Mathematical Methods in the Physical Sciences
3rd Edition
ISBN: 9780471198260
Author: Mary L. Boas
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Videos
Textbook Question
Chapter 10.7, Problem 1P
Verify (7.1).Hints: In Figure 7.1, consider the projection of the slanted face of area dS onto the three unprimed coordinate planes. In each case, show that the projection angle is equal to an angle between the
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
: +0
1
R2X2
العنوان
I need a detailed drawing with explanation
L
L
2) slots per pole per phase = 3/31
B = 180-60
msl
Kd
Kol, Sin (Info)
Isin (6)
sin(30)
Sin (30)
اذا ميريد شرح الكتب بس 0 بالفراغ
3) Cos (30) 0.866
4) Rotating
5) Synchronous speed, 120 x 50
6
50105
1000
S=1000-950
Loco mem
6.
Copper losses: 5kw
Rotor input
loo kw
0.05
اذا ميريد شرح الكتب فقط look
7) rotov
DC
ined sove in peaper
Pu+965
4
Which of the following is converge, and which diverge? Give reasons for your answers
with details. When your answer then determine the convergence sum if possible.
111Σm=1
sin()
Lake
Which of the following is converge, and which diverge? Give reasons for your answers
with details. When your answer then determine the convergence sum if possible.
T
TH
M
い
ined sove in beaper
Anting.
Pu+965
na lake
an accident and lands at the bottom of the lake
Q2// Find the volume of the region in first octant bounded by the coordinate
planes and the plane passing through (1, 0, 0), (0, 2, 0), and (0, 0, 3).
Q/Evaluate({ } } 3xze* dydzdx.
|
Evaluate (3xze** dydzdx.
ined sove in peaper
+9198
PU+965
Lake
Find the volume of th solid bounded above by the Cy
2=6-1
o the sides by the cylinder x+y=9, and below by the xy-plane
Chapter 10 Solutions
Mathematical Methods in the Physical Sciences
Ch. 10.2 - Verify equations (2.6).Ch. 10.2 - Prob. 2PCh. 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. 6PCh. 10.6 - Write the transformation equations for the triple...Ch. 10.6 - Write the transformation equations for WS to...Ch. 10.6 - Prob. 9PCh. 10.6 - Prob. 10PCh. 10.6 - Prob. 11PCh. 10.6 - Prob. 12PCh. 10.6 - Prob. 13PCh. 10.6 - Prob. 14PCh. 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. 3PCh. 10.8 - In the text and problems so far, we have found the...Ch. 10.8 - Prob. 5PCh. 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. 11PCh. 10.8 - Using the expression you have found for ds, and...Ch. 10.8 - Prob. 13PCh. 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. 2PCh. 10.9 - Using cylindrical coordinates write the Lagrange...Ch. 10.9 - Prob. 4PCh. 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. 14PCh. 10.9 - Prob. 15PCh. 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. 4PCh. 10.10 - Write u in polar coordinates in terms of its...Ch. 10.10 - Prob. 6PCh. 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
If n is a counting number, bn, read______, indicates that there are n factors of b. The number b is called the_...
Algebra and Trigonometry (6th Edition)
Two balls are chosen randomly from an urn containing 8 white, 4 black, and 2 orange balls. Suppose that we win ...
A First Course in Probability (10th Edition)
Determining Sample Size. In Exercises 31–38, use the given data to find the minimum sample size required to est...
Elementary Statistics (13th Edition)
Matching In Exercises 17–20, match the level of confidence c with the appropriate confidence interval. Assume e...
Elementary Statistics: Picturing the World (7th Edition)
Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor while 8% visit n...
Probability And Statistical Inference (10th 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.Similar questions
- ... +① العنوان > पर ined sove in peaper ང་ PU+965 Q2// Draw and Evaluate, or Integrate, the function f(u, v) = (1+u2+v²)3 over the region enclosed by one loop of the lemniscate (u² + v²)² - (u² + v²) = 0. Lake 2 4-2² y 7357 r QI// Evaluate f²² cos(y) dxdydz. 4-y 이arrow_forwardPlease show all steps and write out the answer instead of typing it out, thanksarrow_forwardし ined sove in peaper Anot in PV+96252 √4-x²-y² Q4// Convert √ √ √2x-x2 √√4-x-2_ 21xy² dzdydx to (a) cylindrical coordinates, (b) Spherical coordinates. ln3 (m3)2-x2 Q Draw and Evaluate Lake √x²+ dydarrow_forward
- : +0 1 R2X2 العنوان I need a detailed drawing with explanation L L 2) slots per pole per phase = 3/31 B = 180-60 msl Kd Kol, Sin (Info) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 6 50105 1000 S=1000-950 Loco mem 6. Copper losses: 5kw Rotor input loo kw 0.05 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper PU + 96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 5100 2n=2√²+n Lake Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. T (3n)! 00 //Σn=1 (1+n)!(2+n)!" TH Marrow_forward۳/۱ : +♡ العنوان R2 X2 2) slots per pole per phase = 3/31 B-180-60 msl Kd Kas Sin (1) Isin (6) sin(30) Sin (30) اذا ميريد شرح الكتب بس بالفراغ 3) Cos (30) 0.866 レ× 4) Rotating 5) Synchronous speed, 120 x 50 G S=1000-950 50105 1000 looo rem > ined sove in pea Copper losses 5kw Rotor input: 5 0.05 (lookw) bos cid PU+965 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 7) rotor !!Σn=1 (1-1)" が Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 5700 Prove that the p-series Σn=11 (p areal constant) converges if, and diverges otherwise. T Τ Lake Marrow_forwardVo)) %TV .. + 1 R2X2 2) slots per pole per phase = 3/31 B-180-60 msl Kol Sin () Isin () Kd تب بس بالفراغ i Cos (30) 0.866 4) Rotating ۳/۱ 5) Synchronous speed; 12 S=1000-950 50 1000 Copper losses: 5kw Rotor input 5 loo kw 0.05 6) I العنوان Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. اذا ميريد شرح الكتب فقط ok 7) rotor ||| DC 11500 30tan¹() 2n=1' m²+1 1:11 > PV + 16°52 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. 7357 //Σm=1 (m²-5n+6) Lake Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the series' convergence if possible. - (3)(5+)) T d sove in peaper =T Marrow_forward
- PROBLEM 1: A 12-lb rod ABC is impacted by a 2-lb object DE as shown. The object embeds into the end of the rod at point C, determine immediately after the impact (a) the angular velocity of the rod ABC, (b) the angular acceleration of the rod ABC, A 2 B Unit: ft (c) the components of the reaction at B. 12 Assume that the object and the rod move as a single body after the impact. Vo = 35 ft/s C E D 6arrow_forwardPlease answer both questions clearly thanksarrow_forwardL ined sove in peaper Anoting PU+965 4 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. +1Σm=1 00 sin Sn Lake 55 Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 5700 2n=2√2+n Carrow_forward
- Ministry of Higher Education & Scientific Research Babylon University College of Engineering- musayab Homobile Department Subject :Numerical Analyses Stage: Third Time: 90 min Date: 25-4-2023 2nd month exam/2nd semester (2022-2023) Note: Answer all questions, all questions have same degree. Q1:Given the values X 5 7 11 13 17 F(x) 150 392 1452 2366 5202 Evaluate f(9),using Newton's divided difference formula Q2:A slider in a machine moves along a fixed straight rod.its distance (x cm) along the rod is given below for various values of the time.Find the velocity and acceleration of the slider when t=0.3 seconds. t(seconds) 0 X (cm) 30.13 0.1 31.62 0.2 0.3 0.4 0.5 0.6 32.87 33.64 33.95 33.81 33.24 Q3:From the following table,find the area bounded by the curve and x- axis,between the ordinates x=7.74 to x=7.52 using Simpson's 1/3 rule. X y=f(x) 7.47 7.48 1.93 1.95 7.49 1.98 7.50 7.51 7.52 2.01 2.03 2.06 Q4:Given y+x with initial condition y=1 at x=0;find (y) for x=0.1 by Euler's method.…arrow_forwardV ined sove in peaper Pu+96er Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 21/11 55 a Which of the following is converge, and which diverge? Give reasons for your answers with details. When your answer then determine the convergence sum if possible. 1Σn=1 (2-") n° 3" 6"arrow_forwardPROBLEM 2: A baseball catcher includes a 6-kg rod with a small net of negligible mass at point B. A spring of unstretched length 0.3 m is attached to the midpoint of bar AB at one end and to stationary point D at the other. A stopper at point E keeps the catcher in the vertical position before the pitch. Knowing the catcher just barely rotates when it catches a fastball of mass 0.18 kg, determine the required spring constant of the spring. Given = 1.5 m. Bonus: Develop a MATLAB program to solve for this problem. v₁ = 40 m/s Unit: m 1 B L E A D www wwwwwww -L-arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Matrix Factorization - Numberphile; Author: Numberphile;https://www.youtube.com/watch?v=wTUSz-HSaBg;License: Standard YouTube License, CC-BY