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Use a computer to plot the function xne?x and the Gaussian

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 12P Chapter B

An Introduction to Thermal Physics | 1st Edition

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An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

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Problem 12P

Problem 12P

Use a computer to plot the function xnex and the Gaussian approximation to this function, for n = 10, 20, and 50. Notice how the relative width of the peak (compared to n) decreases as n increases, and how the Gaussian approximation becomes more accurate as n increases. If your computer software permits it, try looking at even higher values of n.

Step-by-Step Solution:

Solution to 12P

Step 1

f(x)=xne-x is a gaussian approximation function which reaches maximum value when x=n. We are using Matlab to plot the function. For N=10,20 and 50. The relative width of the gaussian curve is decreased as n increased and the gaussian approximation becomes more accurate as n increases.

Matlab Code:

clear all

clf

clc

x = 0:.01:100;

plot(x,((x.^10).*exp(-x))/max((x.^10).*exp(-x)),'-g');hold on;

plot(x,((x.^20).*exp(-x))/max((x.^20).*exp(-x)),'-r');hold on;

plot(x,((x.^50).*exp(-x))/max((x.^50).*exp(-x)),'-k');hold on;

xlabel('n')

ylabel('x.^n.*exp(-x)')

title('plot of gaussian approximation for N=10,20 and 50')

legend('N=10','N=20','N=50')

grid on;

Step 2 of 2

Chapter B, Problem 12P is Solved
Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

The full step-by-step solution to problem: 12P from chapter: B was answered by , our top Physics solution expert on 07/05/17, 04:29AM. Since the solution to 12P from B chapter was answered, more than 367 students have viewed the full step-by-step answer. The answer to “Use a computer to plot the function xne?x and the Gaussian approximation to this function, for n = 10, 20, and 50. Notice how the relative width of the peak (compared to n) decreases as n increases, and how the Gaussian approximation becomes more accurate as n increases. If your computer software permits it, try looking at even higher values of n.” is broken down into a number of easy to follow steps, and 62 words. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. This full solution covers the following key subjects: Approximation, increases, gaussian, function, Computer. This expansive textbook survival guide covers 10 chapters, and 455 solutions. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279.

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