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Hardy G.H. — A course of pure mathematics

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Название: A course of pure mathematics

Автор: Hardy G.H.

Аннотация:

This book has been designed primarily for the use of first year students at the Universities whose abilities reach or approach something like what is usually described as 'scholarship standard'. I hope that it may be useful to other classes of readers, but it is this class whose wants I have considered first. It is in any case a book for mathematicians: I have nowhere made any attempt to meet the needs of students of engineering or indeed any class of students whose interests are not primarily mathematical.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1908

Количество страниц: 428

Добавлена в каталог: 03.03.2006

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Предметный указатель

Logarithm, common      353
Logarithm, principal value of      382
Logarithmic function      222 et seq. 341 380 392
Logarithmic function and inverse trigonometrical functions      398 et seq.
Logarithmic function, functional equation satisfied by      344 384
Logarithmic function, graph of      343
Logarithmic function, order of infinity of, as $x \rightarrow \infty$       344 et seq. 369 373
Logarithmic function, power-series for      363 et seq. 402
Logarithmic function, representation of, as a limit      142 352
Logarithmic limit      142 352
Logarithmic scale of infinity      346
Logarithmic series      363 et seq. 402
Logarithmic tests for convergence      357 et seq.
Maclaurin's integral test for convergence      303 305
Maclaurin's series      255; see also “Taylor's series”
Maxima and minima      206 et seq. 256
Maxima and minima of       210 et seq.
Maxima and minima, discrimination between      207 257
Maxima and minima, examples of      209 et seq. 244
Maxima and minima, occur alternately      208
Mean value theorem      214 et seq.
Mean Value Theorem for functions of two variables      267
Mean Value Theorem for integrals, Bonnet's form      286
Mean Value Theorem for integrals, first      282
Mean Value Theorem for integrals, generalised      282
Mean Value Theorem for integrals, second      285
Mean Value Theorem of second order      252
Mean Value Theorem, general      252
Measure of curvature      261
Mercator's projection      410
Modulus      82
Modulus of a product      83
Modulus of a sum      84 86 324
Multiplication of series      301 et seq. 334 335 339 373
Newton's method of approximation to the roots of an equation      253
Normal to a curve      190 218
Number $\pi$       17 65
Number $\sqrt 2$       5 et seq. 12
Number e      347 et seq.
Number i      77 et seq.
Number, complex      75 et seq.
Number, complex, conjugate      77
Number, complex, equivalence, addition, multiplication and division of      75 et seq.
Number, complex, factor theorem for      77
Number, complex, geometrical applications of      86 et seq. 101
Number, complex, modulus and amplitude of      82
Number, complex, rational functions of      84 et seq.
Number, complex, real and imaginary parts of      82
Number, complex, roots of      98 et seq.
Number, complex, trigonometrical applications of      95 et seq.
Number, infinite      111 et seq.
Numbers, algebraical      23 et seq.;see also “Numbers irrational” “Quadratic “Surds”
Numbers, irrational      4 et seq.; see also “Numbers algebraical” “Quadratic “Surds”
Numbers, irrational, expression of as decimals      147
Numbers, rational      1 et seq.
Numbers, rational, expression of as decimals      3 146
Orders of smallness and greatness      168 et seq. 183 344 350
Oscillation of $\sin n \theta \pi$ , etc.      125
Oscillation of a function of n      123 et seq.
Oscillation, examples of      124 et seq.
Oscillation, finite and infinite      124
Oscillation, of a function of x      160 et seq.
Oscillation, theorems connected with      126 129
Partial fractions      198 et seq. 222
Polygons, regular, constructions for      100
Polynomials      35 et seq.
Polynomials in a complex variable      80
Polynomials, continuity of      173
Polynomials, differentiation of      196 et seq.
Polynomials, having given values      61
Polynomials, in x, $e^{ax}$ , etc., integration of      354
Polynomials, in x, cos ax, etc., integration of      233 et seq. 248
Polynomials, in x, log x, etc., integration of      236 249
Polynomials, integration of      222
Polynomials, limits of, as $x \rightarrow a$       165
Power-series      331 et seq.
Power-series, circle and radius of convergence of      332 et seq.
Power-series, multiplication of      334
Power-series, recurring      337 et seq.
Power-series, uniqueness of      333
Power-series: Taylor's and Maclaurin's      255 287
Power-series: Taylor's and Maclaurin's for arc tan x      364 404; “Exponential “Logarithmic
Power-series: Taylor's and Maclaurin's for cos x and sin x      255 400
Principal value, of       390
Principal value, of       391
Principal value, of am z      82

Principal value, of Log z      382
Pringsheim's theorem      304 et seq. 309
Pringsheim's theorem, analogue of, for integrals      314
Quadratic surds      5 et seq.
Quadratic surds, approximation to, by binomial theorem      366
Quadratic surds, geometrical constructions for      8 et seq. 64
Quadratic surds, theorems concerning      9 et seq.
Quadrature of circle, approximate      65
Radius of convergence      333
Radius of curvature      261
Rates of variation      188 et seq.
Rational functions      38 et seq. 61
Rational functions of , integration of      354
Rational functions of $\phi (n)$ , $\varphi (n)$ , etc., limits of, as $n \rightarrow \infty$       134
Rational functions of a complex variable      84 et seq.
Rational functions of cos x and sinx, integration of      234
Rational functions of n, limits of, as $n \rightarrow \infty$       135
Rational functions of x, limits of, as $x \rightarrow a$       165
Rational functions, continuity of      173
Rational functions, differentiation of      198 et seq.
Rational functions, integration of      222 et seq.
Rational numbers      see “Numbers” “rational”
Rationalisation, integration by      226 et seq. 231 234 246 354
Rearrangement of series      301 324 327 328 330
Recurring series      337 et seq.
Rolle's theorem in general      205
Rolle's theorem, for polynomials      198
Roots      see “Equations”
Scales of infinity      346 350 370
Series, infinite      142 et seq. 296 322 “Exponential “Geometrical “Logarithmic “Multiplication “Power-series” “Rearrangement “Taylor's
Series, infinite, arithmetic      148
Series, infinite, convergence, divergence, and oscillation of      143
Series, infinite, general theorems concerning      144 et seq.
Series, infinite, harmonic      144 149 300 305 308 335 359 369
Series, infinite, of complex terms      330 et seq.
Series, infinite, of complex terms, absolutely convergent      330
Series, infinite, of positive and negative terms      322 et seq.
Series, infinite, of positive and negative terms, Abel's and Dirichlet's tests of convergence for      328 et seq.
Series, infinite, of positive and negative terms, absolutely convergent      323 et seq.
Series, infinite, of positive and negative terms, alternating      326
Series, infinite, of positive and negative terms, conditionally convergent      325 et seq.
Series, infinite, of positive terms      145 296
Series, infinite, of positive terms Cauchy's and d'Alembert's tests of convergence for      297 et seq.
Series, infinite, of positive terms comparison theorem for      297
Series, infinite, of positive terms condensation test of convergence for      308
Series, infinite, of positive terms integral test of convergence for      305 et seq.
Series, infinite, of positive terms Pringsheim's theorem concerning      304 et seq.
Series, infinite, special: $\Sigma (-1)^n {{x^{2n+1}} \over {2n+1}}$       364 404
Series, infinite, special: $\Sigma (-a)^{n-1} {{cos \ n \theta} \over n}$ , $\Sigma (-a)^{n-1} {{sin \ n \theta} \over n}$ , etc.      404 414
Series, infinite, special: $\Sigma a_n \cos n \theta$ , $\Sigma a_n \sin n \theta$       324 328 329
Series, infinite, special: $\Sigma n^{-s}$       8 299 307 309
Series, infinite, special: $\Sigma P(n) {x^n \over n!}$       362
Series, infinite, special: $\Sigma R(n)$       299 335
Series, infinite, special: $\Sigma x^n \cos n \theta$ , $\Sigma x^n \sin n \theta$       153 154
Series, infinite, special: $\Sigma x^n$ , $\Sigma n x^n$ , $\Sigma P(n) x^n$ , $\Sigma R(n) x^n$ , $\Sigma (-1)^{n-1} {x^n \over n}$ , $\Sigma {x^n \over n}$ , $\Sigma {x^n \over n!}$ , $\Sigma (-1)^n {x^{2n} \over {2n!}}$ , $\Sigma (-1)^n {{x^{2n+1}} \over {(2n+1)!}$ , $\Sigma \binom m n$       see other entries mentioned
Series, infinite, special: $\Sigma {1 \over n}$ , $\Sigma {1 \over {an+b}}$       144 149 300 305 308 335 359 369
Series, infinite, special: $\Sigma {1 \over {n(n+1)\ldots(n+k)}}$       156 299
Series, infinite, special: $\Sigma {\binom m n} P(n) x^n$       367
Simpson's rule      295
Stereographic projection      410
Surds      14 et seq. 21
Surds, approximation to, by binomial theorem      366; see also “Numbers algebraical” “Quadratic
surface      54
Surface of revolution      58
Surface, ruled      59
Symmetric functions of the roots of a trigonometrical equation      96 et seq.
Tangent to a curve      185 et seq.
Tangent to a curve, equation of      190 218
Taylor's series      255 287
Taylor's series for derivative or integral      373
Taylor's series, remainder, Cauchy's form      288
Taylor's series, remainder, Lagrange's form      255
Taylor's theorem      252 et seq. 287
Transformation      90 et seq. 104 409
Transformation       105
Transformation $z=exp(\pi Z /a)$ , $z = c \cosh (\pi Z / a)$ etc.      409 et seq.
Transformation       411
Transformation       94
Transformation ${1 \over 2} \{ Z+(1/Z) \}$       105
Transformation z=(aZ+b)/(cZ+d)      90 et seq. 104
Triangles, geometrical properties of      86 87 101 419
Unity, roots of      99 et seq.
Variable, continuous real      18 et seq.
Variable, positive integral      19 108
Velocity      189
“ $n \rightarrow \infty$ ”      114 et seq.
“Large values'” of n      111 et seq.

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