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
Concept explainers
Videos
Textbook Question
Chapter 11.9, Problem 4P
Show that
(a) by using (9.5) and
(b) by reducing it to a
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The following table shows the IQs of 480 elementary school children. Determine the
four moments (mean, standard deviation, asymmetry, and skewness).
Class mark (X) 70
74
78
82
86 90
94
98
102 106 110 114 118 122 126
Frequencies (f) 4
9
16
28
45
66
85
72
54 38 27 18 11 5 2
Calculate the respective coefficients of variation. Compare the results in each
problem:
Pulse Rates Listed below are the pulse rates (beats per minute) for samples of adult men
and women (from Data Set 1 "Body Data" in Appendix B). Does there appear to be a
difference?
Men: 86 72 64 72 72 54 66 56 80 72 64 64 96 58 66
Women: 64 84 82 70 74 86 90 88 90 90 94 68 90 82 80
Lines at the Bank Customer wait times (in seconds) at the Madison Savings Bank are
recorded using two configurations: single customer line; individual customer lines.
Single Line 390 396 402 408 426 438 444 462 462 462
Individual Lines 252 324 348 372 402 462 462 510 558 600
The following ordered data listing shows the data rates for cellular phones for a telephone
company at an airport.
a) Calculate the measures of central tendency for the list of unclustered data.
b) group the data in an appropriate frequency table.
c) calculate the measures of central tendency using the table resulting from b).
0.8
1.4
1.8
1.9
3.2
3.6
4.5
4.5
4.6
6.2
6.5
7.7
7.9
9.9
10.2
10.3
10.9
11.1
11.1
11.6
11.8
12.0
13.1
13.5
13.7
14.1
14.2
14.7
15.0
15.1
15.5
15.8
16.0
17.5
18.2
20.2
21.1
21.5
22.2
22.4
23.1
24.5
25.7
28.5
34.6
38.5
43.0
55.6
71.3
77.8
Chapter 11 Solutions
Mathematical Methods in the Physical Sciences
Ch. 11.3 - The integral in ( 3.1) is improper because of the...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Use the recursion relation (3.4), and if needed,...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a T...Ch. 11.3 - Express each of the following integrals as a ...
Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - Express each of the following integrals as a ...Ch. 11.3 - A particle starting from rest at x=1 moves along...Ch. 11.3 - Express as a function 01ln1xp1dx, Hint: See...Ch. 11.5 - Using (5.3) with (3.4) and (4.1), find...Ch. 11.5 - Without computer or tables, but just using facts...Ch. 11.5 - In Chapter 1, equations(13.5)and (13.6), we...Ch. 11.5 - Prove that, for positive integral n:...Ch. 11.5 - Use (5.4) to show that (a) 12n12+n=(1)n if n= a...Ch. 11.5 - Prove...Ch. 11.5 - In the Table of Laplace Transforms (end of Chapter...Ch. 11.6 - Prove that B(p,q)=B(q,p). Hint: Put x=1y in...Ch. 11.6 - Prove equation (6.5) (6.5)B(p,q)=0yp1dy(1+y)p+q.Ch. 11.6 - Show that for integral n, m...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Express the following integrals as B functions,...Ch. 11.7 - Prove B(n,n)=Bn,12/22n1. Hint: In (6.4), use the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.7 - Computer plot the graph of x3+y3=8. Write the...Ch. 11.8 - Complete the pendulum problem to find the period...Ch. 11.8 - Suppose that a car with a door open at right...Ch. 11.8 - The figure is part of a cycloid with parametric...Ch. 11.9 - Sketch or computer plot a graph of the function...Ch. 11.9 - Verify equations (9.2),(9.3), and (9.4). Hint:...Ch. 11.9 - Prove that erf(x) is an odd function of x. Hint:...Ch. 11.9 - Show that ey2/2dy=2 (a) by using (9.5) and (9.2a);...Ch. 11.9 - Replace x by $i x in(9.1)andlet t = i u$ to show...Ch. 11.9 - Assuming that x is real, show the following...Ch. 11.10 - Carry through the algebra to get equation (10.4).Ch. 11.10 - The integral xtp1etdt=(p,x) is called an...Ch. 11.10 - Express the complementary error function erfc (x)...Ch. 11.10 - En(x)=1exttndt,n=0,1,2,, and Ei(x)=xettdt, and...Ch. 11.10 - 2(a) Express E1(x) as an incomplete function. (b)...Ch. 11.10 - The logarithmic integral is li(x)=0xdtlnt. Express...Ch. 11.10 - Computer plot graphs of (a) En(x) for n=0 to 10...Ch. 11.11 - Use the term 1/(12p) in (11.5) to show that the...Ch. 11.11 - (a) To see the results in Problem 1 graphically,...Ch. 11.11 - In statistical mechanics, we frequently use the...Ch. 11.11 - Use Stirlings formula to evaluate...Ch. 11.11 - Use Stirlings formula to evaluate limnn+32n(n+1).Ch. 11.11 - Use equations (3.4) and (11.5) to show that...Ch. 11.11 - The function (p)=ddpln(p) is called the digamma...Ch. 11.11 - Sketch or computer plot a graph of y=lnx for x0....Ch. 11.11 - The following expression occurs in statistical...Ch. 11.11 - Use Stirlings formula to find limn(n!)1/n/n.Ch. 11.12 - Expand the integrands of K and E [see ( 12.3 )] in...Ch. 11.12 - Use a graph of sin2 and the text discussion just...Ch. 11.12 - Computer plot graphs of K(k) and E(k) in (12.3)...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - In Problems 4 to 13, identify each of the...Ch. 11.12 - Find the circumference of the ellipse 4x2+9y2=36.Ch. 11.12 - Find the length of arc of the ellipse x2+y2/4=1...Ch. 11.12 - Find the are length of one arch of y=sinx.Ch. 11.12 - Write the integral in equation (12.7) as an...Ch. 11.12 - Computer plot graphs of sn u, cn u, and dn u, for...Ch. 11.12 - If u=ln(sec+tan), then is a function of u called...Ch. 11.12 - Show that for k=0:u=F(,0)=,snu=sinu,cnu=cosu,dnu=1...Ch. 11.12 - Show that the four answers given in Section 1 for...Ch. 11.12 - In the pendulum problem, =sing/lt is an...Ch. 11.12 - A uniform solid sphere of density 12 is floating...Ch. 11.12 - Sometimes you may find the notation F(,k) in...Ch. 11.12 - As in Problem $24,$ show that...Ch. 11.13 - Show that $ 0ymdy(1+y)n+1=1(nm)C(n,m) $ for...Ch. 11.13 - Show that B(m,n)B(m+n,k)=B(n,k)B(n+k,m).Ch. 11.13 - Use Stirlings formula to show that...Ch. 11.13 - Verify the asymptotic series 0etdt(1+xt)~ (1)nn!xn...Ch. 11.13 - Use gamma and beta function formulas to show that...Ch. 11.13 - Generalize Problem 5 to show that...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Identify each of the following integrals or...Ch. 11.13 - Find an expression for the exact value of (55.5)...Ch. 11.13 - Using your result in Problem 23 and equation...Ch. 11.13 - As in problems 23 and 24, find expressions for the...
Additional Math Textbook Solutions
Find more solutions based on key concepts
Ages A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 y...
Introductory Statistics
a. How many different 7-place license plates are possible if the first 2 places are for letters and the other 5...
A First Course in Probability (10th Edition)
True or False The quotient of two polynomial expressions is a rational expression, (p. A35)
Precalculus
Domain in context Determine an appropriate domain of each function. Identify the independent and dependent vari...
Calculus: Early Transcendentals (2nd Edition)
Suppose that f and g are integrable and that
, , .
Use the rules in Table 5.6 to find
University Calculus: Early Transcendentals (4th Edition)
Second derivatives Find d2ydx2 for the following functions. 73. y=e2x2
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.Similar questions
- Ages of Oscar winners: Use the same scale to construct box plots for the ages of the Best Actresses and Best Actors. Compare the results and draw conclusions from them (at least two). ACTRESSES 22 37 28 63 32 26 31 27 27 28 30 26 29 24 38 25 29 41 30 35 35 33 29 38 54 24 25 46 41 28 40 39 29 27 31 38 29 25 35 60 43 35 34 34 27 37 42 41 36 32 41 33 31 74 33 50 38 61 21 41 26 80 42 29 33 35 45 49 39 34 26 25 33 35 35 28 30 29 61 32 33 45 29 62 22 44 54 ACTORS 44 41 62 52 41 34 34 52 41 37 38 34 32 40 43 56 41 39 49 57 41 38 42 52 51 35 30 39 41 44 49 35 47 31 47 37 57 42 45 42 44 62 43 42 48 49 56 38 60 30 40 42 36 76 39 53 45 36 62 43 51 32 42 54 52 37 38 32 45 60 46 40 36 47 29 43 37 38 45 50 48 60 50 39 55 44 33arrow_forwardPlease answer exercise 11.2.9 and 11.4.9 stepwise showing all necessary stepsarrow_forwardsimplify. 22 x (-7+4)arrow_forward
- Find parametric equations for the line through the point (0, 2, 2) that is perpendicular to the line x=3+t, y 2-t, z=3t and intersects this line. (Use the parameter t.) (x(t), y(t), z(t)) = ( t,2 — t,2 + 2t )arrow_forwardLet P be a point not on the line L that passes through the points Q and R. The distance d from the point P to the line L is |a x bl d |a| where a = QR and b = QP. Use the above formula to find the distance from the point to the given line. d = (0, 1, 3); x = 2t, y = 6 - 2t, z = 3 + tarrow_forwardLet L₁ be the line through the origin and the point (2, 0, -1). Let L₂ be the line through the points (1, -1, 1) and (6, 1, 5). Find the distance between L1 and L2. Need Help? Read It Watch Itarrow_forward
- (a) Let P be a point not on the line L that passes through the points Q and R. Show that the distance d from the point P to the line L is |a x bl |a| d where a = QR and b = QP. This answer has not been graded yet. (b) Use the formula in part (a) to find the distance from the point P(1, 1, 1) to the line through Q(0, 7, 6) and R(-1, 2, 6). 29.65arrow_forwardFind the area of the parallelogram with vertices K(1, 2, 2), L(1, 5, 4), M(6, 10, 4), and N(6, 7, 2).arrow_forwardFind the area of the parallelogram with vertices A(-5, 4), B(-3, 7), C(1, 5), and D(-1, 2).arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY