Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Videos

Textbook Question

Chapter 10.9, Problem 20P

Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions

In cylindrical coordinates, ∇ 2 r , ∇ 2 ( 1 / r ) , ∇ 2 ln r .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.9, Problem 19P

Chapter 10.9, Problem 21P

Students have asked these similar questions

A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration. HINT (a) the magnitude (in N) of the magnetic force acting on the ion N (b) the magnitude (in m/s2) of the ion's acceleration m/s2

Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make with a horizontal line in the positive direction?

The motion of a point on the circumference of a rolling wheel of radius 4 feet is described by the vector function r(t) = 4(12t - sin(12t))i + 4(1 − cos(12t))j Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) = =

Chapter 10 Solutions

Mathematical Methods in the Physical Sciences

Ch. 10.2 - Verify equations (2.6).Ch. 10.2 - Prob. 2P Ch. 10.2 - Consider the matrix A in (2.7) or (2.10). Think of...Ch. 10.2 - Any rotation of axes in three dimensions can be...Ch. 10.2 - Write equations (2.12) out in detail and solve the...Ch. 10.2 - Write the transformation equation for a 3rd-rank...Ch. 10.2 - Following what we did in equations (2.14) to...Ch. 10.2 - Write the equations in (2.16) and so in (2.17)...Ch. 10.3 - Write equations (2.11,), (2.12), (2.13), (2.14),...Ch. 10.3 - Show that the fourth expression in (3.1) is equal...

Ch. 10.3 - As we did in (3.3), show that the contracted...Ch. 10.3 - Show that the contracted tensor TijkVk is a 2nd...Ch. 10.3 - Show that TijklmSlm is a tensor and find its rank...Ch. 10.3 - Show that the sum of two 3rd -rank tensors is a...Ch. 10.3 - As in problem 6, show that the sum of two 2nd...Ch. 10.3 - Show that (3.9) follows from (3.8). Hint: Give a...Ch. 10.3 - Prove the quotient rule in each of the following...Ch. 10.3 - Prove the quotient rule in each of the following...Ch. 10.3 - Prove the quotient rule in each of the following...Ch. 10.3 - Prove the quotient rule in each of the following...Ch. 10.3 - Show that the first parenthesis in (3.5) is a...Ch. 10.4 - As in (4.3) and (4.4), find the y and z components...Ch. 10.4 - Complete Example 4 to verify the rest of the...Ch. 10.4 - As in Problem 2, complete Example 5.Ch. 10.4 - Find the inertia tensor about the origin for a...Ch. 10.4 - For the mass distributions in Problems 5 to 7,...Ch. 10.4 - For the mass distributions in Problems 5 to 7,...Ch. 10.4 - For the mass distributions in Problems 5 to 7,...Ch. 10.4 - For the mass distributions in Problems 5 to 7,...Ch. 10.5 - Verify that (5.5) agrees with a Laplace...Ch. 10.5 - Verify for a few representative cases that (5.6)...Ch. 10.5 - Show that ijklm is an isotropic tensor of rank...Ch. 10.5 - Generalize Problem 3 to see that the direct...Ch. 10.5 - Let Tjkmn be the tensor in (5.8). This is a...Ch. 10.5 - Evaluate: (a) ijjkkmim (b) ijkjk (c) jk2k2j (d)...Ch. 10.5 - Write in terms of s as in (5.8) and (5.9): (a)...Ch. 10.5 - Show that the equations (5.10) are correct. Hints:...Ch. 10.5 - (a) Finish the work of showing that the cross...Ch. 10.5 - (a) Write the triple scalar product A(BC) in...Ch. 10.5 - Using problem 10, write A(BA) in tensor notation...Ch. 10.5 - Write and prove in tensor notation: (a) Chapter 6,...Ch. 10.5 - Write in tensor notation and prove the following...Ch. 10.5 - Show that the diagonal elements of an...Ch. 10.5 - Write a 4-by-4 antisymmetric matrix to show that...Ch. 10.5 - Verify that (5.16) gives (5.17). Also verify that...Ch. 10.5 - Write out the components of Tjk=AjBkAkBj to show...Ch. 10.6 - Show that in 2 dimension (say the x, y plane), an...Ch. 10.6 - In Chapter 3, we said that any 3-by-3 orthogonal...Ch. 10.6 - For Example 1, write out the components of U,V,...Ch. 10.6 - Do Example 1 and Problem 3 if the transformation...Ch. 10.6 - Write the tensor transformation equations for...Ch. 10.6 - Prob. 6P Ch. 10.6 - Write the transformation equations for the triple...Ch. 10.6 - Write the transformation equations for WS to...Ch. 10.6 - Prob. 9P Ch. 10.6 - Prob. 10P Ch. 10.6 - Prob. 11P Ch. 10.6 - Prob. 12P Ch. 10.6 - Prob. 13P Ch. 10.6 - Prob. 14P Ch. 10.6 - In equation (5.12), find whether A(BC) is a vector...Ch. 10.6 - In equation (5.14), is (V) a vector or a...Ch. 10.6 - In equation (5.16), show that if Tjk is a tensor...Ch. 10.7 - Verify (7.1).Hints: In Figure 7.1, consider the...Ch. 10.7 - Write out the sums Pijej for each value of i and...Ch. 10.7 - Carry through the details of getting (7.4) from...Ch. 10.7 - Interpret the elements of the matrices in Chapter...Ch. 10.7 - Show by the quotient rule (Section 3) that Cijkm...Ch. 10.7 - If P and S are 2nd-rank tensors, show that 92=81...Ch. 10.7 - In (7.9) we have written the first row of elements...Ch. 10.7 - Do Problem 4.8 in tensor notation and compare the...Ch. 10.8 - Find ds2 in spherical coordinates by the method...Ch. 10.8 - Observe that a simpler way to find the velocity...Ch. 10.8 - Prob. 3P Ch. 10.8 - In the text and problems so far, we have found the...Ch. 10.8 - Prob. 5P Ch. 10.8 - As in Problem 1, find ds2, the scale factors, the...Ch. 10.8 - As in Problem 1, find ds2, the scale factors, the...Ch. 10.8 - As in Problem 1, find ds2, the scale factors, the...Ch. 10.8 - As in Problem 1, find ds2, the scale factors, the...Ch. 10.8 - Sketch or computer plot the coordinate surfaces in...Ch. 10.8 - Prob. 11P Ch. 10.8 - Using the expression you have found for ds, and...Ch. 10.8 - Prob. 13P Ch. 10.8 - Using the expression you have found for ds, and...Ch. 10.8 - Let x=u+v,y=v. Find ds, thea vectors, and ds2 for...Ch. 10.9 - Prove (9.4) in the following way. Using (9.2) with...Ch. 10.9 - Prob. 2P Ch. 10.9 - Using cylindrical coordinates write the Lagrange...Ch. 10.9 - Prob. 4P Ch. 10.9 - Write out U,V,2U, and V in spherical coordinates.Ch. 10.9 - Do Problem 3 for the coordinate systems indicated...Ch. 10.9 - Do Problem 3 for the coordinate systems indicated...Ch. 10.9 - Do Problem 3 for the coordinate systems indicated...Ch. 10.9 - Do Problem 3 for the coordinate systems indicated...Ch. 10.9 - Do Problem 5 for the coordinate systems indicated...Ch. 10.9 - Do Problem 5 for the coordinate systems indicated...Ch. 10.9 - Do Problem 5 for the coordinate systems indicated...Ch. 10.9 - Do Problem 5 for the coordinate systems indicated...Ch. 10.9 - Prob. 14P Ch. 10.9 - Prob. 15P Ch. 10.9 - Use equations (9.2), (9.8), and (9.11) to evaluate...Ch. 10.9 - Use equations (9.2), (9.8), and (9.11) to evaluate...Ch. 10.9 - Use equations (9.2), (9.8), and (9.18) to evaluate...Ch. 10.9 - Use equations (9.2), (9.8) and (9.11) to evaluate...Ch. 10.9 - Use equations (9.2), (9.8), and (9.11) to evaluate...Ch. 10.9 - Use equations (9.2), (9.8), and (9.11) to evaluate...Ch. 10.10 - Verify equation (10.7). Hint: Use equations (2.4)...Ch. 10.10 - From (10.1) find /x=(1/r)coscos and show that...Ch. 10.10 - Divide equation (10.4) by dt to show that the...Ch. 10.10 - Prob. 4P Ch. 10.10 - Write u in polar coordinates in terms of its...Ch. 10.10 - Prob. 6P Ch. 10.10 - As in (10.12), write the transformation equations...Ch. 10.10 - Using (10.15) show that gij is a 2nd-rank...Ch. 10.10 - If Ui is a contravariant vector and Vj is a...Ch. 10.10 - Show that if Vi is a contravariant vector then...Ch. 10.10 - In (10.18), show by raising and lowering indices...Ch. 10.10 - Show that in a general coordinate system with...Ch. 10.10 - Verify (10.20).Ch. 10.10 - Using equations (10.20) to (10.23), write the...Ch. 10.10 - Do Problem 14 for an orthogonal coordinate system...Ch. 10.10 - Continue Problem 8.15 to find the gij matrix and...Ch. 10.10 - Repeat Problems 8.15 and 10.16 above for the (u,v)...Ch. 10.10 - Using (10.19), show that aiai=ji.Ch. 10.11 - Show that the transformation equation for a...Ch. 10.11 - Let e1,e2,e3 be a set of orthogonal unit vectors...Ch. 10.11 - In Chapter 3, Problem 6.6, you are asked to prove...Ch. 10.11 - If E= electric field and B= magnetic field, is EB...Ch. 10.11 - Do Problems 5 to 8 for the (u,v) coordinate system...Ch. 10.11 - Do Problems 5 to 8 for the (u,v) coordinate system...Ch. 10.11 - Do Problems 5 to 8 for the (u,v) coordinate system...Ch. 10.11 - Do Problems 5 to 8 for the (u,v) coordinate system...Ch. 10.11 - If u is a vector specifying the displacement under...Ch. 10.11 - Show that elements Rij of a rotation matrix are...Ch. 10.11 - Show that the nine quantities Tij=Vi/xj (which are...Ch. 10.11 - The square matrix in equation (10.3) is called the...Ch. 10.11 - In equation (10.13) let the x variables be...

Additional Math Textbook Solutions

Find more solutions based on key concepts

In hypothesis testing, the common level of significance is =0.05. Some might argue for a level of significance ...

Basic Business Statistics, Student Value Edition

11. Mensa Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ t...

Elementary Statistics (13th Edition)

Find the additive inverse of each of the following integers. Write the answer in the simplest possible form. a....

A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)

NOTE: Write your answers using interval notation when appropriate. CHECKING ANALYTIC SKILLS Fill in each blank ...

Graphical Approach To College Algebra

True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it a...

Elementary Statistics: Picturing the World (7th Edition)

Domain in context Determine an appropriate domain of each function. Identify the independent and dependent vari...

Calculus: Early Transcendentals (2nd Edition)

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.