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.
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…
Question 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 is
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
Checkpoint1
Use the substitution method to solve this system:
Answers to Checkpoint exercises are found at the...
Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)
15-22: Qualitative versus Quantitative. Determine whether the following variables are qualitative or quantitati...
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
21. Evaluating a Loan Request The Nejems found a house selling for $550,000. The taxes on the house are $5634 p...
A Survey of Mathematics with Applications (10th Edition) - Standalone book
The probability that exactly 5 employees out of 8 newly hired employees will work with the company after 1 year...
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Percentiles. The pth percentile of a sorted data set is a number xp such that p of the data fall at or below xp...
Excursions in Modern Mathematics (9th Edition)
In Problem 9-14, find a formal eigenfunction expansion for the solution to the given nonhomogeneous boundary va...
Fundamentals of Differential Equations and Boundary Value Problems
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_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_forwardA company manufactures two kinds of kitchen gadgets: invertible widgets and collapsible whammies. The production process is divided into three departments: fabricating, packing, and shipping. The hours of labor required for each operation and the hours available in each department each day are shown in the table. Suppose that the profit on each widget is $24 and the profit on each whammy is $26. How many widgets and how many whammies should be made each day to maximize the company's profit? Use the simplex method to solve. Click the icon to view the table of the hours of labor required and available. The maximum profit of $ (Simplify your answers.) occurs when the company makes widgets and Table of Hours of Labor Required and Available Packing Shipping Widgets Whammies Time available Fabricating 5.0 0.2 0.2 2.0 0.5 0.2 Print 210 18 9 whammies each day. Done Xarrow_forward
- Please help me with the below question.arrow_forwardExample 6.3 Show that the following system is inconsistent. + x2 + x3 = 0 2x1 + 2x2 + 2x3 = 4.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
- 2. You have uncovered Ye Olde Linear Algebra, an old text on Linear Algebra! As you are reading you see a system of two equations, but you can only make out the first line, which is 7x – 11y = 3 But, just below this system, you see the conclusion, “..therefore the system is in- consistent, and has no solution." Give an example of a possible second line to this system.arrow_forward3. Solve the following problem by setting up a linear system (remember to describe your variables) and then solving the system using matrices by hand or with a calculator. Remember to document the work and then interpret the results. A football team's point score is made up of some touchdowns worth 6 points each, some field goals worth 3 points each, and some extra points worth 1 point each. Here's what you can remember about how a team earned its score of 50 points: There was an extra point following all but one of the touchdowns. Therefore the number of extra points was one less than the number of touchdowns. There were twice as many touchdowns as there were field goals. Fully describe how the team earned its points.arrow_forwardPlease solve d,e,f sub-partsarrow_forward
- Please read the problem carefully. Thank you!arrow_forwardThree components are connected to form a system as shown in the accompanying diagram. Because the components in the 2–3 subsystem are connected in parallel, that subsystem will function if at least one of the two individual components functions. For the entire system to function, component 1 must function and so must the 2–3 subsystem |-------2-------| ---1------>| |----------> |-------3-------| The experiment consists of determining the condition of each component [S(success) for a functioning component and F(failure) for a nonfunctioning component]. a. Which outcomes are contained in the event A that exactly two out of the three components function? b. Which outcomes are contained in the event B that at least two of the components function? c. Which outcomes are contained in the event C that the system functions? d. List outcomes in C', A U C, B U C.arrow_forwardExample 12.6. A company manufactures two types of cloth, using three different colours of wool. One yard length of type A cloth requires 4 oz of red wool, 5 oz of green wool and 3 oz of yellow wool. One yard length of type B cloth requires 5 oz of red wool, 2 oz of green wool and 8 oz of yellow wool. The wool available for manufacture is 1000 oz of red wool, 1000 oz of green wool and 1200 oz of yellow wool. The manufacturer can make a profit of Rs. 5 on one yard of type A cloth and Rs. 3 on one yard of type B cloth. Find the best combination of the quantities of type A and type B cloth which gives him maximum profit by solving the L.P.P. graphically.arrow_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