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### Mathematic Methods HW Solutions 52

Course: MHF 2312, Fall 2011
School: UNF
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Word Count: 121

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10 9.18 9.19 9.20 9.21 52 Chapter r 1 e , r 1 e r , 3 2e , er cos e sin , 3 r 1 , r 3 , 0 2r1 , 6, 2r4 , k2 eikr cos 11.4 Vector 11.5 ds2 = du2 + h2 dv 2 , hu = 1, hv = u(2v v 2 )1/2 , v dA = u(2v v 2 )1/2 du dv, ds = eu du + hv ev dv , eu = i(1 v ) + j(2v v 2 )1/2 , ev = i(2v v 2 )1/2 + j(1 v ) au = = eu au , av = hv ev , av = ev /hv uv 2 V = = Fu v (2 v ) u uv 2 (v 1) V uv + 2uv = Fv + = u1...

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10 9.18 9.19 9.20 9.21 52 Chapter r 1 e , r 1 e r , 3 2e , er cos e sin , 3 r 1 , r 3 , 0 2r1 , 6, 2r4 , k2 eikr cos 11.4 Vector 11.5 ds2 = du2 + h2 dv 2 , hu = 1, hv = u(2v v 2 )1/2 , v dA = u(2v v 2 )1/2 du dv, ds = eu du + hv ev dv , eu = i(1 v ) + j(2v v 2 )1/2 , ev = i(2v v 2 )1/2 + j(1 v ) au = = eu au , av = hv ev , av = ev /hv uv 2 V = = Fu v (2 v ) u uv 2 (v 1) V uv + 2uv = Fv + = u1 [v (2 v )]1/2 1/2 v [v (2 v )] [v (2 v )]3/2 11.6 m u m 11.7 U = eu U /u + ev u1 v (2 v ) U /v V = u1 (uVu )/u + u1 v (2 v ) Vv /v U 1 1 U 2 u + 2 v (2 v ) U= v (2 v ) u u u u V V 11.8 u1 , u1 k, 0
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UNF - MHF - 2312
Chapter 113.23.53.83.113.143/232/35(5/3)1(4/3)3.33.63.93.123.159/1072(5/4)(2/3)/3(2/3)/417.12 B (5/2, 1/2) = 3/1617.33 B (1/3, 1/2)7.5 B (3, 3) = 1/3017.72 B (1/4, 1/2)7.10 4 B (1/3, 4/3)37.12 (8/3)B (5/3, 1/3) = 32 2 3/27
UNF - MHF - 2312
Chapter 115412.15 2 E 23 E12.14 12E 35 15.86=12.16 2 2 E 1/ 2 3.820=a12.23 T = 8 5g K 1/ 5 ; for small vibrations, T 2 2a=3g13.713.913.1113.1313.1513.1713.1913.2113.2213.24(4) = 3!3/22.4222E135 F arc sin 4 , 4/5 = 0.1834 sn u d
UNF - MHF - 2312
Chapter 121.11.31.51.71.9yyyyy2.1= a1 xex= a1 x= a0 cosh x + a1 sinh x= Ax + Bx3= a0 (1 x2 ) + a1 x3= a0 e x= a0 cos 2x + a1 sin 2x= (A + Bx)ex= a0 (1 + x) + a2 x22= (A + Bx)ex1.21.41.61.81.10yyyyySee Problem 5.32.4Q0 =
UNF - MHF - 2312
Chapter 125610.5 sin (35 cos3 15 cos )/210.4 sin 10.6 15 sin2 cos 11.111.311.511.611.711.811.911.10y = b0 cos x/x211.2 y = Ax3 + Bx332y = Ax + Bx11.4 y = Ax2 + Bx31/21/2y = A cos(2x ) + B sin(2x )y = Aex + Bx2/3 [1 3x/5 + (3x)2 /(5 8
UNF - MHF - 2312
Chapter 1257= Ax + B x sinh1 x x2 + 1= A(1 + x) + Bxe1/x22= A(1 x ) + B (1 + x )exx= Ax Be= A(x 1) + B [(x 1) ln x 4]= A x + B [ x ln x + x]xx= A 1x + B [ 1x ln x + 1+x ]2= A(x2 + 2x) + B [(x2 + 2x) ln x + 1 + 5x x3 /6 + x4 /72 + ]= Ax2 +
UNF - MHF - 2312
Chapter 132.1T=2.2T=2.32.42.7T=nx(1)n+1 ny/10esinn101200 41odd nn22even n22n=2+4knx 1 ny/20sinen20neny sin nx1x 1 3y/30120 y/303x1 5y/305xesinesin+esin2309302530n4sinh n(1 y ) sin nxT= 2 (n2 1) sinh
UNF - MHF - 2312
Chapter 13592.14 For f (x) = x 5: T = 4021odd nnx ny/101cose2n10For f (x) = x: Add 5 to the answer just given.2.15 For f (x) = 100, T = 100 10y/3401For f (x) = x, T = (30 y) 263.23.33.43.53.63.7u=4001odd nu = 100 u=40 1od
UNF - MHF - 2312
Chapter 134.64.74.8y=y=y=604hl2 v9hl3 v4l2 v4.91odd n1nnwnxnvt1sinsinsinsin2n2lllnnxnvt1sinsinsinn33ll1sin(n/2)xvt2x2vtnxnvtsinsin+sinsinsinsin3ll16lln(n2 4)lln=31. n = 1, = v/(2l)2. n
UNF - MHF - 2312
Chapter 136116, n odd, the six solutions on (0, ) aren (4 n2 )1. T = bn eny sin nxbnsinh n(H y ) sin nx2. T =sinh nH23. u =bn e(n) t sin nxh 2 n24. =bn sin nx eiEn t/h , En =2m5. y = bn sin nx cos nvtbn6. y =sin nx sin nvtnv12(1)n+1
UNF - MHF - 2312
Chapter 135.14 u =6250 ln r200+ln 2o dd nln r5.15 u = 50 1 ln 2r n r nsin nn(2n 2n )200o dd nn (2n1 2 n )r2nr2nsin n6.2The rst six frequencies are 10 , 11 = 1.59310 , 12 = 2.1351020 = 2.29510 , 13 = 2.65210 , 21 = 2.91710.6.4
UNF - MHF - 2312
Chapter 136322227.21 n (x) = e (x +y +z )/2 Hnx (x)Hny (y )Hnz (z ), = m/ ,h1113En = (nx + 2 + ny + 2 + nz + 2 ) = (n + 2 ) .hh(n + 2)(n + 1), n = 0 to .Degree of degeneracy of En is C (n + 2, n) =2M e4+12r7.22 (r, , ) = R(r)Ylm (, )
UNF - MHF - 2312
Chapter 1310.12 u =40064o dd n1rna2nsin 2n10.14 Same as 9.1210.15 u =1rn 104006nsin 6n =2(10r)6 sin 6200arc tan1012 r12o dd n10.16 v 5/(2 )10.17 mn , n = 0; the lowest frequencies are:11 = 1.5910 , 12 = 2.1410 , 13 = 2.6510, 21 = 2.
UNF - MHF - 2312
Chapter 141.11.31.51.71.81.91.101.111.121.131.151.171.181.191.201.21u = x3 3xy2 , v = 3x2 y y 31.2 u = x, v = yu = x, v = y1.4 u = (x2 + y 2 )1/2 , v = 0u = x, v = 01.6 u = ex cos y , v = ex sin yu = cos y cosh x, v = sin y sinh xu
UNF - MHF - 2312
Chapter 143.13.53.93.123.173.203.236612+i11(a) 5 (1 + 2i)3(a) 0(a) 072i3.2 (2 + i)/33.6 1, 13.10 (2i 1)e2i(b) 1 (8i + 13)3(b) i(b) 17i/43.24 17i/963.3 03.7 (1 i)/83.11 2i3.43.8i/2i/23.18 i 63/3.22 i 3/1083.16 03.19 16
UNF - MHF - 2312
Chapter 14676.286.306.326.346.146.186.226.266.276.316.3511R(3i) = 16 + 24 i6.29R(0) = 1/6!6.31R(2i) = 3ie2 /326.33R(0) = 7, R(1/2) = 76.35 i/46.15 06.1606.19 06.2006.23 sinh 2 6.2433 2 i(1 + cosh 3 + i 3 sinh 3 )316.29
UNF - MHF - 2312
Chapter 146810.4 T = 200 1 arc tan(y/x)10.5 V = 200 1 arc tan(y/x)2210.6 T = 100y/(x + y ); isothermals y/(x2 + y 2 ) = const.;ow lines x/(x2 + y 2 ) = const.10.7 Streamlines xy = const.; = (x2 y 2 )V0 , = 2xyV0 , V = (2ix 2jy )V010.9 Streamlines
UNF - MHF - 2312
Chapter 151.11.31.51.71.91/10, 1/91/3, 5/91/4, 3/4, 1/3, 1/29/26, 1/2, 1/133/10, 1/31.21.41.61.81.103/8, 1/8, 1/41/2, 1/52, 2/13, 7/1327/52, 16/52, 15/529/100, 1/10, 3/100, 1/103/82.122.142.152.17(a) 3/4(b) 1/5(c) 2/3(d) 3/4(e
UNF - MHF - 2312
Chapter 15704.94.124.174.2125/102, 25/77, 49/101, 12/254.11 0.097, 0.37, 0.67; 1354.14 n!/nnMB: 16, FD: 6, BE: 104.18 MB: 125, FD: 10, BE: 35C (n + 2, n)4.22 0.1354.23 0.305.1 = 0, = 35.2 = 7, = 35/65.3 = 2, = 25.4 = 1, = 21/25.5 = 1, =
UNF - MHF - 2312
Chapter 159.3Number of particles:012345Number of intervals: 406 812 812 541 271 1089.4 P0 = 0.018, P1 = 0.073, P4 = 0.1959.5 P0 = 0.37, P1 = 0.37, P2 = 0.18, P3 = 0.069.6 Exactly 5: 64 days. Fewer than 5: 161 days. Exactly 10: 7 days. Moretha
Michigan State University - MUS - 212
Josh SawyerMUS 212: Music History since 1750Essay #1Classical EnlightenmentMusical eras are defined by the change of musical styles, composers, and compositionalinterpretation of music. Frequently, these changes are brought about by a change in music
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Josh SawyerDr. TattoTE 250 Sec. 16Thought paper based on 1/9/12Teaching IdentityIn this modern age of education, students are bombarded by a variety of external factors.A student is shaped by an ever increasing amount of positive and negative influe
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Josh SawyerTE 250- Section 161/18/12Cultural IdentificationWhen I entered college (and the realm of education) I had never given my personalculture any real thought. I have lived a pretty average, middle class life in suburban Detroit.However, key c
York University - ECON - 2400
Name: _ Date: _1. Which statement below best illustrates the art, rather than the science ofmacroeconomics?A) Macroeconomic data provide the motivation for new macroeconomic theory.B) Macroeconomic relationships can be expressed using symbols and equa
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Economics, Faculty of Liberal Arts &amp; Professional Studies, York UniversityFall 2011 Course OutlineCourse #: AP/ECON 2400 3.0 BFCOURSE TITLE: INTERMEDIATE MACROECONOMIC THEORY IFall 20111. Course Instructor Contact:Name: Dr Shadab QaiserOffice: 1078
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MATH 2131 3.00 MS2Assignment 3Total marks = 50Question 1: Let (X, Y ) have the joint pdffX,Y (x, y ) =ey , 0 &lt; x &lt; y &lt; ,0,otherwise.(a) (4 marks). Find E (XY ).(b) (6 marks). Find Cov(X, Y ).(c) (4 marks). Find X,Y .Question 2: Let X1 , . . . ,
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MATH 2131 3.00 MS2Assignment 4Total marks = 40Question 1: Let r.v. X have pdff (x) =2/x3 , x &gt; 1,0,otherwise.(a) (3 marks). Compute the rst two moments of X .(b) (1 mark). Except for the rst moment, what can you say about all theother moments of
York University - MATH - 2131
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York University - MATH - 2131
York University - MATH - 2131
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York University - MATH - 2131
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York University - MATH - 2131
MATH 2131 3.00 MS2Assignment 2Total marks = 40Question 1: Let X1 , X2 , . . . , X6 be a random sample on X wherefX (x) =1/x2 , x 1,0,otherwise.(a) (5 marks). Find the pdf of X(6) .(b) (5 marks). Find the pdf of X(3) .Question 2: Let (X, Y ) have
York University - MATH - 2131
MATH 2131 3.00 MS2Assignment 1Total marks = 40Question 1: Let (X, Y ) have the joint probability density functionfX,Y (x, y ) =cx/y 2 , y 1 &lt; x &lt; y,0,otherwise.1 &lt; y &lt; 2,(a) (4 marks). Find c such that fX,Y (x, y ) is a joint probability density
York University - ECON - 2350
York University - ECON - 2350
York University - ECON - 2350
York University - ECON - 2350
Price Discrimination Firm charges dierent prices to dierent consumers. Prices are tailored to extract greater surplus from consumers with greaterwillingness to pay and do not reect (only) cost dierences.Prerequisites for Price Discrimination Market
York University - ECON - 2350
The Assumptions of Perfect Competition1. Large Numbers: No individual consumer buys and no individual rm produces asignicant proportion of the total output.(No economies of scale at the rm level; minimum ecient scale is a small portion ofthe total amo
York University - ECON - 2350
York University - ECON2350 - V. BardisPractice Set 11. Find the aggregate demand function, X (p), if the demand of person 1 is given by x1 = 50 pand the demand of person 2 is given by x2 = 25 (1/2)p. Is any of the three demands moreelastic than the ot
York University - ECON - 2350
York University - ECON2350 - V. BardisAnswers to Practice Set 11.X (p) = x1 (p) + x2 (p) = (50 p) + (25 p/2) = 75 3p/2No; all three demands are equally elastic:Xp=x1 px2 p3pp=2 75 3p/250 p= (1)=pp=50 p50 p1pp=2 25 p/250 p2. (a)
York University - ECON - 2350
York University - ECON2350 - V. BardisPractice Set 21. Consider the economics of the following story. Tomorrow, Jerry can either work for his uncle forw dollars an hour or spend his time collecting owers from a forest nearby, which he can sell atthe m
York University - ECON - 2350
York University - ECON2350 - V. BardisAnswers to Practice Set 21. See notes.2. Letting b = 2 gives q = f (L) = a(L t)1/2 . Then Jerrys marginal product is1f (L) = a(L t)1/22Setting pf (L) = w gives Jerrys input demandL =ap2w2+tSubstituting L
York University - ECON - 2350
York University - ECON2350 - V. BardisPractice Set 31. Using the concepts of consumer and producer surplus argue that the equilibrium in a perfectlycompetitive market is ecient.2. Provide a set of assumptions that describes a perfectly competitive mar