# An Elementary Treatise on the Differential Calculus: Founded on the Method of Rates

J. Wiley and sons, 1904 - Differential calculus - 404 pages

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### Contents

 CHAPTER 1 Increasing and decreasing functions 8 Rates of variation 14 The differential of the sum of several variables 20 The derivative 26 Formula and Methods of Differentiation 32 The differential of the reciprocal 41 VI 49
 Application to maxima and minima 197 XXII 214 Complex quantities 221 Quadratic factors of certain algebraic expressions 227 Bernoullis numbers 237 Application to Plane Curves 247 Subtangents and subnormals 233 253 XXV 262

 Differentiation of exponential functions 56 Differentiation of the sine and cosine 62 VIII 70 Differential of a function of two variables 80 Implicit functions 120 82 CHAPTER III 88 Successive derivatives of a function 1 95 XII 103 Computation of e 107 CHAPTER IV 112 Alternation of maxima and minima 124 Maximum and minimum abscissae 132 CHAPTER V 141 Functions which vanish with x 147 Differential formula for the form jg 153 Indeterminate forms of functions of two variables 163 CHAPTER VI 172 Maclaurins theorem 179 Calculation of the development of tan x 184 Expressions for the remainder 19 191
 Maximum and minimum coordinates 268 XXVI 274 The hypocycloid and the hypotrochoid 280 The fourcuspel hypocycloid or astroid 286 Polar subtangents and subnormals 293 Zero values of r 295 The cardioid 32 302 The spiral of Archimedes 39 309 The radius and circle of curvature 315 The radius of curvature in rectangular coordinates 321 The evolute of the cycloid 327 The intrinsic equation and radius of curvature of the evolute 333 XXIX 344 General method 35 352 Partial derivatives 364 Commutative character of differentiation 370 Eulers theorems concerning homogeneous functions 377 Transformations of partial derivatives of the second order 384 Index 401 Copyright

### References from web pages

Exponential curve: Definition with Exponential curve Pictures and ...
An Elementary Treatise on the Differential Calculus Founded on the Method of by John Minot Rice, William Woolsey Johnson (1877) ...
www.lexic.us/ definition-of/ exponential_curve

Mathematics Textbooks and Promotion of Conceptual Understanding ...
1. Mathematics Textbooks. and Promotion of. Conceptual. Understanding. Miroslav Lovric. lovric@mcmaster.ca. Issue of use of textbooks is related to ...
www.math.mcmaster.ca/ lovric/ courses/ Lovric_Texts_Fields.pdf

AMERICAN MATHEMATICAL SOCIETY
BULLETIN. OF THE. AMERICAN. MATHEMATICAL SOCIETY. A HISTORICAL AND CRITICAL REVIEW. OF MATHEMATICAL SCIENCE. 11. fn COLE. de SMITH. VIRGIL SNYDER ...
projecteuclid.org/ DPubS/ Repository/ 1.0/ Disseminate?handle=euclid.bams/ 1183420006& view=body& content-type=pdf_1