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.

395

development, 85, 130, 148, 151, 153.
difference, 2, 73, 114, 150.,, of terms in series, 7, 27,
37, 68, 146-7.,,,, values of a function, 25,
28, 33, 74,87, 102, 170-1,
175, 240.
differences, 58-9.,, [eqation between
[quotients of
differential, 59, 60, 97-8, 158, 176, 303,
320-1.,, calculus, 23, 33, 42, 46,
60, 65, 179n, 181.,, coefficient, 39, 40, 158,
343, 350., coefficients, [mixed..,,,, [ partial, equation, 92, 363.,, [exact,, partial
quotient, 34-n, 37, 58, 60,
105, 140, 142,
158,319,323-4.,,,, indeterminate, 46,
c. 41, 225,256...,, [partial,,,, regressive differs
from progressive, 43, 224.. [total, [total
differentiation, 40, 47, 56, 96, 103,
158, 172, 319, 348., impossible, 46,225,277., must be possible,
318-9, c. 179.,, of infinite series, 76,
147, 222, 232, 368.,, of integral for parameter, 264-9, 274-7,
302, 316.
dimensions of domain, 125-6, 129, 296.,, term, 103, 158, 381.
Dini, 244 n*, 261 n*.
direction of circuit, 137, 162-4, 314.,,, curve, 37, (tangent) 42-3.,,,, differential quotient, 104,
141, 324.
Dirichlet, 121n*, 124n, 193n*, 262n*:,
283n*, 343 n.
disconnected, 128.
discontinuities, 29,46,247-8, s.breaches.,, finite
discontinuity (point), 180.
[intervals of
[points of
discontinuous along a line, 88-9, 133,
296,31 1,332, 334-6,350.,, at points, 29, 89, 126,
169, 172, 221, 227, 246,
307, 351.,, between finite limits,
(finitely) 296.

I
i

discontinuous derived series, 224.,, function, 28-32,239,272,
330.,,,, [discretely,,,, integrable 180,
247-9,256,296.,,,, [linearly,, [infinitely often, series of numbers, 16, 51.
discrete mass of points, 246.,, multiplicity of curves, 311,
c. 296.,, points, 256-7, 259, 323, 325,, quantities, 111.,, set, 246-7, 256, 298, 301-2, 322., set of points, 244n1-8, 255-6,
266, 296, 323, 329.,, set or mass of points, 244.
discretely discontinuous function, 246-8.
discriminant, 154n, 156.
diverge, 72-3, 139 n 337.
divergent integrals, 264.
series, 69, 82-n, 287n.
dividing points, 174, 241-2.
division, 2, 11, 67n, 110, 115.
domain, 86-7, 89, 100, 125, 291, 368.,, [complex,, [connected,, [dimensions of,, of complex numbers, 112.,,,, convergence, 138 s. con.
vergency.,,,, integration, 251, 297, 301-5... ',,, [infinite,,,, lnumber, 85.,,,, real quantities, 129.,,,, validity of double integral,
303.,, [regular
double (s. multiple) integral, [definite,, point of curve, 104.,, sum, 297, 311.
Drobisch, 112 n*.
Du Bois-Reymond (1831-89), 46*,
221 n, 225*, 239 n*, 250 n*, 252 n*, 255n'*,
258n*, 264*, 310n*.
e denotes base of natural logarithms,
52-3, 68, 71n, 114.
eccentric anomaly, 217.
element of a function, 345-6, 378-9.,,,,,,,, lbranched, 380.,,., arc, 313.
elementary functions, 47, 67.,, surface, 297.
elements, [superficial
ellipse, 206, 209n, 217, 299.
elliptic arc, 217.,, integrals, 209, 229.
entire plane, 130-1, 135, 151, 294, 308,
346, 355-7, 363, 374.
equable, (in equal degree 74n), s. uniform convergence, 140, 219.
equal, 2-3.