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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Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…
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Chapter 6.4, Problem 7P

Sketch a figure and verify equation ( 4.12).

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Chapter 6.4, Problem 6P
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= 5 37 A 4 8 0.5 06 9
For each of the time​ series, construct a line chart of the data and identify the characteristics of the time series​ (that is,​ random, stationary,​ trend, seasonal, or​ cyclical). Month    Number (Thousands)Dec 1991    65.60Jan 1992    71.60Feb 1992    78.80Mar 1992    111.60Apr 1992    107.60May 1992    115.20Jun 1992    117.80Jul 1992    106.20Aug 1992    109.90Sep 1992    106.00Oct 1992    111.80Nov 1992    84.50Dec 1992    78.60Jan 1993    70.50Feb 1993    74.60Mar 1993    95.50Apr 1993    117.80May 1993    120.90Jun 1993    128.50Jul 1993    115.30Aug 1993    121.80Sep 1993    118.50Oct 1993    123.30Nov 1993    102.30Dec 1993    98.70Jan 1994    76.20Feb 1994    83.50Mar 1994    134.30Apr 1994    137.60May 1994    148.80Jun 1994    136.40Jul 1994    127.80Aug 1994    139.80Sep 1994    130.10Oct 1994    130.60Nov 1994    113.40Dec 1994    98.50Jan 1995    84.50Feb 1995    81.60Mar 1995    103.80Apr 1995    116.90May 1995    130.50Jun 1995    123.40Jul 1995    129.10Aug 1995…
For each of the time​ series, construct a line chart of the data and identify the characteristics of the time series​ (that is,​ random, stationary,​ trend, seasonal, or​ cyclical). Year    Month    Units1    Nov    42,1611    Dec    44,1862    Jan    42,2272    Feb    45,4222    Mar    54,0752    Apr    50,9262    May    53,5722    Jun    54,9202    Jul    54,4492    Aug    56,0792    Sep    52,1772    Oct    50,0872    Nov    48,5132    Dec    49,2783    Jan    48,1343    Feb    54,8873    Mar    61,0643    Apr    53,3503    May    59,4673    Jun    59,3703    Jul    55,0883    Aug    59,3493    Sep    54,4723    Oct    53,164

Chapter 6 Solutions

Mathematical Methods in the Physical Sciences

Ch. 6.3 - If A=2ijk,B=2i3j+k,C=j+k, find (AB)C,A(BC),(AB)C,...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - A force F=2i3j+k acts at the point (1,5,2). Find...Ch. 6.3 - Prob. 8PCh. 6.3 - Prob. 9PCh. 6.3 - In Figure 3.5, let r be another vector from O to...
Ch. 6.3 - Write out the twelve triple scalar products...Ch. 6.3 - (a) Simplify ( AB)2[(AB)B]A by using ( 3.9). (b)...Ch. 6.3 - Prove that the triple scalar product of (AB),(BC),...Ch. 6.3 - Prove the Jacobi identity: A(BC)+B(CA)+C(AB)=0....Ch. 6.3 - Prob. 15PCh. 6.3 - In the discussion of Figure 3.8, we found for the...Ch. 6.3 - Expand the triple product for a=(r) given in the...Ch. 6.3 - Two moving charged particles exert forces on each...Ch. 6.3 - The force F=i+3j+2k acts at the point (1,1,1). (a)...Ch. 6.3 - Prob. 20PCh. 6.4 - Verify equations (4.5) by writing out the...Ch. 6.4 - Let the position vector (with its tail at the...Ch. 6.4 - As in Problem 2, if the position vector of a...Ch. 6.4 - Prob. 4PCh. 6.4 - The position of a particle at time t is given by...Ch. 6.4 - The force acting on a moving charged particle in a...Ch. 6.4 - Sketch a figure and verify equation ( 4.12).Ch. 6.4 - In polar coordinates, the position vector of a...Ch. 6.4 - The angular momentum of a particle m is defined by...Ch. 6.4 - If V(t) is a vector function oft, find the...Ch. 6.6 - Find the gradient of w=x2y3z at (1,2,1).Ch. 6.6 - Starting from the point (1,1), in what direction...Ch. 6.6 - Find the derivative of xy2+yz at (1,1,2) in the...Ch. 6.6 - Find the derivative of zexcosy at (1,0,/3) in the...Ch. 6.6 - Find the gradient of =zsinyxz at the point...Ch. 6.6 - Find a vector normal to the surface x2+y2z=0 at...Ch. 6.6 - Find the direction of the line normal to the...Ch. 6.6 - (a) Find the directional derivative of =x2+sinyxz...Ch. 6.6 - (a) Given =x2y2z, find at (1,1,1). (b) Find the...Ch. 6.6 - For Problems 10 to 14, use a computer as needed to...Ch. 6.6 - For Problems 10 to 14, use a computer as needed to...Ch. 6.6 - For Problems 10 to 14, use a computer as needed to...Ch. 6.6 - For Problems 10 to 14, use a computer as needed to...Ch. 6.6 - For Problems 10 to 14, use a computer as needed to...Ch. 6.6 - Repeat Problem 14b for the following points and...Ch. 6.6 - Show by the Lagrange multiplier method that the...Ch. 6.6 - Find r, where r=x2+y2, using ( 6.7) and also using...Ch. 6.6 - As in Problem 17, find the following gradients in...Ch. 6.6 - As in Problem 17, find the following gradients in...Ch. 6.6 - As in Problem 17, find the following gradients in...Ch. 6.6 - Verify equation ( 6.8 ); that is, find f in...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Compute the divergence and the curl of each of the...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Calculate the Laplacian 2 of each of the following...Ch. 6.7 - Verify formulas (b), (c), (d), (g), (h), (i), (i),...Ch. 6.7 - For r=xi+yj+zk, evaluate (kr)Ch. 6.7 - For r=xi+yj+zk, evaluate rrCh. 6.7 - For r=xi+yj+zk, evaluate rrCh. 6.8 - Evaluate the line integral x2y2dx2xydy along each...Ch. 6.8 - Evaluate the line integral (x+2y)dx2xdy along each...Ch. 6.8 - Evaluate the line integral xydx+xdy from (0,0) to...Ch. 6.8 - Prob. 4PCh. 6.8 - Find the work done by the force F=x2yixy2j along...Ch. 6.8 - Prob. 6PCh. 6.8 - For the force field F=(y+z)i(x+z)j+(x+y)k, find...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Verify that each of the following force fields is...Ch. 6.8 - Given F1=2xi2yzjy2k and F2=yixj (a) Are these...Ch. 6.8 - Which, if either, of the two force fields...Ch. 6.8 - For the force field F=yi+xj+zk, calculate the work...Ch. 6.8 - Show that the electric field...Ch. 6.8 - For motion near the surface of the earth, we...Ch. 6.8 - Consider a uniform distribution of total mass m...Ch. 6.9 - Write out the equations corresponding to ( 9.3 )...Ch. 6.9 - In Problems 2 to 5 use Greens theorem [formula (...Ch. 6.9 - In Problems 2to5useGree n stheorem[formula(9.7)]...Ch. 6.9 - In Problems 2 to 5 use Greens theorem [formula (...Ch. 6.9 - In Problems 2 to 5 use Greens theorem [formula (...Ch. 6.9 - For a simple closed curve C in the plane show by...Ch. 6.9 - Use Problem 6 to show that the area inside the...Ch. 6.9 - Use Problem 6 to find the area inside the curve...Ch. 6.9 - Apply Greens theorem with P=0,Q=12x2 to the...Ch. 6.9 - Evaluate each of the following integrals in the...Ch. 6.9 - Evaluate each of the following integrals in the...Ch. 6.9 - Evaluate each of the following integrals in the...Ch. 6.10 - Evaluate both sides of ( 10.17) if V=r=ix+jy+kz,...Ch. 6.10 - Given V=x2i+y2j+z2k, integrate Vnd over the whole...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - Evaluate each of the integrals in Problems 3 to 8...Ch. 6.10 - If F=xi+yj, calculate Fnd over the part of the...Ch. 6.10 - Evaluate Vnd over the curved surface of the...Ch. 6.10 - Given that B= curl A, use the divergence theorem...Ch. 6.10 - A cylindrical capacitor consists of two long...Ch. 6.10 - Draw a figure similar to Figure 10.6 but with q...Ch. 6.10 - Obtain Coulombs law from Gausss law by considering...Ch. 6.10 - Suppose the density of a fluid varies from point...Ch. 6.10 - The following equations are variously known as...Ch. 6.11 - Do case (b) of Example 1 above.Ch. 6.11 - Given the vector A=x2y2i+2xyj. (a) Find A (b)...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Use either Stokes' theorem or the divergence...Ch. 6.11 - Vnd over the entire surface of the volume in the...Ch. 6.11 - (curlV)nd over the part of the surface z=9x29y2...Ch. 6.11 - Vnd over the entire surface of a cube in the first...Ch. 6.11 - Vdr around the circle (x2)2+(y3)2=9,z=0, where...Ch. 6.11 - (2xi2yj+5k)nd over the surface of a sphere of...Ch. 6.11 - (yixj+zk)dr around the circumference of the circle...Ch. 6.11 - cydx+zdy+xdz, where C is the curve of intersection...Ch. 6.11 - What is wrong with the following proof that there...Ch. 6.11 - Prob. 17PCh. 6.11 - Find vector fields A such that V=curlA for each...Ch. 6.11 - Find vector fields A such that V= curl A for each...Ch. 6.11 - Find vector fields A such that V=curlA for each...Ch. 6.11 - Find vector fields A such that V=curlA for each...Ch. 6.11 - Find vector fields A such that V=curlA for each...Ch. 6.12 - Prob. 1MPCh. 6.12 - If A and B are the diagonals of a parallelogram,...Ch. 6.12 - The force on a charge q moving with velocity...Ch. 6.12 - Prob. 4MPCh. 6.12 - Use Greens theorem (Section 9) to do Problem 8.2.Ch. 6.12 - Prob. 6MPCh. 6.12 - Let F=2i3j+k act at the point (5,1,3). (a) Find...Ch. 6.12 - Prob. 8MPCh. 6.12 - Let F=i5j+2k act at the point (2,1,0). Find the...Ch. 6.12 - Given u=xy+sinz, find (a) the gradient of u at...Ch. 6.12 - Given =z23xy, find (a) grad ; (b) the directional...Ch. 6.12 - Given u=xy+yz+zsinx, find (a) u at (0,1,2); (b)...Ch. 6.12 - Given =x2yz and the point P(3,4,1), find (a) at...Ch. 6.12 - If the temperature is T=x2xy+z2, find (a) the...Ch. 6.12 - Show that...Ch. 6.12 - Given F1=2xzi+yj+x2k and F2=yixj: (a) Which F, if...Ch. 6.12 - Find the value of Fdr along the circle x2+y2=2...Ch. 6.12 - Is F=yi+xzj+zk conservative? Evaluate Fdr from...Ch. 6.12 - Given F1=2yi+(z2x)j+(y+z)k,F2=yi+2xj: (a) Is F1...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...Ch. 6.12 - In Problems 20 to 31, evaluate each integral in...

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