An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Question
Chapter B.1, Problem 5P
To determine
ToFind: An asymptotic expansion for the integral
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Plot the graphs of f(x) = x^2 and y(x) = √(4-x^2), where x [-2; 2]. Calculate analytically the overlap integral between
these functions on x [-2; 2] (show all steps). Show the overlap on the graph and explain why the value is what you have
calculated
A triangle in the xy plane is defined with
corners at (x, y) = (0,0), (0, 2) and
(4, 2). We want to integrate some
function f(x, y) over the interior of this
triangle.
Choosing dx as the inner integral, the
required expression to integrate is given
by:
Select one:
o Sro S-o f(x, y) dx dy
x=0
2y
y=0
O S-o So F(x, y) dæ dy
O o S f(x, y) dy dæ
O So So F(x, y) dx dy
x/2
=0
Step 1
Rewrite the original integral
Therefore,
let
du
a² + u²
(²)
dt as
+ 16
= arctan(y) to
Step 2
Use the following integration formula for the inverse trigonometric functions.
1.20
t
(27²2² +42 (2) ot = (-
t
1
+
X
X
4
2 (2) dt
arctant
arctan
tan()+c
4
✓)) + C
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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