Mathematical Methods in the Physical Sciences
Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
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Differential Equations
Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…
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Chapter 5.4, Problem 26P

Find the Jacobians ∂ x , y / ∂ u , v of the given transformations from variables x , y to variables u , v

Use the parallel axis theorem (Problem 3.1)

  1. and Example 3, to find the moment of inertia of a solid ball about a line tangent to it;
  2. and Problem 3b to find the moment of inertia of a solid cylinder about a ruling.

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Chapter 5 Solutions

Mathematical Methods in the Physical Sciences

Ch. 5.1 - 2sincocd=sin2or-cos2or-12cos2. Hint: Use trig...Ch. 5.1 - dxx2+a2=sinh1xaorInx+x2+a2. Hint:To find the sinh1...Ch. 5.1 - dyy2a2=cosh1yaorIny+y2a2. Hint: See Problem 2...Ch. 5.1 - ...Ch. 5.1 - Kdr1k2r2=sinh1Kror-cos1Krortan1Kr1k2r2 Hints:...Ch. 5.1 - Kdrrr2k2cos1krorsec1rkor-sin1kror-tan1Kr2k2Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...
Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In the problems of this section, set up and...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 7 to 18 evaluate the double integrals...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 19 to 24, use double integrals to find...Ch. 5.2 - In Problems 25 to 28, sketch the area of...Ch. 5.2 - In Problems 25 to 28, sketch the area of...Ch. 5.2 - In Problems 25 to 28, sketch the area of...Ch. 5.2 - In Problems 25 to 28, sketch the area of...Ch. 5.2 - In Problems 29 to 32, observe that the inside...Ch. 5.2 - In Problems 29 to 32, observe that the inside...Ch. 5.2 - In Problems 29 to 32, observe that the inside...Ch. 5.2 - In Problems 29 to 32, observe that the inside...Ch. 5.2 - A lamina covering the quarter disk x2+y24,x0,y0,...Ch. 5.2 - A dielectric lamina with charge density...Ch. 5.2 - A triangular lamina is bounded by the coordinate...Ch. 5.2 - A partially silvered mirror covers the square area...Ch. 5.2 - In Problems 37 to 40, evaluate the triple...Ch. 5.2 - In Problems 37 to 40, evaluate the triple...Ch. 5.2 - In Problems 37 to 40, evaluate the triple...Ch. 5.2 - In Problems 37 to 40, evaluate the triple...Ch. 5.2 - Find the volume between the planes...Ch. 5.2 - Find the volume between the planes...Ch. 5.2 - Find the volume between the surfaces...Ch. 5.2 - Find the mass of the solid in Problem 42 if the...Ch. 5.2 - Find the mass of the solid in Problem 43 if the...Ch. 5.2 - Find the mass of a cube of side 2 if the density...Ch. 5.2 - Find the volume in the first octant bounded by the...Ch. 5.2 - Find the volume in the first octant bounded by the...Ch. 5.2 - Find the volume in the first octant bounded by the...Ch. 5.2 - Find the mass of the solid in Problem 48 if the...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - Prob. 4PCh. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - The following notation is used in the problems:...Ch. 5.3 - Prove the following two theorems of Pappus: The...Ch. 5.3 - Prove the following two theorems of Pappus: An arc...Ch. 5.3 - Prove the following two theorems of Pappus: Use...Ch. 5.3 - Prove the following two theorems of Pappus: Use...Ch. 5.3 - Prove the following two theorems of Pappus: Let a...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - In Problems 17 to 30, for the curve y=x, between...Ch. 5.3 - Revolve the curve y=x1, from x=1 to x=, about the...Ch. 5.3 - Use a computer or tables to evaluate the integral...Ch. 5.3 - Verify that (3.10) gives the same result as (3.8).Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - As needed, use a computer to plot graphs of...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Prob. 23PCh. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Find the Jacobians x,y/u,v of the given...Ch. 5.4 - Prob. 28PCh. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.5 - For these problems, the most important sketch is...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...Ch. 5.6 - As needed, use a computer to plot graphs and to...

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