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.

393

concrete numbers or units, 1.
condensation in a point, 245.
condition for convergence, 69, 122.,,,, differentiation, 179, c. 46.,,,,,, of series,
222.,,, double integration, 295.,,,, esxact differential, 318-20.,,,, integration, 240.,,,,,, of series, 226..,, representation by curve,
24, 37, 93, 179.,,,, representation by a surface, 93.
of continuity, 25-7,29, 87,129.,,,, theorem of total differential, 92, c. 303n.,, that a complex integral be
unique, 326.,,,, function be analytic,
141, 321.,,,, integrations be interchangeable, 300.
conditional convergence, 73-4, 80-2,
123, 138, 264, 337.
cone, 93.
conics in integral, 206.
conjugate complexes, 116, 153, 167,
189, 192, 212.
connected along branching sections,
164, 347, 375,
area, 128.,, [branches,, cycle, 364, 376., [cyclically,, domain, 126, 129, 311, 321,
341, 345.,, functions, 345.,, in points, 351, 374-5, c. 378.,, [multiply,, [simply,, surface, 133-5, 375.,, values of function, 375.
connexion between definite and indefinite integrals,
178,181,256,318.,,,, elementary functions, 23, 114n,
119 n, 190.
constant, 17, 40, 56, 169-72, 256, 357.
constituents of complex, 118, 126, 136,
140-2, 153, 321.
contact, 377-8, 380.
contents of an equation, 59, 98, 344.
continually approach, 43.,, change sign, 361n.
continuation of function, 103, 150, 345,
359, s. extension.,, partition, 175, 243, 295.
continued arbitrarily, 239.,, subdivision, 5, 60, 175., uniquely, 103, 359.,, unlimitedly, 68.,, - unrestrictedly, 219, 289.

continuity, 1, 46, 87, 101, 127, 343n.,, at a point, 26, 38, 129, 221,,, [breaches of,, [condition of, [criterion of,, of complex, 126.,,,, convergent infinite series,
220.,,,, convergent infinite series
of powers, 74-n, 139.,,,, implicit function, 101, 156.,,,, terms of a series, 74n, 219.,, [uniform
continuous along a curve (path), 132,
156, 163, 324.,, change, 16, 101, 126.,, function, 26, 30, 38, 102,
129, 139, 154, 169,173,220,
256, 311, 321.,, [generally (in general),, in a domain, 87, 300-1.,,,, an interval, 16, 26, 69,
181, 225.,,,, neighbourhood of a point,
34-5, 90, 93, 95.,, inclusive of a value, 35., increase or decrease, 170., on both sides of a point,
25, 31, 70.,, ' [restrictedly,, series, 221 n.,,,,, of numbers, 1, 15-6,
32, 51, 244.,,,,, points, 42, 29.,,,,,, values, 101, 160,
184, 208., towards one side, 43.,, transition, 76, 91, 255.,, u[unrestrictedly, variables, 17, 43, 59, 126.
without exception, 301, 316.
continuously variable, 16, 126.
continuum, 5, 15.
contracted about a point, 353.
converge, 16, 24, 72, 93, 127, 337, 356., absolutely, 138, 221, 292, 336.,, conditionally, 73, 123, 138.,, continuously, 25, 265.,, more rapidly, 59, 81, 230,292.
to infinity, 338.,,,, zero, 17, 39, 124-5, 140,
170-1, 239-41, 295, 324-5.,, unconditionally, 73.,, unequably, 221-21n, 225, 227.,, uniformly, 219-28, 231-2, 249,
336, 338-9.
convergence, 68, 73, 122, 341.,, [absolute,, I[circle of,, [condition for,, [conditional,, I[criterion of
[domain of,, [equable