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 4.1, Problem 3P
If
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For each of the following series, determine whether the absolute convergence series test
determines absolute convergence or fails. For the ¿th series, if the test is inconclusive then let
Mi = 4, while if the test determines absolute convergence let Mi
1 :
2:
∞
Σ(−1)"+¹ sin(2n);
n=1
Σ
n=1
Σ
((−1)”.
COS
n²
3+2n4
3: (+
4:
5 :
n=1
∞
n
2+5n3
ПП
n²
2 5+2n3
пп
n²
Σ(+)+
n=1
∞
n=1
COS
4
2 3+8n3
П
ηπ
n-
(−1)+1 sin (+727) 5 + 2m³
4
= 8.
Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M) + sin(M5) is
-0.027
-0.621
-1.794
-1.132
-1.498
-4.355
-2.000
2.716
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.
i need help with this question i tried by myself and so i am uploadding the question to be quided with step by step solution and please do not use chat gpt i am trying to learn thank you.
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
If you multiply an odd number by 2 and add 1, is your answer even or odd?
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
CHECK POINT 1 In a survey on musical tastes, respondents were asked: Do you listed to classical music? Do you l...
Thinking Mathematically (6th Edition)
have tocalculate the perimeter of the given figure.
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)
Fill in each blank so that the resulting statement is true. If n is a counting number, bn, read ______, indicat...
College Algebra (7th 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
- Class, the class silues, and the class notes, whether the series does alternate and the absolute values of the terms decrease), and if the test does apply, determine whether the series converges or diverges. For the ith series, if the test does not apply the let Mi = 2, while if the test determines divergence then M¿ = 4, and if it determines convergence then M¿ = 8. 1: 2: 3 : 4: 5 : ∞ n=1 ∞ (−1)n+1. Σ(-1) +1 n=1 ∞ п 3m² +2 Σ(-1)+1 sin(2n). n=1 ∞ 2n² + 2n +3 4n2 +6 1 e-n + n² 3n23n+1 9n² +3 In(n + 1) 2n+1 Σ(-1) +1 n=1 ∞ Σ(-1)". n=1 Then the value of cos(M₁) + cos(2M2) + cos(3M3) + sin(2M4) + sin(M5) is 1.715 0.902 0.930 -1.647 -0.057 ● 2.013 1.141 4.274arrow_forward3. FCX14) = x²+3xx-y3 +.arrow_forwardBH is tangent to circle A and DF is a diameter. I don't know where to go from here. May you help please?arrow_forward
- A cylindrical chemical storage tank with a capacity of 950m3 is going to be constructed in a warehouse that is 11m by 14m with a height of 10m. The specifications call for the case to be made of sheet metal that costs $90/m2, the top to be made from sheet metal that costs $45/m2 and the wall to be made of sheet metal that costs $80/m2. If you want to minimize the cost to make the storage house, how much would you end up spending to build the tank?arrow_forwardCalculate the max value of the directional derivatearrow_forwardselect bmw stock. you can assume the price of the stockarrow_forward
- This problem is based on the fundamental option pricing formula for the continuous-time model developed in class, namely the value at time 0 of an option with maturity T and payoff F is given by: We consider the two options below: Fo= -rT = e Eq[F]. 1 A. An option with which you must buy a share of stock at expiration T = 1 for strike price K = So. B. An option with which you must buy a share of stock at expiration T = 1 for strike price K given by T K = T St dt. (Note that both options can have negative payoffs.) We use the continuous-time Black- Scholes model to price these options. Assume that the interest rate on the money market is r. (a) Using the fundamental option pricing formula, find the price of option A. (Hint: use the martingale properties developed in the lectures for the stock price process in order to calculate the expectations.) (b) Using the fundamental option pricing formula, find the price of option B. (c) Assuming the interest rate is very small (r ~0), use Taylor…arrow_forwardQuestion 1. Prove that the function f(x) = 2; f: (2,3] → R, is not uniformly continuous on (2,3].arrow_forwardCalculus III May I please have the example, definition semicolons, and all blanks completed and solved? Thank you so much,arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Quadrilaterals: Missing Angles and Sides; Author: rhornfeck;https://www.youtube.com/watch?v=knVj1O0L2TM;License: Standard YouTube License, CC-BY
STD IX | State Board | Types of Quadrilateral; Author: Robomate;https://www.youtube.com/watch?v=wh0KQ4UB0EU;License: Standard YouTube License, CC-BY