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 10.6, Problem 4P
Do Example 1 and Problem 3 if the transformation to a left-handed system is an inversion (see Problem 2).
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The Phony TV company makes two different types of television sets,
OLED and LED, which are assembled by two different assembly lines.
When Line One operates it assembles 30 units of the OLED model
and 50 units of the LED model per hour. Line Two assembles 40 units
of the OLED model and 40 units of the LED model per hour. Let x
be the number of hours that Line One operates and y the number of
hours Line Two operates. Phony needs to produce at least 3000 units
of the OLED model and 4000 units of the LED model to fill an order.
(a) Write down the inequalities that describe the assembly constraints.
(b) Graph the feasible region determined by these constraints.
The following statements are true regarding the ages of Sammy, Pammy, and Tammy.
"Sammy's age plus Pammy's age plus two times Tammy's age is 100."
"Two times Sammy's age minus three times Pam's age plus fourteen times Tammy's age also
equals 100."
"Sammy's age plus two times Pammy's age minus four times Tammy's age also equals 100."
(a) Set up a system of linear equations that represents the statements above.
(b) Solve the system in part (a) using Gauss elimination and backwards substitution.
A company rents moving trucks out of two locations: Detroit and Milwaukee. Some of their customers rent a
truck in one city and return it in the other city, and the rest of their customers rent and return the truck in
the same city. The company owns a total of 500 trucks.
The company has seen the following trend:
About 35 percent of the trucks in Detroit move to Milwaukee each week.
About 25 percent of the trucks in Milwaukee move to Detroit each week.
Suppose right now Detroit has 330 trucks.
[2₁]
If the vector t
represents the distribution of trucks, where 21 is the number in Detroit and 22 is
F2
the number in Milwaukee, find the matrix A so that At is the distribution of trucks after 1 week. [Note:
You will want to use Sage to complete this problem.]
A
How many trucks will be in each city after 1 week? [Round answers to the nearest whole number.]
Detroit:
Milwaukee:
How many trucks will be in each city after 3 weeks? [Sage makes this one easier. Round answers to the
nearest whole…
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
Sisters and Brothers The scatterplot shows the numbers of brothers and sisters for a large number of students. ...
Introductory Statistics
In Hamilton County, Ohio, the mean number of days needed to sell a house is 86 days (Cincinnati Multiple Listin...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
CHECK POINT I You deposit $3000 in s savings account at Yourtown Bank, which has rate of 5%. Find the interest ...
Thinking Mathematically (6th Edition)
Testing Hypotheses. In Exercises 13-24, assume that a simple random sample has been selected and test the given...
Elementary Statistics Using The Ti-83/84 Plus Calculator, Books A La Carte Edition (5th 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
- Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.arrow_forwardQuestion 1 Consider the following network of one-way streets and intersections. The arrows indicate the direction of traffic flow along the one-way streets, and the numbers refer to the exact number of cars observed to enter or leave the intersections during one minute. Each I, denotes the unknown number of cars which passes along the indicated streets during the same period. 500 400 1000 300 200 a) (1pt) Write down a linear system corresponding to the flow of traffic in the network. You must explain how you get your equations Do not simply copy the equations implicit in part (b). you will not receive any points if you do this b) (2pts) The RREF of the system isarrow_forwardProblem 1.2. In each of the following traffic networks consisting of one- way streets, a number along an edge refers to the number of cars per hour passing through the street in the indicated direction. For each network, write down a linear system whose solutions give the possible tuples of values for the traffic flow (cars per hour) passing through the unlabelled edges in the indicated direction in the network. (You don't need to solve the systems.) (a) (b) 200 300 50 200 150 200 150 100 300 50 Problem 1.3. For invertible square matrices A,B,C of the same size, (a) prove that C-¹B-¹A-¹ is the inverse of ABC and (b) assuming AB = BA, prove that (A + B)³ = A³ +3A²B+3AB² + B³. 200arrow_forward
- Problem 4. The number of memory chips M needed in a personal computer depends on how many application programs, A, the owner wants to run simulta- neously. The number of chips M and the number of application programs A are described by (4 chips for 1 program, 4 chips for 2 programs, [0.1(5 – a) a = 1,2,3, 4, M = PA(a) = 6 chips for 3 programs, 8 chips for 4 programs, otherwise. (1) (a) What is the expected number of programs uA = E[A]? (b) Express M, the number of memory chips, as a function M = g(A) of the number of application programs A. (c) Find E[M] = E[g(A)]. Does E[M] = g(E[A])? (d) Find Variance of A and Marrow_forwardConsider two small companies, each with 9 employees including 1 boss with the highest salary in each company, and 8 people working for them with lower salaries. The table below gives the annual salaries of the people in each company. These salaries are identical except for the fact that Small Company B is more profitable overall, and their boss decides to keep a much higher salary than the boss of Small Company A. Small Company A Small Company B $85 000 (boss A) $360 000 (boss B) $65 000 $65 000 $60 000 $60 000 $40 000 $40 000 $35 000 $35 000 $35 000 $35 000 $35 000 $35 000 $30 000 $30 000 $30 000 $30 000 For each of the two companies, calculate the mean, median, and mode, and show your answers and calculations in the space below (rounded to the nearest thousands place). After you answer this question, answer the two follow-up questions about the results you just calculated.arrow_forwardA company makes two types of calculators, one that uses batteries and one that is solar powered. The production of each battery operated calculator involves 1 hour on Machine A, 2 hours on Machine B, and 1 hour on Machine C. The production of each solar powered calculator involves 2 hours on Machine A, 1 hour on Machine B, and 1 hour on Machine C. The company can use Machine A for a total of 14 hours, Machine B for a total of 17 hours, and Machine C for a total of 9 hours. If the company can earn a profit of $2 for each battery powered calculator and $6 for each solar powered calculator, how many of each should it produce in order to maximize profit? What is the maximum profit it can earn?arrow_forward
- PROBLEM 03: The Jokia Cell Phone Company manufactures two models of cell phones - the Wombat and the Sloth. Each Wombat phone uses 2.5 ounces of gold leaf and 3 ounces of plastic, whereas each Sloth phone uses 2 ounces of gold leaf and 2 ounces of plastic. Each day, the company has only 370 ounces of gold leaf and 420 ounces of plastic to be used for making cell phones. If the company makes the correct number of each type of phone on a given day to use up all of the available gold leaf and plastic, how many Wombat phones will be made? A) 60 B) 100 C) 50 D) 90 E) 110 N) none of the abovearrow_forwardA product is made by only two competing companies. Suppose Company X retains two-thirds of its customers and loses one-third to Company Y each year, and Company Y retains three-quarters of its customers and loses one-quarter to Company X each year. We can represent the number of customers each company had last year by D where xo is the number Company X had and yo is the number Company Y had. Then the number that each will have this year can be represented by 3 If Company X has 2900 customers and Company Y has 2500 customers this year, how many customers did each have last year? Company X Company Y Need Help? Read It customers customersarrow_forwardProblem 5 Find whether the following system are linearly dependent or independent (10(1 1) B = { 1 1/5 2) B, = {1,1+x²,1+x+x*} /5 3) B, = { /5 0 0 ( 1arrow_forward
- A company wishes to produce two types of souvenirs: Type A and Type B. Each Type A souvenir will result in a profit of $1, and each Type B souvenir will result in a profit of $1.20. To manufacture a Type souvenir requires 2 minutes on Machine I and 1 minute on Machine II. A Type B souvenir requires 1 minute on Machine I and 3 minutes on Machine II. There are 3 hours available on Machine I and 5 hours available on Machine II. (a) The optimal solution holds if the contribution to the profit of a Type B souvenir lies between $ THER and $ (Enter your answers from smallest to largest.) (b) Find the contribution to the profit of a Type A souvenir (with the contribution to the profit of a Type B souvenir held at $1.20), given that the optimal profit of the company will be $208.80. $ (c) What will be the optimal profit of the company if the contribution to the profit of a Type B souvenir is $3.00 (with the contribution to the profit of a Type A souvenir held at $1.00)? $arrow_forwardPlease help me with the below question.arrow_forwardA company that operated 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data for the problem: Please answer the two questionsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY