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.

399

integral calculus, 23, 172, 239, 244n.
[definite
[definition of,, [double, s. definite.,, found by expansion, 199, 218,
235, 281, 286.,, function, 181, 207, 238, 329,372., [indefinite,, of analytic function, 327, 355.,,,, continuous function, 173.,,,, discontinuous function, 180,
239, 249, 272.,,,,, function that becomes infinite, 181, 257.
[real, round a point, 329, 353, 372.,,,,,, circle independent of
its radius, 334, 342.,, sign, 176, 267-9, 277, 315-6., [simple,, unique, 181, 326, 330.
up to a point, 329, 355, 372.
with infinite limits, 181, 261.
integrals, [elliptic,, [multiple,, of explicitly irrational functions, 197.,,,, rational algebraic functions, 186.,,,, transcendental functions,
233.,,. that take a rational form, 201,
c. 209.,, [singular
integrated, [function that is to be
integration by parts. 183, 229, 251-2.,,,, substitution, 184, 202.
[domain of
[interval of
[limits of
of an infinite series, -225.,,,, integral, 269-77, 300.
[path of
within multiply connected
domain, 329.
integrations interchangeable, 251, 272,
279, 285, 300, 306.,, not interchangeable, 272,
306, 309.
interchange, 164, s. change.,, cyclically, 360, 374.,, of integration and differentiation, 265, 319.,, order of differentiations, 267, 301, 348.,,,, order of integrations,
272, 276, 283.
interchangeability of factors, 115.
f,, integrations, 308.
interpretation, [geometric
interval, 7, 15-6, 25-6, 65, 169, 323, 311.,, [continuous in an,, [linear,,.of convergence, 73.

interval of integration, 172-3, 250-7, 31.
intervals of discontinuity, 244., [partial
intuition, 2, 60, 86, 112, 125, 180.
intuitive,, 15, 111,1-27.
inverse functions, 22, 54, 129, 346, 358., operations, 112, 115.
inversion, 128, 163-4, 328, 362.,, of an arithmetical operation,
2, 13, 68n, 120.
7,,,, differentiation, 172, 176.,,,, function or series, 358,
363, 377, 380.
involution, 6, 11, 110.
irrational exponent, 12, 20, 118, 135,
c. transcendental functions.,, function, [explicitly,, lnumber, 8, 52,60,67,246,280.
irreducible, 154, 351, 375-6, 381, 387.
irregular curve, 351.,, point, 363, 374.
isolated point, 104, 126, 172, 305, 312,
329, c. discrete.
Jacobi, 90.
kinds of elliptic integrals, 212, 218.
Kliigel, 84 n*.
Konigsberger, 217 n*.
1 denotes natural logarithm, 53.
Lagrange, 39, 67n*, 99, 361-2.
Laplace's integrals, 276.
Laurent, 148 n*.
leaf of Riemann's n-leaved surface, 134,
162, 346, 350, 361, 375.
leaves cyclically connected, 359, 364,
366-7, 371, 378.,, meeting in a critical point, 378.,, [plane
Legendre, 210 1*, 212, 216, 217, 218-n*,
230:-n*, 281-n*, 284, 292, 293-n.
Leibnitz, 42*, 80n, 176, 180n, 186n*.
Lim, briefly for limiting value, 10.
limiting circle of convergence, 140, 337.,, points of infinite set, 245-6., position, 24, 36, 42, 93.,, value of a function or series,
8-9, 25, 34, 172.,,,,,,,, sum, 121, 176, 239,
294-6, 322.

limits, 7, 60, 86.,, of a function, 30, 252.,,,, an integral, Lpper and lower,
176.,,,, integration, 311.,,,, magnitude, superior and inferior, 9, 84n, 240-1.
line at infinity, 127, 207-8.
linear, 56, 131, 186, 197, 212, 217n.,, figure, 125-6.,, interval, 295-n.,, mass or set of points, 245 6, 296.,, set, 244n-7, 259, 266, 315.