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Carr G.S. — Formulas and Theorems in Pure Mathematics

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Название: Formulas and Theorems in Pure Mathematics

Автор: Carr G.S.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Second Edition

Год издания: 1970

Количество страниц: 988

Добавлена в каталог: 07.05.2008

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Предметный указатель

Numbers, prime to and < the product of the first n primes      A.66
Numbers, prime to the radix having multiples made up of repeating digits      Me.76
Numbers, prime with respect to a given ar.p      C.54
Numbers, products of divisors of      Q.20
Numbers, quadratic forms of      Mem.53
Numbers, rational linear functions taken with respect to a prime modulus, and connected substitutions      C.48
Numbers, relation of the theory to i.c      C.82
Numbers, representation of by forms      C.92
Numbers, representation of by infinite products      A.1
Numbers, square having prime factors of the form 4n+1      N.78
Numbers, squares of      J.84 M.13 Pr.6 7
Numbers, squares of, three in ar.p      N.62
Numbers, sum and difference of two squares      thsN.63
Numbers, sums depending upon E(x)      L.60
Numbers, sums of digits      Me.66 TE.16
Numbers, sums of divisors      377 Ac.6 G.7 L.63 Mel.2 Mem.50
Numbers, sums of powers of      276 2939 An.61 65 thCD.5 Me.75 N.42 56 70 Q.8 see
Numbers, sums of powers of 4th powers      A.54
Numbers, sums of powers of cubes      An.65 L.66
Numbers, sums of powers of n primes      N.79
Numbers, sums of powers of squares      A.67
Numbers, sums of powers of the odd nos.      A.64
Numbers, sums of powers of uneven orders      Mo.57
Numbers, symmetrical functions of      Q.7
Numbers, systems      Z.14
Numbers, systems, history of, by Humboldt      J.4
Numbers, theorems      A.7 10 20 49 An.70 C.25 43 83 CM.2 G.8 L.48 52 N.75
Numbers, theorems on $(n+1)^{m}-n^{m}$       N.44
Numbers, theorems on $2^{n} \pm 1$       N.85 86 Me.78
Numbers, theorems on $n^{r}-n(n-1)^{r}+$ , &c.      285 A.30
Numbers, theorems on $P(m)+E(\frac{m}{m-1})P(1)+$       Q.3
Numbers, theorems on $\phi (a)+ \phi (a^{'})+$ , &c.=n, where a, a', &c., are the divisors of n      Cm.3
Numbers, theorems on 2, 4, 8, and 16 squares      Q.17
Numbers, theorems on 2m positive numbers      N.43
Numbers, theorems on 4 squares      N.57
Numbers, theorems on an odd sum of 12 squares      L.60
Numbers, theorems on products of sums of squares      G.2
Numbers, theorems on the greatest product in whole numbers of given sums      J.57
Numbers, theorems, $p^{n}+q^{n}$ in terms of pq      N.75
Numbers, theorems, $p_{2}(n)$       L.69
Numbers, theorems, 2, biquadratic character of      C.57 66 L.59
Numbers, theorems, Cauchy's      gzC.53
Numbers, theorems, Eisenstein's      J.27 50 83 LM.7 Q.5 6
Numbers, theorems, Gauss's on $X=\frac{x^{p}-y^{p}}{x-y}$       C.98
Numbers, theorems, Lagrange's arithmetical      A.47
Numeration, ancient decimal      C.6 8
Numerical approximations      N.42 53
Numerical functions      L.57 Me.62
Numerical functions, simply periodic      AJ.1
Numerical functions, sums of, approximately      C.96
Numerical functions, which express for a negative determinant the number of classes of a quadratic form, one at least of whose extreme coefficients is odd      C.62
Obelisks      A.9 11
Oblique and osculating circle of a conic      G.22
Oblique, bevilled wheels, cn      J.2
Oblique, coordinates      4050 5511—5519 fN.54
Oblique, cyclic surface      TI.9
Octahedron function      Q.16
Octahedron, centroid of      LM.9
Octic equations      G.7 10
Octic equations and curves      M.15
Octic surface      G.13 M.4 Q.14
Operative or symbolic calculus      1483 3470—3628 AJ.4 C.17 G.20 J.5 59 LM.12 Me.82 85 P.37 44 60—63 Pr.10 11 12 13 Q.4 5 8
Operative or symbolic calculus on the symbols $x^{y}$ , $log_{b}x$ , sin x, cos x, $sin_{-1} x$ , $cos^{-1} x$       A.9 11
Operative or symbolic calculus, algebraic      TE.14
Operative or symbolic calculus, algebraic, $\pm$       CM.3
Operative or symbolic calculus, algebraic, ap. to geometry      CM.1 2
Operative or symbolic calculus, applications      G.19 Me.82
Operative or symbolic calculus, expansions      Pr.14
Operative or symbolic calculus, formulae      C.39
Operative or symbolic calculus, index symbol      1485 CD.6
Operative or symbolic calculus, integration      CD.3 exMe.76
Operative or symbolic calculus, representation of functions      C.43 CD.2
Operative or symbolic calculus, seminvariant operators      Q.20
Operative or symbolic calculus, theorems      A.57 CD.8 LM.11 Q.3 15 16
Operative or symbolic calculus, theorems, from $\pi \rho u - \rho \omega u=\rho u9$       CD.5
Operative or symbolic calculus, theorems, from Lagrange's series      Q.16
Operators, $^{2m+1}\surd \{ a\surd v\pm b\surd (wi)\}$ , &c.      C.96
Operators, $(d_{\theta}-m)^{-1}$ , &c.      3470—3485
Operators, $C(u,m)u_{n}/m!$       3514
Operators, $D^{n}f(xD)U$       E.36
Operators, $d_{x}$       1405
Operators, $e^{D+\frac{1}{x}}F(x)=\frac{x+1}{x}F(x+1)$       E.36
Operators, $e^{hd_{x}}$       1520—1521 Q.9
Operators, $e^{x+D}F(x)$ , &c.      E.34
Operators, $F(\pi)U and F^{-1}(\pi)U$       3509—3510
Operators, $\Omega F(a,x)$       Q.13
Operators, $\pi=xd_{x}+yd_{y}+\&c.$       3500
Operators, $\psi (d_{x}+y)\phi x=\phi (d_{y}+x)\psi y$       3498
Operators, $\{\phi (D)e^{\rho \theta}\}^{n}Q$       3491
Operators, D(D-1)...(D-n+1)      3489
Operators, expansions and formulae for $F(xd_{x})U$ , where $U=f(x)=a+bx+cx^{2}+$       3486
Operators, f(D)uv      3494
Operators, f(x+hD).1      E.39
Operators, gz of      3474 C.43
Operators, reduction of $F({\pi}_{1})$       3503
Operators, transformation of $Vd_{x}$ , $Ud_{x}...$ , &c      G.21
Operators, uf(D)v      3495
Orthocycle      Q.17
Orthogonal circle and conic      E.7
Orthogonal circles      4170 4182—4184
Orthogonal circles, of in- and circum-circles of a triangle      Q.18
Orthogonal conics      N.84
Orthogonal conics, families of      A.63
Orthogonal coordinates      C.60
Orthogonal coordinates, curvilinear      JP.26
Orthogonal curves      J.35 N.52 81
Orthogonal curves, system from logarithmic representation      Z.16
Orthogonal lines and conics      C.72
Orthogonal lines of a triangle      4633
Orthogonal projection      1087
Orthogonal projection in metrical projective geometry      GM.14
Orthogonal projection of a circle into an ellipse      A.2
Orthogonal projection of a triangle      E.30 31 36 37
Orthogonal substitution      J.67 M.13 Z.24
Orthogonal surfaces      C.29
Orthogonal surfaces and isothermal      C.84 JP.18 L.43 49
Orthogonal surfaces with elliptic coordinates      C.53 J.62
Orthogonal surfaces, cubic eq. for      C.76
Orthogonal surfaces, spheres      36 54 59 72 79 87 ths17 21 J.84 JP.17 L.43 44 46 47 63 N.51 P.73 Pr.21 Q.19
Orthogonal surfaces, systems      C.67 75 M.7
Orthogonal surfaces, systems, condition      J.83
Orthogonal surfaces, systems, parallel      M.24
Orthogonal surfaces, systems, quadric      J.76
Orthogonal surfaces, triple      A.55—58 An.63 77 85 C.alg58 67
Orthogonal surfaces, triple, cyclic      G.21 22 J.84
Orthogonal surfaces, triple, quartic      82 Z.23
Orthogonal trajectories      L.45 Me.80 Z.17
Orthogonal trajectories of a moveable plane      Pr.41
Orthogonal trajectories of a moveable sphere      C.42
Orthogonal trajectories of a surface      Mem.20
Orthogonal trajectories of circles      Me.85
Orthogonal trajectories of circular sections of an ellipsoid      L.47
Orthogonal, coefficient system      A.2 61
Orthogonals, algebraic system of      C.69
Orthomorphic projection of an ellipsoid on a sphere      AJ.3
Orthomorphosis of a circle into a parabola      Q.20
Orthoptic lines of a conic      A.57
Orthoptic surface of a quadric      J.50
Orthoptic, loci of      LM.13 Pr.37
Orthoptic, loci of, of 3 tangs. to a quadric      E.40
Orthotomic circles      Me.64 66 Q.2
Osculating circle      5724 L.39
Osculating circle of a family of curves      N.70
Osculating circle of a parabola, ths      N.66
Osculating circle of conics      A.70 N.60
Osculating circle of quadric curves      N.43
Osculating circle of tortuous curves      N.81
Osculating cone      5727
Osculating cone, angle of      5752
Osculating conic      L.39

Osculating conic, of a cubic curve      J.68 Z.17
Osculating conic, triply      A.69 Z.19
Osculating curves      Q.11
Osculating helix      N.71
Osculating line of a surface      C.82 J.81
Osculating parabola      N.81
Osculating paraboloid      JP.15 N.82
Osculating paraboloid of a quadric      L.38
Osculating plane      5721
Osculating plane and radii of curv. at a multiple point of a gauche curve      An.71 C.68
Osculating plane of a tortuous curve      C.96 J.41 63
Osculating plane, eq      5733
Osculating sphere      Mem.20 N.70
Osculating sphere of curve of intersection of two surfaces, cn      C.83
Osculating sphere of two curves having a common principal normal      LM.16
Osculating surfaces      C.79
Osculating surfaces of quadrics      N.60
Osculating surfaces, degree of 98      L.41 80
Oval of Cassini      see "Cassinian oval"
Oval of Descartes      see "Cartesian oval"
P.D.E., any order      No.73 C.80 89 M.11 13
P.D.E., any order and ap. to physics      JP.13
P.D.E., any order and elliptic functions      J.36
P.D.E., any order and elliptic functions, hyper-ell.      J.99
P.D.E., any order of cylinders      Me.77
P.D.E., any order of dynamics      C.5 J.47
P.D.E., any order of heat      L.48
P.D.E., any order of heat, of sound      L.38
P.D.E., any order of Laplace      G.23
P.D.E., any order of orthogonal systems of surfaces      Ac.4 C.77
P.D.E., any order of physics      L.72 47
P.D.E., any order with periodical coefficients      C.29
P.D.E., any order, $x^{\frac{n}{2}}z_{nx}=z_{ny}$       Z.7
P.D.E., any order, any number of functions and independent variables      C.80
P.D.E., any order, Hamiltonian      M.23 Z.11
P.D.E., any order, integrated in series      C.15 16
P.D.E., any order, integration by definite integrals      An.59 C.94 L.54
P.D.E., any order, linear      An.77 C.13 90 CD.9 CM.2 J.69 JP.12 L.39
P.D.E., any order, two independent variables      C.75 CP.8
P.D.E., first order      3399—3410 A.33 tr50 An.55 69 C.14 53 54 CD.7 CM.12 J.2 17 trJP.22 L.75 M.9 11 th20 Z.22
P.D.E., first order and Poisson's function      C.91
P.D.E., first order, $(1+P_{1}+...+P_{n})(d_{x},d_{y})^{n}Z=Q$       Z.13
P.D.E., first order, $x^{a}y^{b}z^{c}p^{m}q^{n}=A$       CM.1
P.D.E., first order, 3 variables      J.64
P.D.E., first order, complete primitive connected with any solution      3405
P.D.E., first order, derivation of a singular solution from the differential equation      3403
P.D.E., first order, derivation of the general primitive and singular solution from the complete primitive      3401
P.D.E., first order, integration by Abelian functions      C.94
P.D.E., first order, integration by Cauchy's method      C.81
P.D.E., first order, integration by Charpit's method      3399
P.D.E., first order, integration by Jacobi — Hamilton method      M.3
P.D.E., first order, integration by Jacobi's first method      C.79 82
P.D.E., first order, integration by Jacobi's first method and ap. to Pfaff's pr      J.59
P.D.E., first order, integration by Lie's method      M.6 8
P.D.E., first order, integration by Weiler's method      M.9
P.D.E., first order, law of reciprocity      3446
P.D.E., first order, linear      3381—3395
P.D.E., first order, linear, $(x-a)z_{x}+(y-b)z_{y}=c-z$       3392
P.D.E., first order, linear, $a(yu_{z}-zu_{y}) + b(zu_{x}-xu_{z})+c(xu_{y}-yu{x})=1$       Q.8
P.D.E., first order, linear, $Pt_{x}+Qt_{y}+...+Rt_{z}=S$       3387
P.D.E., first order, linear, $Pz_{x}+Qz_{y}=R$       3383
P.D.E., first order, linear, $Pz_{x}+Qz_{y}=R$ , extension to n variables      3384
P.D.E., first order, linear, $u=v_{y}$ and $u_{y}=-v_{x}$       J.70
P.D.E., first order, linear, $x^{2}+y^{2}+z^{2}=2ax$       3393
P.D.E., first order, linear, $z_{x}=\frac{y}{\surd (y^{2}-x^{2})}$ ; $z_{xy}=x^{2}+y^{2}$       3390—3391
P.D.E., first order, linear, L(px + qy - z) - Mp - Nq + R=0      C.83
P.D.E., first order, linear, reduction to      C.15 J.81 Me.78
P.D.E., first order, linear, simultaneous      3396—3397
P.D.E., first order, linear, simultaneous, ex.      3398 J.81
P.D.E., first order, n variables      3409 A.22 J.60 LM.10 11
P.D.E., first order, n variables with constant coefficients      Mel.5
P.D.E., first order, n variables, integration by calc. of variations      C.14
P.D.E., first order, simultaneous      C.68 76 L.79 M.4 5
P.D.E., first order, singular solution      3401—3403 J.66
P.D.E., first order, systems of      A.56 M.11 17
P.D.E., first order, theorem of Jacobi      C.45
P.D.E., first order, with a general first integral      Me.78
P.D.E., first order, z=px+qy+F(p,q)      Z.5
P.D.E., fourth order $\triangle \triangle u=0$       C.69
P.D.E., second order      3420—3445 A.33 C.54 70 78 98 JP.tr22 L.72 M.15 Me.76 77 Mel.3 N.83 P.46
P.D.E., second order, $(ax+by+c)s+a\lambda q+b\mu p=0$       A.33
P.D.E., second order, $(x+y)^{2}s+a(x+y)p+b(x+y)q+cz=0$       A.33 38
P.D.E., second order, $(\log z)_{xy}+az=0$       C.36
P.D.E., second order, $4s^{2}+(r-t)^{2}=4k^{2}$ approx. integn.      C.74
P.D.E., second order, $As+Bq+\Psi(r, p, q, x, y, z)=0$       C.93
P.D.E., second order, $au_{x}+bu_{y}+cu_{z}=xyz$ , &c.      3554
P.D.E., second order, $a^{2}(u_{2x}+u_{2y}+u_{2z})=u_{2t}$       3629 C.7 LM.7
P.D.E., second order, $a^{2}d_{xy}\log \lambda \pm \lambda=0$       L.53
P.D.E., second order, $d_{x}(p \sin{x})+t+n(n+1)z \sin^{2}{x}=0$       L.46
P.D.E., second order, $d_{x}(px)+d_{y}(qx)=0$       Z.28
P.D.E., second order, $P=(rt-s^{2})^{n}Q$ , Poisson's eq.      3441
P.D.E., second order, $q^{2}r-A^{2}t+\frac{A^{2}}{\eta}\eta_{y}q=0$       E.22
P.D.E., second order, $r(1+q^{2})=t(1+p^{2})$       J.58
P.D.E., second order, $r+t+k^{2}z=0$       M.1
P.D.E., second order, $r-a^{2}t=0$       3433
P.D.E., second order, $r-a^{2}t=\phi (x,y)$ , &c.      3565
P.D.E., second order, $r-a^{2}y^{2b}t=0$       E.27 28
P.D.E., second order, $r=q^{2m}t$       C.98
P.D.E., second order, $Rr+Ss+Tt+U(rt-s^{2})=V$       3424 3434—3440 J.61
P.D.E., second order, $rt-s^{2}$       geoQ.2
P.D.E., second order, $s=\frac{2f^{'}(x)F^{'}(y)}{\{f(x)+F(y)\}^{2}}z$       C.81
P.D.E., second order, $u_{2t}=R_{r}\frac{u}{r}$ where $t=\int \frac{r dr}{\surd (2Rr^{2}+A^{2})}$       L.38
P.D.E., second order, $u_{2x}+u_{2y}+u_{2z}=0$       3551 3626 J.36 Mo.78 see
P.D.E., second order, $u_{x}+u_{y}+u_{z}=xyz$       3552
P.D.E., second order, $x(r-a^{2}t)=2np$       E.13
P.D.E., second order, $xu_{2x}+au_{x}-q^{2}xu=0$       3618
P.D.E., second order, $z^{2}(zs-pq)^{2}+q=F(y)$       A.70
P.D.E., second order, (1+r)t+(1+t)r-2pqs=0      An.53
P.D.E., second order, construction of explicitly integrable equations of the form $s=z\lambda (x,y)$       JP.28
P.D.E., second order, in 4 and 5 variables      Mem.13
P.D.E., second order, in two independent variables      trA.54 trNo.81 C.92
P.D.E., second order, in two independent variables, transf. of      97 M.24
P.D.E., second order, integration by change of variables      C.74
P.D.E., second order, q(1+q)r+p(1+p)t-(p+q+2pq)s=0      3432
P.D.E., second order, r+t=0      A.2 CM.1 J.59 73 74 L.43
P.D.E., second order, r=q      J.72
P.D.E., second order, Rr+Ss+Tt+Pp+Qq+Zz=U      3442
P.D.E., second order, Rr+Ss+Tt=V, Monge's method      3423 CM.3 N.76 Q.6
P.D.E., second order, s+ap+bq+abz=V      3444
P.D.E., second order, s+Pp+Qq+Z=0      Me.76
P.D.E., second order, transf. of      C.97
P.D.E., simultaneous      C.92 th78 LM.9 M.23 Z.20
P.D.E., simultaneous, linear      J.65
P.D.E., system of      C.13 74 81
P.D.E., system of, $Az_{nt}+(d_{2x}+d_{2y}+...)^{n}z=0$       C.94
P.D.E., system of, $a^{m}z_{mt}=x^{2m}x_{mx}$       A.30 31
P.D.E., system of, $z_{nx}=x^{m}z_{(m+n)y}+F_{1}(y)+xF_{2}(y)+...+x^{m-1}F_{m}(y)$       A.51
P.D.E., system of, dz=Hdx+Kdy+Ldp+Mdq+Ndr+ &c.      J.14
P.D.E., third order, two independent variables      LM.8 N.83
Pangeometry      G.5 15
Pantograph      5423 Mem.31 TE.13
Paper currency      A.42
Pappus, prs in plane geometry      A.38 Z.5
Parabola anal.      4200—4239 eqCM.2 N.42 54 70
Parabola anal., geo      CM.4 Me.71 cn1249 thsN.60 63 71 76 80
Parabola and right line      see "Right line"
Parabola geo.      1220—1244
Parabola in space      A.3
Parabola, chords of      1239 4224
Parabola, chords of, two intersecting      1242
Parabola, circle of curvature of      1260 A.61
Parabola, circum-hexagon and triangle      CM.1
Parabola, determination of vertex and axis      N.58
Parabola, eq. deduced from eq. of ellipse      1219
Parabola, focal chord      4235—4239
Parabola, focus and directrix      N.49
Parabola, latus rectum      1222 Me.75
Parabola, normal, length of      4233—4234
Parabola, plane and spherical      A.60
Parabola, quadrature of      1244 A.32

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