Chapter 14 Integral Transforms Dennis G Zill Differential

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Chapter 14 Integral Transforms Dennis G. Zill, Differential Equations with Boundary Value Problems, 9

Chapter 14 Integral Transforms Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018

Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 2

Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 2

FIGURE 14. 1. 1 Bell curve Dennis G. Zill, Differential Equations with Boundary Value

FIGURE 14. 1. 1 Bell curve Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 3

FIGURE 14. 1. 2 Graphs of erf(x) and erfc(x) Dennis G. Zill, Differential Equations

FIGURE 14. 1. 2 Graphs of erf(x) and erfc(x) Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 4

TABLE 14. 1. 1 Laplace Transforms Dennis G. Zill, Differential Equations with Boundary Value

TABLE 14. 1. 1 Laplace Transforms Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 5

FIGURE 14. 2. 1 “Infinitely long” string falling under its own weight in Example

FIGURE 14. 2. 1 “Infinitely long” string falling under its own weight in Example 3 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 6

FIGURE 14. 2. 2 Graph of solution given in (10). In (b) and (c)

FIGURE 14. 2. 2 Graph of solution given in (10). In (b) and (c) x is held constant. In (d) and (e) t is held constant. Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 7

FIGURE 14. 2. 3 Moving elastic beam in Problem 8 Dennis G. Zill, Differential

FIGURE 14. 2. 3 Moving elastic beam in Problem 8 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 8

FIGURE 14. 2. 4 Ant responding to chemical signal in Problem 33 Dennis G.

FIGURE 14. 2. 4 Ant responding to chemical signal in Problem 33 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 9

FIGURE 14. 3. 1 Piecewise-continuous function defined on (-∞, ∞) in Example 1 Dennis

FIGURE 14. 3. 1 Piecewise-continuous function defined on (-∞, ∞) in Example 1 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 10

FIGURE 14. 3. 2 Piecewise-continuous even function defined on (-∞, ∞) in Example 2

FIGURE 14. 3. 2 Piecewise-continuous even function defined on (-∞, ∞) in Example 2 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 11

FIGURE 14. 3. 3 Function defined on (0, ∞) in Example 3 Dennis G.

FIGURE 14. 3. 3 Function defined on (0, ∞) in Example 3 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 12

FIGURE 14. 3. 4 (a) is the even extension of f; (b) is the

FIGURE 14. 3. 4 (a) is the even extension of f; (b) is the odd extension of f Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 13

FIGURE 14. 3. 5 Convergence of Fb(x) to f(x) in Example 3(b) as b

FIGURE 14. 3. 5 Convergence of Fb(x) to f(x) in Example 3(b) as b ∞ Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 14

FIGURE 14. 4. 1 Plate in Problem 17 Dennis G. Zill, Differential Equations with

FIGURE 14. 4. 1 Plate in Problem 17 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 15

FIGURE 14. 4. 2 Plate in Problem 18 Dennis G. Zill, Differential Equations with

FIGURE 14. 4. 2 Plate in Problem 18 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 16

FIGURE 14. 4. 3 Infinite strip in Problem 21 Dennis G. Zill, Differential Equations

FIGURE 14. 4. 3 Infinite strip in Problem 21 Dennis G. Zill, Differential Equations with Boundary Value Problems, 9 e, © 2018 17