Numerical Methods for Engineers
7th Edition
ISBN: 9780073397924
Author: Steven C. Chapra Dr., Raymond P. Canale
Publisher: McGraw-Hill Education
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Question
Chapter 16, Problem 18P
To determine
To calculate: The exact location of the peak concentration of the pollutant described by the function
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18.10. Let f be analytic inside and on the unit circle 7. Show that, for
0<|z|< 1,
f(E)
f(E)
2πif(z) =
--- d.
18.4. Let f be analytic within and on a positively oriented closed
contoury, and the point zo is not on y. Show that
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f(z)
(-20)2 dz = '(2) dz.
2-20
18.9. Let denote the boundary of the rectangle whose vertices are
-2-2i, 2-21,2+i and -2+i in the positive direction. Evaluate each of
the following integrals:
(a).
rdz, (b).
dz (b).
COS 2
coz dz,
(z+1)
(d).
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z 2 +2
dz, (e).
dz
(c). (2z + 1)2dz,
(2z+1)
1
(f). £,
· [e² sin = + (2² + 3)²] dz.
z
(22+3)2
Chapter 16 Solutions
Numerical Methods for Engineers
Ch. 16 - 16.1 Design the optimal cylindrical container...Ch. 16 - 16.2 (a) Design the optimal conical container...Ch. 16 - Design the optimal cylindrical tank with...Ch. 16 - The specific growth rate of a yeast that produces...Ch. 16 - A chemical plant makes three major products on a...Ch. 16 - 16.6 Recently chemical engineers have become...Ch. 16 - 16.7 A mixture of benzene and toluene are to be...Ch. 16 - 16.8 A compound A will be converted into B in a...Ch. 16 - In problem 16.8, only one reactor is used. If two...Ch. 16 - 16.10 For the reaction:
equilibrium can be...
Ch. 16 - A chemical plant requires 106L/day of a solution....Ch. 16 - You must design a triangular open channel to carry...Ch. 16 - 16.13 As an agricultural engineer, you must design...Ch. 16 - 16.14 Find the optimal dimensions for a heated...Ch. 16 - A finite-element model of a cantilever beam...Ch. 16 - 16.16 Suppose that you are asked to design a...Ch. 16 - TheStreeter-Phelps model can be used to compute...Ch. 16 - Prob. 18PCh. 16 - 16.19 The flow in an open channel can be predicted...Ch. 16 - A cylindrical beam carries a compression load...Ch. 16 - The Splash River has a flow rate of 2106m3/d, of...Ch. 16 - 16.22 Determine the beam cross-sectional areas...Ch. 16 - AtotalchargeQ is uniformly distributed around a...Ch. 16 - A system consist softwopower plants that must...Ch. 16 - 16.25 The torque transmitted to an induction motor...Ch. 16 - (a) A computer equipment manufacture rproduces...Ch. 16 - A manufacturer provides specialized microchips....Ch. 16 - 16.28 The total drag on an airfoil can be...Ch. 16 - Mechanical/Aerospace Engineering
16.29 Roller...Ch. 16 - 16.30 An aerospace company is developing a new...Ch. 16 - 16.31 A manufacturing firm produces four types of...Ch. 16 - In a similar fashion to the case study described...Ch. 16 - 16.33 Recent interest in competitive and...
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Similar questions
- 18.8. (a). Let be the contour z = e-≤0≤ traversed in the า -dz = 2xi. positive direction. Show that, for any real constant a, Lex dzarrow_forwardf(z) 18.7. Let f(z) = (e² + e³)/2. Evaluate dz, where y is any simple closed curve enclosing 0.arrow_forward18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]arrow_forward
- For each real-valued nonprincipal character x mod k, let A(n) = x(d) and F(x) = Σ : dn * Prove that F(x) = L(1,x) log x + O(1). narrow_forwardBy considering appropriate series expansions, e². e²²/2. e²³/3. .... = = 1 + x + x² + · ... when |x| < 1. By expanding each individual exponential term on the left-hand side the coefficient of x- 19 has the form and multiplying out, 1/19!1/19+r/s, where 19 does not divide s. Deduce that 18! 1 (mod 19).arrow_forwardBy considering appropriate series expansions, ex · ex²/2 . ¸²³/³ . . .. = = 1 + x + x² +…… when |x| < 1. By expanding each individual exponential term on the left-hand side and multiplying out, show that the coefficient of x 19 has the form 1/19!+1/19+r/s, where 19 does not divide s.arrow_forwardLet 1 1 r 1+ + + 2 3 + = 823 823s Without calculating the left-hand side, prove that r = s (mod 823³).arrow_forwardFor each real-valued nonprincipal character X mod 16, verify that L(1,x) 0.arrow_forward*Construct a table of values for all the nonprincipal Dirichlet characters mod 16. Verify from your table that Σ x(3)=0 and Χ mod 16 Σ χ(11) = 0. x mod 16arrow_forwardFor each real-valued nonprincipal character x mod 16, verify that A(225) > 1. (Recall that A(n) = Σx(d).) d\narrow_forward24. Prove the following multiplicative property of the gcd: a k b h (ah, bk) = (a, b)(h, k)| \(a, b)' (h, k) \(a, b)' (h, k) In particular this shows that (ah, bk) = (a, k)(b, h) whenever (a, b) = (h, k) = 1.arrow_forward20. Let d = (826, 1890). Use the Euclidean algorithm to compute d, then express d as a linear combination of 826 and 1890.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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