Download presentation
Presentation is loading. Please wait.
1
First-Order Differential Equations
Chapter 2 First-Order Differential Equations
3
FIGURE 2.1.1 A solution curve is tangent to lineal element at (2, 3)
4
FIGURE 2.1.2 Solution curves following flow of a direction field
5
FIGURE 2.1.3 Direction field and solution curves in Example 1
6
FIGURE 2.1.4 Direction field in Example 2 on page 38
7
FIGURE 2.1.5 Phase portrait of the DE in Example 3
8
FIGURE 2.1.6 Lines y(x) = c1 and y(x) = c2 partition R into three horizontal subregions
9
FIGURE 2.1.7 Phase portrait and solution curves in Example 4
10
FIGURE 2.1.8 Behavior of solutions near y = 1 in Example 5
11
FIGURE Critical point c is an attractor in (a), a repeller in (b), and semi-stable in (c) and (d).
12
FIGURE 2.1.10 Direction field for an autonomous DE
13
FIGURE 2.1.11 Translated solution curves of an autonomous DE
14
FIGURE 2.1.12 Direction field for Problem 1
15
FIGURE 2.1.13 Direction field for Problem 2
16
FIGURE 2.1.14 Direction field for Problem 3
17
FIGURE 2.1.15 Direction field for Problem 4
18
FIGURE 2.1.16 Graph for Problem 13
19
FIGURE 2.1.17 Graph for Problem 14
20
FIGURE 2.1.18 Graph for Problem 29
21
FIGURE 2.1.19 Graph for Problem 30
22
FIGURE 2.2.1 Solution curve for the IVP in Example 2
23
FIGURE 2.2.2 Level curves of G(x, y) = ey + ye−y + e −y + 2 cos x
24
FIGURE 2.2.3 Level curves c = 2 and c = 4
25
FIGURE 2.2.4 Piecewise-defined solutions of (9)
26
FIGURE 2.2.5 Shape of a cable in Problem 57
27
FIGURE 2.2.6 Level curves in Problem 60
28
FIGURE 2.3.1 Solution curves of DE in Example 2
29
FIGURE 2.3.2 Solution curves of DE in Example 5
30
FIGURE 2.3.3 Discontinuous f(x) in Example 6
31
FIGURE 2.3.4 Graph of (10) in Example 6
32
FIGURE 2.3.5 Graph of (15) in Example 7
33
FIGURE 2.4.1 Solution curves of DE in Example 3
34
FIGURE 2.4.2 Uncoiling chain in Problem 45
35
FIGURE 2.5.1 Solutions of DE in Example 3
36
FIGURE 2.6.1 Magnification of a neighborhood about the point (2, 4)
37
FIGURE 2.6.2 Approximating y(x1) using a tangent line
38
TABLE h = 0.1
39
TABLE h = 0.05
40
TABLE h = 0.1
41
TABLE h = 0.05
42
FIGURE 2.6.3 Comparison of the Runge-Kutta (RK4) and Euler methods
43
FIGURE 2.6.4 A not-very helpful numerical solution curve
44
FIGURE 2.R.1 Graph for Problem 13
45
FIGURE 2.R.2 Graph for Problem 14
46
FIGURE 2.R.3 Graph for Problem 16
47
FIGURE 2.R.4 Portion of a direction field for Problem 17
48
FIGURE 2.R.5 Graph for Problem 37
49
FIGURE 2.R.6 Portion of a direction field for Problem 39
50
FIGURE 2.R.7 Portion of a direction field for Problem 40
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.