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.

394

Index.

COnrvT.rgence, [interval of,, of infinite product, 289.,,,,, series, 68, 122,
219.,, ~,,,,,, of powers,
72, 138.,,,, integrals, 264.,, [unconditional,, -[uniform
convergency, 151, 220-1, 228, 339.,, of series of powers, 73-6,
138,146,150,227,336-8,
345-8, 357.
[radius of
convergent, 68.,, in equal degree or uniformly, 74n.,, [not,, series, 73, 104,121,139,219.
coordinated, 127, 133-4, 161-2, 346,
360, 364-5.
coordinates, s. Cartesian, homogeneous,
polar.,, of points on conic, 206.
course of a function, 24-5, 33, 86, 128.
correspond uniquely, 128, 184, 321.
Cramer, 380 n*.
Crelle, 39n.
criterion of continuity, 28, 89, 221.,,,convergence, 76, 219, 290.,,,, differentiation of series, 223.,,, integrability, 262.,,,, uniform convergence, 219.
critical points, 155-65, 347, 350, 363-4,
376-89.,,,, with ramification, 162,
351, 378, 380.
crossing a branching section, 134-7,
161-7, 329, 334-5., along a branching section, 134.
cubature, 60, c. 296-n.
cubic equation, 104, 110n.
curve, [algebraic,, defined in two ways, 42, 294.,, illustrates implicit function, 104,
377-80.,, [irregular,, of integration, 321, 344, 372.,,,, singularities, 307, 331, 351.,, representing function, 24, 37, 86,
93, 179.,, surrounding point infinity, 332,373.
with angles, 43, 323.
curved surfaces, 296n.
curves intersecting, 144, 303.
cycle, 163-4, 376, 385-6.,, of branches, 364, 386, 389.,,,, leaves, 162.,,,, values, 163, 381-6.
cyclically connected, [leaves,, ~,, values, 368, 372.

Darboux, 221n, 225*, 227.
decimals, 8, 52, 84.
Dedekind, 14 n*.
definite double integral, 270, 296, 314.,, integral, 176, 243, (simple, 296)., a continuous function,
177, 252, 256, 301.,,,, discontinuous function
of a parameter, 268,
276.,,,, formed from indefinite,
181, 194, 208, 257.,,,, in two variables, 317.,,, of complex function
along a path, 322.
definition of a number, 1, 9.,,,, atithmetical operations,
114-20.,,,, continuity, 27, 87.,,,, curve, 42.,,,, equality, 10-1.,,,, functions, 19, 22, 55, 128,
321, 341.,,,, higher derivates, 56-7.,,,, infinitely great, 16.,,,, integral as a sum, 176,
242, 257, 261,
296, 322-5.,,,, positively along
a curve, 313-4.,,,, trigonometric functions,
20, 53, 71.,,,, zero, 2, 17.
degree of equation, 153, 374-6.,,,, expression, function, polynomial, 20, 155, 375.
Ax, increment of x, 33, c. 129, 140.
De Moivre, 11611*, 118.
dependence, 19, 68n, 97, 101, 128.
dependent variable, 19, 22, 25, 43.
derivate, 39-n, 55-7, 94, 158, 171, 256,
321, 327, 331, 369.,, of a term, 147, 226.,,,, an equation, 156, 386.,, [partial
derived (derivate), 45, 65-6, 70, 143,
178, 222.,, equations, 349.
function, 39, 53, 141, 172, 325.,,,, ~[partial,,, [total,, of a function, 39, 40, 45, 48,
96, 99, (differential quotient) 90, 141.,,,,, series, 223, 228.,, series (or terms), 223-6, 292.,, sets of points, 245-7.
Descartes, 15-1, s. Cartesian.
descending powers, 84.
determinant, 156.
determinate, 8, 16, 35, 108, 148n.
determinately finite, 31, 305.,, infinite, 16, 22, 28-32,
37, 39, 43-5, 108,148 n, 257-8,260,306,312.

cylinder,
cylinder,

[interchange
[ramify
296.