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

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
Differential equations, simultaneous system of, Hamiltonian      Q.14
Differential equations, simultaneous system of, integration and inversion of the integrals      C.23
Differential equations, simultaneous system of, Jacobi's      CD.3
Differential equations, simultaneous system of, method of multipliers      3353
Differential equations, simultaneous system of, number of arbitrary constants      Me.77
Differential equations, simultaneous system of, reduction of order      3350
Differential equations, simultaneous system of, reduction to a P.D. eq      C.44
Differential equations, simultaneous system of, theorem analogous to Lagrange's in the Perturbation theory      L.51
Differential equations, simultaneous system of, theorem of a new multiplier      J.27
Differential equations, simultaneous system of, theorem of Abel      C.24
Differential equations, simultaneous system of, transformation and integration of      L.45
Differential equations, singular solution of      3169—3178 3301—3306 3401—3403 C.19 94 CM.2 JP.18 M.22 Man.83 84 Q.12 14
Differential equations, symbolic methods      3470—3636 CD.1 P.61 Q.3 17
Differential equations, symbolic methods to reduce a homog. eq. to the form $y_{nx}+qy=X$      3585
Differential equations, symbolic methods to transform $(a+bx+...)u_{nx}+(a^{'}+b^{'}x+...)u_{(n-1)x}+_{+}...&c.=Q$ into the symbolic form, and the converse      3571 3573
Differential equations, symbolic methods to transform $u+\phi (D) e^{r^{\theta}}u = U$      3579—3580
Differential equations, symbolic methods, $ax^{m}y_{mx}+bx^{n}y_{nx}+&c.=Q$      3531
Differential equations, symbolic methods, $ay{m\theta}+by_{n\theta}+&c.=Q$      3535
Differential equations, symbolic methods, $E(d_{\theta})u=Q$      3515
Differential equations, symbolic methods, $F(xd_{x}, yd_{y}, ...)u=\sum Ax^{m}y^{n}...$      3558
Differential equations, symbolic methods, $F(\pi)u=Q$      3541
Differential equations, symbolic methods, $u+\alpha_{1}\phi (D)e^{\theta}u+&c.=U$      3575
Differential equations, symbolic methods, $u_{2x}+\alpha^{2}u=Q$ and similar      3522
Differential equations, symbolic methods, $\alpha\pi_{1}^{m}z+b\pi_{1}^{n}z+&c.=u_{1}+u_{2}+&c.$      3540
Differential equations, symbolic methods, exceptional case of the inverse process      3526
Differential equations, symbolic methods, reduction of an integral of the nth order      3530
Differential equations, symbolic methods, Reduction to the form $(\Pi^{n}+A_{a}\Pi^{n-1}+...+A_{n})u=Q, where \Pi=Mdx+Ndy+&c.$      3546
Differential equations, synectic integrals of      C.40
Differential equations, transformation of      An.52 CD.9
Differential equations, transformation of, in curvilinear coords      J.85
Differential equations, whose integrals are satisfied by the periodicity modulus of elliptic integrals of the first kind      J.83
Differential equations, whose integrals satisfy relations of the form $F[\phi x]=\psi x Fx$      C.93
Differential expressions      1407 prAn.85
Differential expressions, algebraic      An.79
Differential expressions, algebraic, by homog. cords      M.9
Differential expressions, linear      J.85
Differential expressions, transf. of      J.85 Q.16 Mo.69
Differential formulae, theory of      L.52
Differential functions, theory of      C.60
Differential parameters of functions      C.66 78
Differential quadratic forms      An.84
Differential quadratic forms, transformation of      A.16
Differential resolvents of $12 (y^{4}+ay^{2}+xy)=a^{2}$      Me.82
Differential resolvents of $y^{m}+by^{r}+cx = 0$      Q.17
Differential resolvents of $y^{n}-ny^{n-r}+(n-1)x=0$&c.      3633—3636 Man.65
Differential resolvents of alg. eqs      3631—3637 An.83 C.91 LM.1 9 14 M.geo4 18 Me.75 82 Man.65 84 Q.6 11
Differentiants in terms of differences of roots of parent quantities      AJ.1
Differentiation      1402—1482 CM.1 see
Differentiation by the method of "Rates"      Me.75
Differentiation under the sign $\int$      2253 A.17
Differentiation when the function becomes infinite      C.88
Differentiation, formulae      1411—1472 An.59 CD.2 CM.1 Pr.9
Differentiation, general, i.e., with any fractional or imaginary      An.58 AJ.3 CD.3 4 5 J.12 JP.13 L.55 N.84 Q.3 4 TE.14 15 Z.16
Differentiation, general, i.e., with any fractional or imaginary, change of independent variable      JP.15
Differentiation, successive      A.20 Q.12
Digits, calculus of, Sbonimsky's th      J.30
Digits, frequency of in numbers      AJ.4
Digits, origin of      L.39
Diophantine analysis      see "Partition of numbers"
Direction ratios and cosines      5511—5514
Directive algebra      N.68
Directrix of a conic      1160 gn.eq E.36 Me.80 t.c
Directrix of a curve      A.20 J.2
Directrix of a parabola      gn.eqE.29
Directrix of a quadric      N.74 75
Directrix of in-parabola of a triangle      Me.80
Discontinuity in curves      CM.4 Z.26
Discontinuity in fractions      Man.48
Discontinuity in maxima and minima      CD.3
discontinuous functions      A.7 C.15 28 G.19 J.7 10 LM.6 Man.48 TI.21
Discriminant      1627 1638—1639 1644 Ac.1 J.90 LM.2 M.12 N.59 Pr.14 Q.10 11
Discriminant of a binary sextic      An.68
Discriminant of a quartic      N.83
Discriminant of a ternary quadratic form      Me.68
Discriminant of alg. eqs., resolution into factors      M.24
Discriminant of alg. functions      J.91
Discriminant of an algebraic d.e of 1st order in 4 variables, and of its complete primitive      An.84
Discriminant of binary quantic      An.56
Discriminant, applied to conics and quadrics      A.58
Discriminating cubic      1849 5693 G.16 J.26 71
Discriminating cubic, proof of real roots      1850 A.29
Displacement of a figure, two of whose points slide on two curves      C.82
Displacement of a solid      L.40
Displacement of a solid, determination of the normals to the lines or surfaces described      C.62
Displacement of a system of points      C.78
Displacement of a system of points, virtual displacement      J.11
Displacement of an invariable dihedron      Me.85
Displacement of an invariable dihedron, infinitesimal ditto      C.84
Displacement of an invariable figure      C.51 52 66 92 JP.26 L.74 75
Displacement of plane figures      C.80 N.73
Displacement, infinitesimal, of a parallelogram      C.97
Displacement, infinitesimal, of an alg. surface      C.70
Displacement, infinitesimal, of bodies only defined by 4 coordinates      C.73
Displacement, theory of      N.82
Distance between 2 points      4034—4035 t.c Q.7 sd5508 5510
Distance between 2 points, some relations      G.9
Distance of a point from a line and from a plane      A.57
Distance of a point from a plane in a given direction      5559
Distance, correspondences for quadric surfaces      LM.16
Distance, relations      Z.27
Distributive law      1488
Divisibility      C.96 E.8 M.39 N.67 74
Divisibility of $(x+y)^{n}+(-x)^{n}+(-y)^{n}$      Me.79
Divisibility of a quotient by the powers of a factorial      C.94
Divisibility of decadic numbers      Z.22
Divisibility of numbers of the form $2^{2m}+1$      Mel.5
Division      prJ.47 prL.56
Division and transformation of plane figures      A.4
Division by 73 or 47; rule for remainder      E.22
Division of a rectilineal figure and of a spherical polygon      J.10
Division of a right line into equal parts      950
Division of planes and spaces      J.1 2
Division of trapeziums, pyramids, and spheres      A.11
Division of triangles      A.11 17
Division, abridged      28 arithj.31 N.45 46 52 54 57 81 algN.42
Division, effected by determinants      581
Division, Fourier's rule      N.52
Divisors of $x^{2}+Ay^{2}$      L.49
Divisors of a polynomial with commensurable coefficients      N.75
Divisors of an integer, number of      374 C.96 N.68
Divisors of integral rational functions      Mem.57
Divisors, Newton's method of      459
Divisors, rational, of 2nd and 3rd degree      N.45
Divisors, sum of      377 Ac.f4 L.56 57
Divisors, sum of powers of      L.58
Double algebra      LM.15
Double function, laws of change of higher order      A.21
Double point, Clebseh's ths of these quantics      C.84
Double points      5178
Double points in a locus defined by alg. conditions      C.88
Double points in the projected intersection of 2 quadrics      N.84
Double points of a pencil of curves      An.64
Double points of plane curves in cubic space      Z.28
Double points of tortuous curves      M.3
Double points with $\frac{1}{2}(n-1)(n-2)$      M.2
Double points, n-tic with $\frac{1}{2}(m-1)(m-2)-2$ double points      L.80
Double points, n-tic with $\frac{1}{2}n(n-3)$      C.60
Double relations      A.60
Double tangents      An.51 J.49 P.59 Q.4 Z.21
Double tangents of a Cartesian      E.30
Double tangents of a quartic      C.37 J.49 55 68 72 M.1 N.67 P.61 Pr.11
Double tangents of a quartic with a double point, reciprocity of 28 double tangents      M.4 6
Double tangents of an n-tic      M.7
Double tangents of an n-tic, $number=\frac{1}{2}n(n-2)(n^{2}-9)$      J.40 63 N.53
Double tangents to the surface of centres of a quadric      C.78
Drilling, shape of hole      Pr.35
Dual relation between figures in space      J.10
Duplication of the cube, approx.      Pr.20
e      151 N.67 68 see
e and $\pi$, numerical th      Q.15
e, combinatorial definition of      A.1
e, geo meaning      E.4 N.55
e, incommensurable      295 CM.2 L.40 Me.74
Edge of regression      5729 tg.eC.71
Edge of regression, radius of curvature of      5742
Eisenstein's theorem      G.16
Elastic curve      C.18 19 JP.34
Elementary calculation      N.45
Eliminants      583 1626
Eliminants and associated roots      LM.16
Eliminants of two cubics      J.64
Eliminants, degree of      G.11
Eliminants, degree of, two eqs      12 J.22 31
Elimination      582—594 A.2 Ac.6 7 C.12 87 90 CD.3 6 CM.3 G.15 17 J.34 43 60 JP.4 L.41 44 LM.11 M.5 11 N.42 45 46 80 82 83 Q.7 th12 Z.23
Elimination of functions      3153 C.84 87 Me.73 76
Elimination of x between two equations      586—594 C.12 CM.2 J.15 27 Mo.81 N.43 76 77
Elimination of x between two equations by Bezout's method      586 A.79 J.53 Me.64 N.74 79
Elimination of x between two equations by cross multiplication      CM.1
Elimination of x between two equations by h.c.f      593 JP.8
Elimination of x between two equations by indeterminate multipliers      CM.1
Elimination of x between two equations by symmetrical functions      588
Elimination of x between two equations by the dialytic method      587 N.79
Elimination of x between two equations in geodetic operations      Z.3
Elimination of x between two equations, degree of the final equation      J.27 L.41
Elimination with linear differentials      L.36
Elimination with linear equations      At.53
Elimination with n variables      CP.5
Elimination, ap to alg. curves      M.4
Elimination, ap to in- and circum-conics of a polygon      At.63
Elimination, calculation of Sturm's functions      C.80
Elimination, problems      C.84 97 J.58 M.12 Q.8 11
Elimination, problems in metrical geo      A.63
Elimination, resultants, comparison of      J.57
Elimination, resultants, comparison of, and interpolation      J.57
Elimination, transformation and canonical forms      CD.6
ellipse      1160 4250 cn1245 geoQ.9 see
Ellipse and hyperbola      1160 4250 A.24 28
Ellipse and hyperbola, sectors      TE.14
Ellipse and hyperbola, theorems      A.23 CM.3 N.85
Ellipse and triangle      thQ.4
Ellipse as the projection of a circle      4921 N.75
Ellipse of maximum surface      N.65
Ellipse, eq. r+r'=2a      A.2
Ellipse, equal chords      tg.eE.22
Ellipse, quadrature of      6108 6113 t.c A.46
Ellipse, quadrature of sector      6098 A.20
Ellipse, quadrature of segment      6103
Ellipse, rectification of      6083—6096 A.3 22 27 30 At.39
Ellipse, rectification of, graphic      Mel.1 N.43 TE.4 Z.6
Ellipse, rectification of, graphic when e is very small      TI.9
Ellipse, representation by a circle      An.70
Ellipse, theorems      A.30 47 prs49 N.76
Ellipse, theorems, Mc Cullagh's      N.72
Ellipsoid      5600 6132 A.28 thCD.2 prC.20 L.38 cnM.20 P.9
Ellipsoid and enveloping cone      5664—5672 Q.6
Ellipsoid and plane of constant segment, th      E.32
Ellipsoid of gyration      5930
Ellipsoid of inertia      5925—5939
Ellipsoid of revolution      5604
Ellipsoid of revolution, area      N.42
Ellipsoid, a locus in space      Q.16 17
Ellipsoid, centro-surface      CP.12 LM.3
Ellipsoid, cubature of some derived surfaces      A.12
Ellipsoid, generation of (Jacobi)      CD.3
Ellipsoid, quadrature of      6143 J.17 Z.1
Ellipsoid, quadrature of zone      A.22
Ellipsoid, volume      6144 6148 A.46
Ellipsoidal geometry      A.10 LM.4
Ellipsoidal geometry, surfaces      G.17
Elliptic functions      2125 A.1 12 16 21 35 48 trAc.5 6 ths7 An.61 84 C.46 50 90 96 97 CD.2 3 5 CM.3 E.23 G.1 J.2 3 4 6 8 16 26 27 30 32 35 37 39 46 72 83 JP.25 L.55 56 61 LM.7 10 29 M.3 11 12 pr25 Me.79 80 81 82 Mo.81 82 83 85 N.77 78 79 P.31 34 75 78 Pr.6 9 10 12 23 Q.11 17 19 Z.2 11 27
Elliptic functions and spherical trigonometry      Q.17
Elliptic functions and theory of numbers      L.58
Elliptic functions in complex regions      Z.28
Elliptic functions of $\frac{1}{3}K$      Me.85
Elliptic functions of first and second kind      C.10
Elliptic functions of first and second kind, as functions of their amplitude      JP.14
Elliptic functions of first and second kind, representation in a simple form      Z.21
Elliptic functions of first and second kind, series by which they are computed      J.16 17
Elliptic functions of first kind      A.12 21 C.16 J.93 L.43
Elliptic functions of first kind with complementary moduli extension of a theorem of Lagrange      An83
Elliptic functions of first kind, normal forms of 3rd and 5th degree      M.17
Elliptic functions of first kind, replaced by one of second kind      J.55
Elliptic functions of first kind, represented by gauchebiquadratics      C.83
Elliptic functions of second and third kind, expression by $\theta$ function      Z.10
Elliptic functions of second kind      J.93
Elliptic functions of second kind, mechanical representation      Me.75
Elliptic functions of second kind, reduction to first kind from same modulus      A.56
Elliptic functions of third kind      C.94 96 CD.8 J.14 47 LM.13
Elliptic functions, $KE^{'}+K^{'}E-KK^{'}=-frac{1}{2}\pi$      Me.75
Elliptic functions, $\Delta^{\pm r}\alpha m\frac{2K}{\pi}cos^{\pm s}\alpha m\frac{2K}{\pi}sin\frac{2K}{\pi}\times x\int^{x}_{0}\Delta^{2}\alpha m\frac{2K}{pi}xdx$      J.37
Elliptic functions, addition of      A.47 geo64 AJ.7 C.59 78 J.35 41 44 54 88 90 LM.13 M.17 Me.80 84 Q.18 Z.1
Elliptic functions, addition of 1st kind      Z.26
Elliptic functions, addition of 2nd kind by q series      Me.83
Elliptic functions, addition of 3rd kind      Me.81
Elliptic functions, application of      C.85 86 89 90 93 94
Elliptic functions, application of, to algebra      J.7
Elliptic functions, application of, to arithmetic      C.98 L.62
Elliptic functions, application of, to confocal conics      Z.7
Elliptic functions, application of, to geometry      G.12 J.38 53
Elliptic functions, application of, to in- and circum-circles of a polygon      L.45
Elliptic functions, application of, to rectification      L.45
Elliptic functions, application of, to spherical conics      Z.22
Elliptic functions, application of, to spherical curves and quadrature      An.50
Elliptic functions, application of, to spherical polygons with in- and circum-circles      L.46
Elliptic functions, application of, to spherical trigonometry      Q.20
Elliptic functions, approximation to      2127—2132 P.60 62
Elliptic functions, arg sn a and $(arg\, sn a)^{2}$2, as def. integrals      Q.19
Elliptic functions, arithmetical consequences      Ac.5
Elliptic functions, arithmetico-geometric mean      J.58 85 89
Elliptic functions, development of      2127—2132 J.81
Elliptic functions, development of 1st and 2nd kind      C.92
Elliptic functions, development of 1st and 2nd kind with respect to the modulus of $\lambda (x), \mu (x)$ and their powers      C.86
Elliptic functions, development of an imaginary period when the modulus is small enough      An.70
Elliptic functions, differentiation by periods and invariants      J.92
Elliptic functions, discriminant of modular equations      M.8 9
Elliptic functions, double substitution      J.15
Elliptic functions, eqs. for the division of      Mo.75
Elliptic functions, formulae      AJ.5 J.15 36 50 LM.13 Me.78 80 85
Elliptic functions, formulae for sn, cn, dn, of u+v+w      Me.82
Elliptic functions, formulae from confocal conics      LM.14
Elliptic functions, formulae, differential      Me.82
Elliptic functions, formulae, Jacobi      Mel.1 Q.16 19
Elliptic functions, Galois' resolvent      M.18
Elliptic functions, geo. problems      M.19
Elliptic functions, geo. properties      L.43 45 P.52 54
Elliptic functions, geo. representation      A.22 61 An.60 61 At.53 C.19 21 J.63 L.44 78
Elliptic functions, geo. representation in solid geo      M.9
Elliptic functions, geo. representation of 1st kind      An.53 C.70 CD.1 JP.28 L.43 45 46 78
Elliptic functions, geo. representation of 3rd kind      A.24
Elliptic functions, identities      Me.77
Elliptic functions, imaginary periods      AJ.6
Elliptic functions, infinite double products      A.14
Elliptic functions, infinite double products with elliptic functions as quotients      J.35
Elliptic functions, inversion of      J.4 JP.34 L.69
Elliptic functions, modular equations      C.47 J.58 LM.9 10 M.12
Elliptic functions, modular functions      A.11 13 G.12 J.72 83 L.40 M.17 18
Elliptic functions, modular functions, differentiation for modulus of am      LM.13
Elliptic functions, modular functions, expansion in powers of modulus      J.41
Elliptic functions, modular functions, formulae      L.64
Elliptic functions, modular functions, relation between the modulus and the invariant of a binary quartic      Z.18
Elliptic functions, multiplication of      C.88 J.14 39 41 74 76 81 86 88 M.8 Mo.57 83
Elliptic functions, multiplication of, and division      Z.7
Elliptic functions, multiplication of, complex      M.25 Mo.62 Q.19 20
Elliptic functions, multiplication of, formulae      trA.36 C.59 J.39 48
Elliptic functions, multiplication of, mod. $-\surd \frac{1}{2}$      J.48
Elliptic functions, periodicity moduli of hyper-elliptic integrals as functions of a parameter      J.71 91
Elliptic functions, products of powers      Mem.71
Elliptic functions, q-formula for sin am      LM.11
Elliptic functions, q-series      f85
Elliptic functions, q-series for $\frac{\pi}{2K}+\frac{2G}{\pi}$ coeffs.      Q.21
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