Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 8.9, Problem 39P

Evaluate each of the following definite integrals by using the Laplace transform table.

∫ 0 ∞ e − t − e − 2 t t d t

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Chapter 8.9, Problem 38P

Chapter 8.9, Problem 40P

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find integral of curves dx/(x + y) = dy/(x + y) = dz/−(x + y + 2z)

Consider the integral X -dx with n = 4. a. Find the trapezoid rule approximations to the integral using n and 2n subintervals. b. Find the Simpson's rule approximation to the integral using 2n subintervals. c. Compute the absolute errors in the trapezoid rule and Simpson's rule with 2n subintervals. a. What is the trapezoid approximation with n subintervals? T(4)=(Round to six decimal places as needed.) What is the trapezoid approximation with 2n subintervals? T(8) = (Round to six decimal places as needed.) b. What is the Simpson's rule approximation with 2n subintervals? S(8)=(Round to six decimal places as needed.) c. What is the error in the trapezoid rule approximation with 2n subintervals? (Round to six decimal places as needed.) What is the error in the Simpson's rule approximation with 2n subintervals? (Round to six decimal places as needed.)

00 fe Suppose that the probability that a particular computer chip fails after t = a hours of operation is 0.00004 0.00004 dt. a a. Find the probability that the computer chip fails after 16.000 hr of operation (that is, the chip lasts at least 16,000 hr). b. Of the chips that are still in operation after 16,000 hr, what fraction of these will operate for at least another 16,000 hr? c. Evaluate 0.00004 Se -0.000041 dt and interpret its meaning. a. The probability that the chip fails after 16,000 hr of operation is (Round to three decimal places as needed.) b. The fraction that will still be operating for at least another 16.000 hr is (Round to three decimal places as needed.) c. Choose the correct answer below. OA. The probability that the chip never fails is 0.00004 -0.00004t dt= OB. The probability that the chip eventually fails is 0.00004 S 0.00004 dt = dt= -0.000041 dt= OC. The probability that the chip fails immediately is 0.00004 OD. There is not enough information to interpret…

Chapter 8 Solutions

Mathematical Methods in the Physical Sciences

Ch. 8.1 - Verify the statement of Example 2. Also verify...Ch. 8.1 - Solve Example 4 using the general solution...Ch. 8.1 - Verify that y=sinx,y=cosx,y=eix, and y=eix are all...Ch. 8.1 - Find the distance which an object moves in time t...Ch. 8.1 - Find the position x of a particle at time t if its...Ch. 8.1 - A substance evaporates at a rate proportional to...Ch. 8.1 - The momentum p of an electron at speed v near the...Ch. 8.2 - For each of the following differential equations,...Ch. 8.2 - For each of the following differential equations,...Ch. 8.2 - For each of the following differential equations,...

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