An Introduction to the Study of the Elements ...

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By Axel Harnack, George
Lambert Cathcart

Translated by George
Lambert Cathcart

Published 1891
Williams and Norgate

404 pages

Original from the University of Michigan

Digitized Nov 23, 2005

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Real numbers and functions of real numbers	1
summands, divisor, minuend
The continuous series of numbers 10 Calculation with variables	9
unlimitedly, logarithm, exponent
Conception of a variable quantity and calculation	15
determinate, cosa, assignable
Geometric representation of a function	24
quotient, determinately, derivate
Points of discontinuity Superior and inferior limits	43
scholium, integer, arbitrarily
rational algebraic functions 28 Exponential function 29 Trigonometric	55
derivate, binominal, become infinitely

Calculation of functions by infinite series	65
converges, regressively, elog
Fu notions of m ore than one independe n t variable	86
dxdy, dydx, theorem
Implicit functions Application of Taylors	105
quantités, numerator, algebraic
Complex numbers and functions of complex numbers	112
modulus, exponent, moduli
Complex series Complex variable Functions	121
abscissae, moduli, modulus
of two series 79 Complex variable Geometric representation of infinite	147
uniformes, inappreciably, vanishing
of factors 89 Cauchys theorem 90 The fundamental theorem	153
branching, branching points, whose modulus
Integrals of functions of real variables	169
const, ordinates, indefinite integral
functions Partial fractions	186
numerator, conjugate, fractions
I 116 Substitutions	194
integrals, hyperbola, binomial
Uniform convergence differentiation	219
darboux, remainders, uniformly convergent
Integrals of transcendental functions	233
sinx, rational function, circular functions
General theorems concerning the definite	239
neighbourhoods, annal, finite
necessary properties of integrable functions 144 Discrete and linear	247
proxime, becomes infinite, zero along
quotient of the integral 148 149 Definition of the integral of	265

Examples in the calculation of definite	274
inappreciably, eulerian, gamma
integrals 160 161 Eulerian integrals 162 Gamma function expressed	292
double integral, boundary curve, simple integral
Integrals of complex functions General properties of analytic functions	321
analytic, corollaries, connected domain
Substitution 181 The integral within a multiply connected domain	329
ordinates, branching, positive axis
Expansion of unique analytic functions	341
analytic, integer powers, singular points
order m l and integration round it 195 Expansion in	363
infinitudes, polygon, cyclically

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References from books

Bulletin of the New York Mathematical Society - Page 59
by New York Mathematical Society - 1892
Published by: Macmillan & Co. for the Society, 1893-1894.
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The History of the Calculus and Its Conceptual Development - Page 322
by Carl Benjamin Boyer - Mathematics - 1959
This book, for the first time, provides laymen and mathematicians alike with a detailed picture of thehistorical development of one of the most momentous achievements of the human...
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Other editions

An Introduction to the Study of the Elements of the Differential and Integral Calculus
by Axel Harnack - 2005 - 416 pages
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