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 11.10, Problem 6P
The logarithmic
(a)
(b)
(c)
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.
Topic 2
Evaluate S
x
dx, using u-substitution. Then find the integral using
1-x2
trigonometric substitution. Discuss the results!
Topic 3
Explain what an elementary anti-derivative is. Then consider the following
ex
integrals: fed dx
x
1
Sdx
In x
Joseph Liouville proved that the first integral does not have an elementary anti-
derivative Use this fact to prove that the second integral does not have an
elementary anti-derivative. (hint: use an appropriate u-substitution!)
1. Given the vector field F(x, y, z) = -xi, verify the relation
1
V.F(0,0,0) = lim
0+ volume inside Se
ff F• Nds
SE
where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then,
determine if the origin is sink or source.
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
In Exercises 11-20, express each decimal as a percent.
11. 0.59
Thinking Mathematically (6th Edition)
Fill in each blank so that the resulting statement is true. The quadratic function f(x)=a(xh)2+k,a0, is in ____...
Algebra and Trigonometry (6th Edition)
Telescoping series For the following telescoping series, find a formula for the nth term of the sequence of par...
Calculus: Early Transcendentals (2nd Edition)
Fill in each blank so that the resulting statement is true.
1. A combination of numbers, variables, and opera...
College Algebra (7th Edition)
Length of a Guy Wire A communications tower is located at the top of a steep hill, as shown. The angle of incli...
Precalculus: Mathematics for Calculus (Standalone Book)
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
- 4 3 2 -5 4-3 -2 -1 1 2 3 4 5 12 23 -4 The function graphed above is: Increasing on the interval(s) Decreasing on the interval(s)arrow_forwardQuestion 4 The plot below represents the function f(x) 8 7 3 pts O -4-3-2-1 6 5 4 3 2 + 1 2 3 5 -2+ Evaluate f(3) f(3) = Solve f(x) = 3 x= Question 5arrow_forwardQuestion 14 6+ 5 4 3 2 -8-2 2 3 4 5 6 + 2 3 4 -5 -6 The graph above is a transformation of the function f(x) = |x| Write an equation for the function graphed above g(x) =arrow_forward
- Question 8 Use the graph of f to evaluate the following: 6 f(x) 5 4 3 2 1 -1 1 2 3 4 5 -1 t The average rate of change of f from 4 to 5 = Question 9 10 ☑ 4parrow_forwardQuestion 15 ✓ 6 pts 1 Details The function shown below is f(x). We are interested in the transformed function g(x) = 3f(2x) - 1 a) Describe all the transformations g(x) has made to f(x) (shifts, stretches, etc). b) NEATLY sketch the transformed function g(x) and upload your graph as a PDF document below. You may use graph paper if you want. Be sure to label your vertical and horizontal scales so that I can tell how big your function is. 1- 0 2 3 4 -1- Choose File No file chosen Question 16 0 pts 1 Detailsarrow_forwardAND B A Ꭰarrow_forward
- ANBNC ND B こ Ꭰarrow_forward1 Matching 10 points Factor and Solve 1)x3-216 0, x = {6,[B]} 2) 16x3 = 54 x-[3/2,[D]] 3)x4x2-42 0 x= [ +/-isqrt(7), [F] } 4)x+3-13-9x x=[+/-1.[H]] 5)x38x2+16x=0, x = {0,[K}} 6) 2x6-10x-48x2-0 x-[0, [M], +/-isqrt(3)) 7) 3x+2x²-8 x = {+/-i sqrt(2), {Q}} 8) 5x³-3x²+32x=2x+18 x = {3/5, [S]} [B] [D] [F] [H] [K] [M] [Q] +/-2 sqrt(2) +/- i sqrt(6) (-3+/-3 i sqrt(3))/4 +/- 1 +/-sqrt(6) +/- 2/3 sqrt(3) 4 -3 +/- 3 i sqrt(3) [S]arrow_forwardD U(AUBUC) B Darrow_forward
- helparrow_forwardAnswer question 2.28 please.arrow_forwardQuestion 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY