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.

403

series of powers, i. e. of ascending
positive integer
powers, 72, 332.,,,,,, identical for unique
function, 85, 148.
Serret, 27n, 41n*.
set [derived,[discrete
[ linear,, of numbers, 67, 125.,, points, 244-8, 296.
[plane
sign [integral
of infinity, 16.
signs + or -, 2, 15, 73, 80-1, 90, 121-4.,, [rules of
similar smallest parts, 144.
simple branch, 158.,, element, 379.,, forms in integration, 198, 316.,, integral or integration, 295-7,
309-14., root, 156, 161, 380.
simplest value of a logarithm, 119-20,
136, 152.,,,,,, radical, 117.,,,,,, an exponential, 120,
125.
simply connected, 315, 317, 326-9, 342.
sine, 20-2, is continuous, 25, except
at infinity, 30, 238, 244.
single-valued, 19, 131,374, s. one-valued,
unique.
singular, c. irregular, peculiarity, remarkable, special.,, along a curve, 331, 351,
c. 307, 311.,, double integral, 306, 309.,, integrals, 2581n.,, point (in general), 130, 141,
148n, 155-6, 256, 321,
329, 351.,,,, [essential,,,, [non-essential,,,, of curve, 105-6, s. multiple point.,,,, s. infinity point.
singularities, 25, 104, 106, 130, 155,
330, 342, 351, 363, 374.
slow convergence, 84.
solutions of equations, 104, llln, 153.
space, 1, 15, 86.
special points, 55.
specialities, 363.
species, 20, 153, c. 5.,, of sets of points, 24411, 246n.
sphere illustrates complexes, 127, 144,
163.
Stirling, 380n*.
Stolz, 44n*, 108n*.
strips, 136, 309.
subdivision, 5, 15, 60.
of intervals, 31, 175.
239-40, c. 26, s. partition

subdivisions, 174-5, 241-2.
subordinate units, 4.
substitution in integration, 196-7, 209,
212, 233, 320.,,,,, geometrically
treated, 184,
206, 303., of reciprocal variable,
127, 130-1,262,328,
334, 338, 356, 372.
subtraction, 2, 10, 67n, 110.
succession of integrations, 306-10n,
c. order.,,,, points, 24, 294, c. sequence.,,,, summands, 295n.
successive derivates, 56, 65, 145, 343,
349, 357, 361, 369, 379.,, integrations, 299 n, 304, 308,
312.
sudden change, 25, 29, 244.
sum, 1, 17, 47, 61, 102, 112, 114-5, 121-5.,, [double
summands, 2, 123, 176, 181, 239.
summation, 67n, 146, 195, 297.
superficial elements, 294-7, 303.
superincumbent points, 364.
superior or inferior limit, 157, 240-1,248.
superposed planes, 134, c. 161.
surface, s. area.,, [connected,, (curved), 86, 93, 112, 144n,
296-n.,, [elementary,, [Riemann's
~ [winding
symbol, 4, 50, 67, 68n, 114, 120.,, of integration, 176, 181, 243.
symbolic, 10, 22, 78, 288, 297.
symmetric function, 374.
symmetrical, 92, 97, 136, 213.
synectic, 141 n.
system of numbers, 110, 127.,,,, points, 244.,,,, values, 24, 86, s. point,
table, 6, 19, 22, 71.
tangent line, 36n, 40n, 41n, 42, c. 37,
43, 103, 207-8, 303n, 377-80.
of an angle, 22, 36, 42.,, plane, 93.
Taylor, 69-n*.
Taylor's series, 71, 77, 85, 103, 147,
168, 191, 341, 344, 363-4.
terms of an infinite series, 74n, 219, 249.
the infinite, 127-8, 130, 332.
theorem of addition of angles, 77.,,.,,,,, complexes, 114,
122.,,,,,,, elliptic integrals, 210n.,,,, interchange of differen~. f~tiations, 301, 348.
26 **