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 4.9, Problem 7P
Repeat Problem 6 if the plane is
A box has three of its faces in the coordinate planes and one vertex on the plane
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Give an example of a graph with at least 3 vertices that has exactly 2 automorphisms(one of which is necessarily the identity automorphism). Prove that your example iscorrect.
3. [10 marks]
Let Go (Vo, Eo) and G₁
=
(V1, E1) be two graphs that
⚫ have at least 2 vertices each,
⚫are disjoint (i.e., Von V₁ = 0),
⚫ and are both Eulerian.
Consider connecting Go and G₁ by adding a set of new edges F, where each new edge
has one end in Vo and the other end in V₁.
(a) Is it possible to add a set of edges F of the form (x, y) with x € Vo and y = V₁ so
that the resulting graph (VUV₁, Eo UE₁ UF) is Eulerian?
(b) If so, what is the size of the smallest possible F?
Prove that your answers are correct.
Let T be a tree. Prove that if T has a vertex of degree k, then T has at least k leaves.
Chapter 4 Solutions
Mathematical Methods in the Physical Sciences
Ch. 4.1 - If u=x2/x2+y2, find u/x,u/y.Ch. 4.1 - Prob. 2PCh. 4.1 - If z=lnu2+v2+w2, find z/u,z/v,z/w.Ch. 4.1 - For w=x3y32xy+6, find 2w/ax2 and 2w/ay2 at the...Ch. 4.1 - For w=8x4+y42xy2, find 2w/x2 and 2w/y2 at the...Ch. 4.1 - For u=excosy, (a) verify that 2u/xy=2u/yx; (b)...Ch. 4.1 - Prob. 7PCh. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...
Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - Prob. 12PCh. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - If z=x2+2y2,x=rcos,y=rsin, find the following...Ch. 4.1 - Prob. 24PCh. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Find the two-variable Maclaurin series for the...Ch. 4.2 - Prob. 7PCh. 4.2 - Find the two-variable Maclaurin series for excosy...Ch. 4.3 - Consider a function f(x,y) which can be expanded...Ch. 4.4 - Use differentials to show that, for very large...Ch. 4.4 - Use differentials to show that, for large n and...Ch. 4.4 - The thin lens formula is 1i+1o=1f, where f is the...Ch. 4.4 - Do Problem 3 if i=12 when o=18, to find i if...Ch. 4.4 - Let R be the resistance of R1=25 ohms and R2=15...Ch. 4.4 - The acceleration of gravity can be found from the...Ch. 4.4 - Coulombs law for the force between two charges q1...Ch. 4.4 - About how much (in percent) does an error of 1 in...Ch. 4.4 - Show that the approximate relative error (df)/f of...Ch. 4.4 - A force of 500 nt is measured with a possible...Ch. 4.4 - Show how to make a quick estimate (to two decimal...Ch. 4.4 - As in Problem 11, estimate (2.05)2+(1.98)23.Ch. 4.4 - Without using a computer or a calculator, estimate...Ch. 4.4 - Estimate the change in f(x)=0xett2+0.51dt if x...Ch. 4.4 - For an ideal gas of N molecules, the number of...Ch. 4.4 - The operating equation for a synchrotron in the...Ch. 4.4 - Here are some other ways of obtaining the formula...Ch. 4.5 - Given z=xey,x=cosht,y=cost, find dz/dt.Ch. 4.5 - Prob. 2PCh. 4.5 - Given r=ep2q2,p=es,q=es, Find dr/ds.Ch. 4.5 - Given x=lnu2v2,u=t2,v=cost, find dx/dt.Ch. 4.5 - If we are given z=z(x,y) and y=y(x), show that the...Ch. 4.5 - Given z=(x+y)5,y=sin10x, find dz/dx.Ch. 4.5 - Given c=sin(ab),b=ae2a, find dc/da.Ch. 4.5 - Prove the statement just after (5.2), that dz...Ch. 4.6 - If pva=C (where a and C are constants), find dv/dp...Ch. 4.6 - If yexy=sinx find dy/dx and d2y/dx2 at (0,0).Ch. 4.6 - If xy=yx, find dy/dx at (2,4).Ch. 4.6 - If xey=yex, find dy/dx and d2y/dx2 for y1.Ch. 4.6 - If xy3yx3=6 is the equation of a curve, find the...Ch. 4.6 - In Problem 5 find d2y/dx2 at (1,2).Ch. 4.6 - If y3x2y=8 is the equation of a curve, find the...Ch. 4.6 - In Problem 7 find d2y/dx2 at (3,1).Ch. 4.6 - For the curve x2/3+y2/3=4, find the equations of...Ch. 4.6 - For the curve xey+yex=0, find the equation of the...Ch. 4.6 - In Problem 10, find y at the origin.Ch. 4.7 - If x=yz and y=2sin(y+z), find dx/dy and d2x/dy2.Ch. 4.7 - IfP=rcostandrsint2ter=0,finddP/dt.Ch. 4.7 - Ifz=xeyandx=cosht,y=coss,findz/sandz/t.Ch. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - If x=rcos and y=rsin, find (y/)r and (y/)x. Also...Ch. 4.7 - If xs2+yt2=1 and x2s+y2t=xy4, find...Ch. 4.7 - Verify (7.16) in three ways: (a) Differentiate...Ch. 4.7 - Prob. 10PCh. 4.7 - Finish Example 4 above, both for the general case...Ch. 4.7 - Ifw=x+ywithx3+xy+y3=sandx2y+xy2=t,findw/s,w/t.Ch. 4.7 - Prob. 13PCh. 4.7 - Ifu=x2+y2+xyzandx4+y4+z4=2x2y2z2+10, find (u/x)z...Ch. 4.7 - Prob. 15PCh. 4.7 - Let w=x2+xy+z2 (a) If x3+x=3t,y4+y=4t,z5+z=5t,...Ch. 4.7 - ...Ch. 4.7 - Ifm=a+bandn=a2+b2find(b/m)nand(m/b)a.Ch. 4.7 - Prob. 19PCh. 4.7 - Prob. 20PCh. 4.7 - Prob. 21PCh. 4.7 - If w=f(ax+by), show that bwxawy=0. Hint: Let...Ch. 4.7 - Prob. 23PCh. 4.7 - Prob. 24PCh. 4.7 - The formulas of this problem are useful in...Ch. 4.7 - Given f(x,y,z)=0 and g(x,y,z)=0, find a formula...Ch. 4.7 - Given u(x,y) and y(x,z), show that uxz=uxy+uyxyxz.Ch. 4.7 - Prob. 28PCh. 4.8 - Use the Taylor series about x=a to verify the...Ch. 4.8 - Using the two-variable Taylor series [say ( 2.7)]...Ch. 4.8 - Use the facts stated in Problem 2 to find the...Ch. 4.8 - Use the facts stated in Problem 2 to find the...Ch. 4.8 - Use the facts stated in Problem 2 to find the...Ch. 4.8 - Use the facts stated in Problem 2 to find the...Ch. 4.8 - Given z=yx2y2x2, show that z has neither a maximum...Ch. 4.8 - A roof gutter is to be made from a long strip of...Ch. 4.8 - An aquarium with rectangular sides and bottom (and...Ch. 4.8 - Repeat Problem 9 if the bottom is to be three...Ch. 4.8 - Find the most economical proportions for a tent as...Ch. 4.8 - Find the shortest distance from the origin to the...Ch. 4.8 - Given particles of masses m, 2m, and 3m at the...Ch. 4.8 - Repeat Problem 13 for masses m1,m2,m3 at...Ch. 4.8 - Find the point on the line through (1,0,0) and...Ch. 4.8 - To find the best straight line fit to a set of...Ch. 4.8 - Repeat Problem 16 for each of the following sets...Ch. 4.9 - What proportions will maximize the area shown in...Ch. 4.9 - What proportions will maximize the volume of a...Ch. 4.9 - Find the largest rectangular parallelepiped (box)...Ch. 4.9 - Find the largest box (with faces parallel to the...Ch. 4.9 - Find the point on 2x+3y+z11=0 for which 4x2+y2+z2...Ch. 4.9 - Prob. 6PCh. 4.9 - Repeat Problem 6 if the plane is ax+by+cz=d. A box...Ch. 4.9 - A point moves in the (x,y) plane on the line...Ch. 4.9 - Find the largest triangle that can be inscribed in...Ch. 4.9 - Complete Example 4 above.Ch. 4.9 - Find the shortest distance from the origin to the...Ch. 4.9 - Find the right triangular prism of given volume...Ch. 4.10 - Find the shortest distance from the origin to...Ch. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Find the shortest distance from the origin to each...Ch. 4.10 - Find the shortest distance from the origin to each...Ch. 4.10 - Find the shortest distance from the origin to each...Ch. 4.10 - Prob. 7PCh. 4.10 - If the temperature at the point (x,y,z) is T=xyz,...Ch. 4.10 - The temperature T of the disk x2+y21 is given by...Ch. 4.10 - The temperature at a point (x,y,z) in the ball...Ch. 4.10 - The temperature of a rectangular plate bounded by...Ch. 4.10 - Find the largest and smallest values of the sum of...Ch. 4.10 - Find the largest and smallest values of the sum of...Ch. 4.10 - Do Example 3b using Lagrange multipliers.Ch. 4.11 - In the partial differential equation...Ch. 4.11 - As in Problem 1, solve 22zx2+2zxy102zy2=0 by...Ch. 4.11 - Prob. 3PCh. 4.11 - Verify the chain rule formulas Fx=Frrx+Fx, and...Ch. 4.11 - Solve equations (11.11) to get equations (11.12)....Ch. 4.11 - Reduce the equation x2d2ydx2+2xdydx5y=0 to a...Ch. 4.11 - Change the independent variable from x to by...Ch. 4.11 - Change the independent variable from x to u=2x in...Ch. 4.11 - If x=escost,y=essint, show that...Ch. 4.11 - Given du=Tdspdv, find a Legendre transformation...Ch. 4.11 - Given L(q,q) such that dL=pdq+pdq, find H(p,q) so...Ch. 4.11 - Using du in Problem 10, and the text method of...Ch. 4.11 - As in Problem 12, find three more Maxwell...Ch. 4.12 - Ify=0xsint2dt,finddy/dx.Ch. 4.12 - If s=uv1ettdt, find s/v and s/u and also their...Ch. 4.12 - If z=ainxcosxsinttdt, find dzdx.Ch. 4.12 - Use L'HĂ´pitals rule to evaluate...Ch. 4.12 - If u=xyxsinttdt, find ux,uy, and yx at x=/2,y=....Ch. 4.12 - Ifw=xy2x3ydulnu,findwx,wy,andyxatx=3,y=1.Ch. 4.12 - Ifuvet2dt=xanduv=y,finduxy,uy,andyxuatu=2,v=0.Ch. 4.12 - If0xes2ds=u,finddxdu.Ch. 4.12 - If y=0sinxtdt, find dy/dx (a) by evaluating the...Ch. 4.12 - Find dy/dx explicitly if y=01exu1udu.Ch. 4.12 - Find ddx3xx2(xt)dt by evaluating the integral...Ch. 4.12 - Findddxxx2duln(x+u).Ch. 4.12 - Findddx1/x2/xsinxttdt.Ch. 4.12 - Given that 0dxy2+x2=2y, differentiate with respect...Ch. 4.12 - Given that 0eaxsinkxdx=ka2+k2 differentiate with...Ch. 4.12 - In kinetic theory we have to evaluate integrals of...Ch. 4.12 - Complete Example 4 to obtain (12.10)....Ch. 4.12 - Showthatu(x,y)=yf(t)dt(xt)2+y2satisfiesuxx+uyy=0.Ch. 4.12 - Showthaty=0xf(u)sin(xu)dusatisfiesy+y=f(x).Ch. 4.12 - (a) Show that y=0xf(xt)dt satisfies (dy/dx)=f(x)....Ch. 4.13 - Prob. 1MPCh. 4.13 - (a) Given the point (2,1) in the (x,y) plane and...Ch. 4.13 - In Problems 3 to 6, assume that x, y and r, are...Ch. 4.13 - In Problems 3 to 6, assume that x,y and r, are...Ch. 4.13 - In Problems 3 to 6, assume that x, y and r, are...Ch. 4.13 - In Problems 3 to 6, assume that x, y and r, are...Ch. 4.13 - About how much (in percent) does an error of 1 in...Ch. 4.13 - Assume that the earth is a perfect sphere. Suppose...Ch. 4.13 - Ifz=xyand2x3+2y3=3t2,finddz/dt3x2+3y2=6t.Ch. 4.13 - Ifw=(rcos)rsin,findw/.Ch. 4.13 - If x2a2+y2b2=1, find dydx and d2ydx2 by implicit...Ch. 4.13 - Prob. 12MPCh. 4.13 - ...Ch. 4.13 - If w=f(x,s,t),s=2x+y,t=2xy, find (w/x)y in terms...Ch. 4.13 - Prob. 15MPCh. 4.13 - Ifz=1xfyx,provethatxzx+yzy+z=0.Ch. 4.13 - Find the shortest distance from the origin to the...Ch. 4.13 - Find the shortest distance from the origin to the...Ch. 4.13 - Find by the Lagrange multiplier method the largest...Ch. 4.13 - Find the largest and smallest values of...Ch. 4.13 - Find the hottest and coldest points on a bar of...Ch. 4.13 - Find the hottest and coldest points of the region...Ch. 4.13 - Findddt0sintsin1xxdx.Ch. 4.13 - Findddxt=1/xt=2/xcoshxttdt.Ch. 4.13 - Findddx11/xexttdt.Ch. 4.13 - Findddx0x2sinxttdt.Ch. 4.13 - Showthatddxcosxsinx1t2dt=1.Ch. 4.13 - In discussing the velocity distribution of...Ch. 4.13 - The time dependent temperature at a point of a...Ch. 4.13 - Evaluated2dx20x0xf(s,t)dsdt.
Additional Math Textbook Solutions
Find more solutions based on key concepts
Show that the mean, variance, and mgf of the uniform distribution are as given in this section. Also verify tha...
Probability And Statistical Inference (10th Edition)
To make a table showing the number of people that will have received the letter after 1,2,3,4 stages.
Pre-Algebra Student Edition
The equivalent expression of x(y+z) by using the commutative property.
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
CHECK POINT I You deposit $1000 in a saving account at a bank that has a rate of 4%. a. Find the amount, A, of ...
Thinking Mathematically (6th Edition)
A Bloomberg Businessweek subscriber study asked, In the past 12 months, when travelling for business, what type...
STATISTICS F/BUSINESS+ECONOMICS-TEXT
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
- Homework Let X1, X2, Xn be a random sample from f(x;0) where f(x; 0) = (-), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep. -arrow_forwardHomework Let X1, X2, Xn be a random sample from f(x; 0) where f(x; 0) = e−(2-0), 0 < x < ∞,0 € R Using Basu's theorem, show that Y = min{X} and Z =Σ(XY) are indep.arrow_forwardrmine the immediate settlement for points A and B shown in figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth of foundation (DF-0), thickness of layer below footing (H)=20m. 4m B 2m 2m A 2m + 2m 4marrow_forward
- 2 Q /showthat Z +4 Z(Z-21) has aɣemovable discontinuity at z = 21.arrow_forward13.4. Let f(z) =y-x-3ir² and y be given by the line segment z = 0 to z 1+i. Evaluate. L f(z)dz.arrow_forwardenter | Infinite Camp ilc 8.3 End-of-Unit Assessment, Op x Pride is the Devil - Google Drive x + 2 sdphiladelphia.ilclassroom.com/assignments/7FQ5923/lesson?card=806642 3 Problem 2 A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines l, j, m, and d over the course of a month. Which line represents an artist whose downloads remained constant over the month? Select the correct choice. = Sidebar Tools M 45 song downloads days d 1 2 3 4 5 6 7 8 00 8 m l RA 9 > КУ Fullscreen G Save & Exit De ☆arrow_forward
- Q/Determine the set of points at which - f(z) = 622 2≥ - 4i/z12 i and differentiable analytice is:arrow_forwardsy = f(x) + + + + + + + + + X 3 4 5 7 8 9 The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem and the Mean Value Theorem for f on the closed interval [0, 9] ? (A A B B C Darrow_forward= Q6 What will be the allowable bearing capacity of sand having p = 37° and ydry 19 kN/m³ for (i) 1.5 m strip foundation (ii) 1.5 m x 1.5 m square footing and (iii)1.5m x 2m rectangular footing. The footings are placed at a depth of 1.5 m below ground level. Assume F, = 2.5. Use Terzaghi's equations. 0 Ne Na Ny 35 57.8 41.4 42.4 40 95.7 81.3 100.4arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
08 - Conic Sections - Hyperbolas, Part 1 (Graphing, Asymptotes, Hyperbola Equation, Focus); Author: Math and Science;https://www.youtube.com/watch?v=Ryj0DcdGPXo;License: Standard YouTube License, CC-BY