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Chapter 2 First-Order Differential Equations
2
3FIGURE 2.1.1 A solution curve is tangent to lineal element at (2, 3)
4FIGURE 2.1.2 Solution curves following flow of a direction field
5FIGURE 2.1.3 Direction field and solution curves in Example 1
6FIGURE 2.1.4 Direction field in Example 2 on page 38
7FIGURE 2.1.5 Phase portrait of the DE in Example 3
8FIGURE 2.1.6 Lines y ( x ) = c 1 and y ( x ) = c 2 partition R into three horizontal subregions
9FIGURE 2.1.7 Phase portrait and solution curves in Example 4
10FIGURE 2.1.8 Behavior of solutions near y = 1 in Example 5
11FIGURE 2.1.9 Critical point c is an attractor in (a), a repeller in (b), and semi-stable in (c) and (d).
12FIGURE 2.1.10 Direction field for an autonomous DE
13FIGURE 2.1.11 Translated solution curves of an autonomous DE
14FIGURE 2.1.12 Direction field for Problem 1
15FIGURE 2.1.13 Direction field for Problem 2
16FIGURE 2.1.14 Direction field for Problem 3
17FIGURE 2.1.15 Direction field for Problem 4
18FIGURE 2.1.16 Graph for Problem 13
19FIGURE 2.1.17 Graph for Problem 14
20FIGURE 2.1.18 Graph for Problem 29
21FIGURE 2.1.19 Graph for Problem 30
22FIGURE 2.2.1 Solution curve for the IVP in Example 2
23FIGURE 2.2.2 Level curves of G ( x , y ) = e y + ye − y + e −y + 2 cos x
24FIGURE 2.2.3 Level curves c = 2 and c = 4
25FIGURE 2.2.4 Piecewise-defined solutions of (9)
26FIGURE 2.2.5 Shape of a cable in Problem 57
27FIGURE 2.2.6 Level curves in Problem 60
28FIGURE 2.3.1 Solution curves of DE in Example 2
29FIGURE 2.3.2 Solution curves of DE in Example 5
30FIGURE 2.3.3 Discontinuous f ( x ) in Example 6
31FIGURE 2.3.4 Graph of ( 10) in Example 6
32FIGURE 2.3.5 Graph of (15) in Example 7
33FIGURE 2.4.1 Solution curves of DE in Example 3
34FIGURE 2.4.2 Uncoiling chain in Problem 45
35FIGURE 2.5.1 Solutions of DE in Example 3
36FIGURE 2.6.1 Magnification of a neighborhood about the point (2, 4)
37FIGURE 2.6.2 Approximating y ( x 1) using a tangent line
38TABLE 2.6.1 h = 0.1
39TABLE 2.6.2 h = 0.05
40TABLE 2.6.3 h = 0.1
41TABLE 2.6.4 h = 0.05
42FIGURE 2.6.3 Comparison of the Runge-Kutta (RK4) and Euler methods
43FIGURE 2.6.4 A not-very helpful numerical solution curve
44FIGURE 2.R.1 Graph for Problem 13
45FIGURE 2.R.2 Graph for Problem 14
46FIGURE 2.R.3 Graph for Problem 16
47FIGURE 2.R.4 Portion of a direction field for Problem 17
48FIGURE 2.R.5 Graph for Problem 37
49FIGURE 2.R.6 Portion of a direction field for Problem 39
50FIGURE 2.R.7 Portion of a direction field for Problem 40