Chapter 3 Modeling with FirstOrder Differential Equations 2 3 FIGURE 311 Time in which population triples in Example 1 4 FIGURE 312 Growth k gt 0 and decay k lt 0 5 FIGURE 313 ID: 773720
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Chapter 3 Modeling with First-Order Differential Equations
2
3FIGURE 3.1.1 Time in which population triples in Example 1
4FIGURE 3.1.2 Growth ( k > 0) and decay ( k < 0)
5FIGURE 3.1.3 Willard Libby (1908–1980)
6FIGURE 3.1.4 A page of the Gnostic Gospel of Judas
7FIGURE 3.1.5 Temperature of cooling cake in Example 4
8FIGURE 3.1.6 Pounds of salt in the tank in Example 5
9FIGURE 3.1.7 Graph of A ( t ) in Example 6
10FIGURE 3.1.8 LR -series circuit
11FIGURE 3.1.9 RC -series circuit
12FIGURE 3.1.10 Population growth is a discrete process
13FIGURE 3.1.11 Cave wall painting in Problem 11
14FIGURE 3.1.12 Shroud image in Problem 12
15FIGURE 3.1.13 Find the maximum height of the cannonball in Problem 36
16FIGURE 3.1.14 Find the time to reach the ground in Problem 38
17FIGURE 3.1.15 Model of a pacemaker in Problem 47
18FIGURE 3.1.16 Box sliding down inclined plane in Problem 48
19FIGURE 3.2.1 Simplest assumption for f ( P ) is a straight line (blue color)
20FIGURE 3.2.2 Logistic curves for different initial conditions
21FIGURE 3.2.3 Number of infected students in Example 1
22FIGURE 3.2.4 Number of grams of compound C in Example 2
23TABLE 3.2.1
24FIGURE 3.2.5 Inverted conical tank in Problem 14
25FIGURE 3.2.6 Decorative pond in Problem 20
26FIGURE 3.2.7 Skydiver in Problem 26
27FIGURE 3.2.8 Path of swimmer in Problem 28
28FIGURE 3.2.9 Clepsydra in Problem 33
29FIGURE 3.2.10 Clepsydra in Problem 34
30FIGURE 3.3.1 Connected mixing tanks
31FIGURE 3.3.2 Populations of predators (red ) and prey (blue) in Example 1
32FIGURE 3.3.3 Network whose model is given in (17)
33FIGURE 3.3.4 Network whose model is given in (18)
34FIGURE 3.3.5 Igneous rocks are formed through solidification of volcanic lava
35FIGURE 3.3.6 Mixing tanks in Problem 8
36FIGURE 3.3.7 Mixing tanks in Problem 9
37FIGURE 3.3.8 Mixing tanks in Problem 10
38FIGURE 3.3.9 Network in Problem 14
39FIGURE 3.3.10 Network in Problem 15
40FIGURE 3.3.11 Nutrient flow through a membrane in Problem 19
41FIGURE 3.3.12 Container within a container in Problem 22
42FIGURE 3.R.1 Ötzi the iceman in Problem 5
43FIGURE 3.R.2 Cell in Problem 8
44FIGURE 3.R.3 Sliding bead in Problem 12
45FIGURE 3.R.4 Mixing tanks in Problem 14
46FIGURE 3.R.5 Orthogonal families
47FIGURE 3.R.6 Sawing a log in Problem 20
48FIGURE 3.R.7 Triangular cross section in Problem 21