An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter B.3, Problem 13P
To determine
To Derive: The formula for Stirling’s approximation
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Calculate the values of ⟨x3⟩v and ⟨x4⟩v for a harmonic oscillator by using the properties of the Hermite polynomials given in Table 7E.1; follow the approach used in the text.
B=re-²9,
find curl(B) analytically. Compare the value of the divergence at points P1 = (x1, y1) = (0.5, 0.5) and P2 = (x2, y2) = (3, 2).
A (nonconstant) harmonic function takes its maximum value and its minimum value on the boundary of any region (not at an interior point). Thus, for example, the electrostatic potential V in a region containing no free charge takes on its largest and smallest values on the boundary of the region; similarly, the temperature T of a body containing no sources of heat takes its largest and smallest values on the surface of the body. Prove this fact (for two-dimensional regions) as follows: Suppose that it is claimed that u(x, y) takes its maximum value at some interior point a; this means that, at all points of some small disk about a, the values of u(x, y) are nolarger than at a. Show by Problem 36 that such a claim leads to a contradiction (unless u = const.). Similarly prove that u(x, y) cannot take its minimum value at an interior point.
Chapter B Solutions
An Introduction to Thermal Physics
Ch. B.1 - Sketch an antiderivative of the function ex2.Ch. B.1 - Prob. 2PCh. B.1 - Prob. 3PCh. B.1 - Prob. 4PCh. B.1 - Prob. 5PCh. B.1 - Prob. 6PCh. B.2 - Prob. 7PCh. B.2 - Prob. 8PCh. B.2 - Prob. 9PCh. B.3 - Prob. 10P
Ch. B.3 - Prob. 11PCh. B.3 - Prob. 12PCh. B.3 - Prob. 13PCh. B.4 - Prob. 14PCh. B.4 - Prob. 15PCh. B.4 - Derive a formula for the volume of a d-dimensional...Ch. B.5 - Derive the general integration formulas B.36Ch. B.5 - Prob. 18PCh. B.5 - Prob. 19PCh. B.5 - Evaluate equation B.41 at x=/2, to obtain a famous...Ch. B.5 - Prob. 21PCh. B.5 - Prob. 22P
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