1549312215-Complex_Analysis_for_Mathematics_and_Engineering_5th_edition__Mathews

504 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS and obtain the equation x^2 + 2xycotc -y^2 = 1. If we express this equation ...

11.11 • SOURCES AND SINKS 5 0 5 Figure 11.9 6 A source in the center of a strip. located at the origin. T he conformal mapping w ...

506 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Figure 11.97 A source and a sink on the edges of a strip. determines a fluid ...

ll • SOURCES AND SINKS 507 Figure 11 .98 Effluence from a channel into a half-plane. -------•EXERCISES FOR SECTION 11.11 Let ...

508 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Let the lines x = 0 and x = ~ form the walls of a containing vessel for a f ...

11.11 • SOURCES AND SINKS 509 Figure 11.103 T he complex potential F (z) = !. determines an electrostatic field that is referre ...

510 CHAPTER 11 • APPLICATIONS OF HARMONIC FUNCTIONS Use a Schwarz-Christoffel transformation to find a conformal mapping w = S ...

11.11 • SOURCES AND SINKS 511 Use a Schwarz-Christoffel transformation to find a conformal mapping w = S (z) that will map the ...

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c a ter 12 our1 r series anll the I place transform Overview In this chapter we show how Fourier series, the Fourier transform, ...

514 CHAPTER. 12 • FOURIER. SER.JES AND THE LAPLACE TRANSFORM Familiar examples of real functions that have period 211" are sin n ...

12. l • FOURIER SERIES 515 Definition 12.2: Fourier series HU (t) is periodic with period 211' and is piecewise continuous on [- ...

516 CHAPTER 12 • FOURIER SERIES AND THE LAPLACE TRANSFORM s Figure 12.3 T he function U (t) =;,and the approximations S1 (t), S2 ...

1 2.l • FOURIER SERIES 517 ...

1>18 CHAPTER 12 • FOURIER SERIES AND THE LAPLACE TRANSFORM EXAMPLE 12 .2 The function U (t) = It! , forte (-7r, 7r), extende ...

12.l • FOURIER SERIES 519 The value of the first integral on the right side of this equation is 27T, and all the other integrals ...

520 CHAPTER 1 2 • FOURIER SERIES AND THE LAPLACE TRANSFORM Therefore, we can use the results of Equations (12-6)-(12-9) in Equat ...

12.l • FOURIER SERIES 521 For Exercises 1 and 2, verify that U (t) = -V' (t) by termwise differentiation of the Fourier series ...

522 CHAPTER 12 • FOURlER SERlES AND THE LAPLACE TRANSFORM U (t), given in F igure 12.8. n F igure 12 .8 u (t) = 0, 1! 2 { ...

12.2 • THE DIRICHLET PROBLEM FOR THE UNIT DISK 523 U (t), given in Figure 12.11. s s = U(t) _;!'. -It 2 lJ. 1t 2 Figure 12.11 ...