An introduction to the study of the elements of the differential and integral calculus. From the German of the late Axel Harnack, With the permission of the author.

Index.

397

function, [implicit
), [integer,, integrable,, [integral,, [odd or even,,.of a complex variable, 128,
139-44n, 321.,,,,,, continuous variable, 19.,,,, two variables, 86, 102.,, [rational,, regular, 148n, 333, 352-5, 363.,, represented at a point by
a curve or surface, 24, 93.,, that is to be integrated, 181,
214, 229, 257, 268.
functional, 19, 42.
functionality, 196.
fundamental definite integrals, 182,195.,, elliptic integrals, 210-2.,, formulas of integration,
181, 185.,, integrals, 188-9, 207.:, principle for multiple
integrals, 296n.,, problem of integral calculus, 169, 172, 239.,, property of the exponential, 118.,, proposition of addition,
1, 112, 123.,, theorem concerning the
unique analytic function, 366, c. 328, 342.,, theorem of algebra, 153.,, theorems concerning the
definite integral, 249,
259, s. 296, 323.
gamma functions, 281-93.
Gauss, 110, 111n, 112n, 113n*, 116,
144n*, 153n*, 288-n*, 293n*.
general rules of differentiation, 47, 54.,,,,.. integration, 183., theorems concerning series of
powers, 72, 138, 145.
generalisation, 252, 367, s. extension.
generalise, 9, 111n, 150, 364.
generally (- in general):,, analytic, 256, 324, 351, 355.,, continuous, 162, 246, 248,
266, 301-2, 312, 314.,, integrable, 298.
geometric definition, 20, 42, 53, 68 n, 71.,, interpretation, 20, 111-2n,
179, 296.,, inversion, 163.,, meaning, 42, 218.,, problems, 179n, 209n, 280n,
296 n.,, representation of a function,
24, 37, 86, 93, 128.,, statement, 133, 138, 380.
transformation, 128, 143.
geometry, 1, 15, 20, 60, 127, 206-7.

I

given along a curve, 343-5, 357.
goniometric, 20.
graphic solution, 382.
greatest integer in x, G(x), 22, 29, 169.
Green's theorem, 311-n*, 314, 326.
Gregory, 81n*.
HIamburger, 380n*.
Hankel, 112n*, 246ns1, 3451n*.
harmonic series, 82 n.
Harnack, 27 n.
Heine, 14n*, 28, 219 n'.
Hermite, 52n*, 233n*.
homogeneous coordinates, 207.
Hoppe, 63 n*.
Hoiiel, 112 n*.
hyperbola, 184, 206, 209n, 217, 309.
hypothesis, (data, iii), 38-9n, 172,
240, 341.
i denotes imaginary unit, 110.
identical curves in different planes, 161.,, differential quotients, progressive and regressive, 38-41,
141, 169, 178, 255.,, limiting values, 95, 2-2-3.,, series, 85, 147, 150, 232.
identity, 39 n 59, 169, 232, 333.
image of a complex number, 127.,,,,,, continuum, 15.,,,,,, function, 24, 86.,,,,,, motion, 15.
imaginaries, 111.
imaginary constants, 189, 202.,, numbers, 110-2.,, [purely, quantities, 233.
implicit algebraic function, 47, 104,
1.53-68, 347-51, 363, 373-89.,, functions, 19, 86, 101, 128.
importance of series of powers, 341.
impossible, 2, 5, 52, 89, 111.
improper fractional rational function,
356.
inappreciably (= arbitrarily little), 152,
224, 278, 288-9, 354-5.
inclusion within limits, 7, 47, 67, 153.
increment, 33, 97, 129, 140.
indefinite integral, 178, 180-1, 189,
208, 256, 318.
independent formulas for differentiation, 63, 83.,, limits of double integration, 270, 300.,, of path of integration,
316, 320, 326-7, 339.,, variable, 19, 25, 49, 58-9,
85-7, 97-9, 361.
indeterminate, 5, 30-1, c. oscillate.,, along a curve, 311.,, a at a point, 29, 89.,, between finite limits,
238, 241, 246,262,296.