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 13.7, Problem 7P

Find the steady-state temperature distribution inside a sphere of radius 1 when the surface temperatures are as given in Problems 1 to 10.5 cos θ 0 0 < θ < π / 2 , π / 2 < θ < π , that is, lower hemisphere. that is, upper hemisphere,

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Chapter 13.7, Problem 6P

Chapter 13.7, Problem 8P

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4. The table shows the number C of cars in an office parking lot over the course of a work day. The time t is measured in hours, with t 0 representing 7:00am. 10 11 12 0. 1 3 6. 7 75 100 110 86 34 12 C 13 67 92 108 82 52 15 a) You want to write a sinusoidal model for the data in the table without using a graphing calculator. Is it more convenient to model the data with a sine or cosine function? Explain. b) Write a sinusoidal model for the number C of cars as a function of the time t (in hours) without using a graphing calculator. Identify and explain how you calculated your values for the amplitude, period, horizontal shift, and vertical shift. c) Use a graphing calculator to write a sinusoidal model that gives C as a function of t. d) Using your model from part (c), at about what time(s) will there be 45 cars in the parking lot? Revised May 2016 Page 4

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Chapter 13 Solutions

Mathematical Methods in the Physical Sciences

Ch. 13.1 - Assume from electrostatics the equations E=/0 and...Ch. 13.1 - Show that the expression u=sin(xvt) describing a...Ch. 13.1 - Assume from electrodynamics the following...Ch. 13.1 - Obtain the heat flow equation (1.3) as follows:...Ch. 13.2 - After you find the series solution of a problem,...Ch. 13.2 - T=0,0x10,100,10x20. Solve the semi-infinite plate...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Solve the semi-infinite plate problem if the...Ch. 13.2 - Show that the solutions of (2.5) can also be...Ch. 13.2 - Show that the series in (2.12) can be summed to...

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Find the steady-state temperature distribution inside a sphere of radius 1 when the surface temperatures are as given in Problems 1 to 10.5 cos θ 0 0 &lt; θ &lt; π / 2 , π / 2 &lt; θ &lt; π , that is, lower hemisphere. that is, upper hemisphere,