A Treatise on the Differential Calculus

William Walton

Deightons, 1846 - Differential calculus - 263 pages

Contents

• FIRST PART CHAPTER: 1
• 6: 3
• 8: 4
• Principles of Differentiation 10 Definition of a differential coefficient: 6
• Differentiation of a constant: 7
• Differentiation of the sum of a function and a constant 13 Differentiation of the product of a function and a constant: 8
• Differentiation of a sum of functions 15 Differentiation of the product of two functions: 9
• Differentiation of the ratio of two functions: 10
• Differentiation of the product of any number of functions 18 Relation between inverse differential coefficients: 11
• Differentiation of a function of a function a 20 Differentiation of a function of two functions: 12
• Differentiation of a function of any number of functions of a single variable: 15
• Differentiation of an implicit function of a single variable: 17
• General theory of the differentiation of implicit functions of a single variable: 18
• Total differentiation of a function of functions of independent variables: 19
• Article Page 25 Partial differentiation of an explicit function of three variables one of which is a function of the other two: 21
• Partial differentiation of an explicit function of n + r variables r independent and n dependent: 22
• Partial differentiation of an implicit function of two independent variables: 23
• Simple functions: 25
• Differential coefficient of loga X: 26
• Differential coefficient of qx: 28
• Differential coefficient of sin a: 29
• Differential coefficient of tan x: 30
• Differential coefficient of sec x: 31
• Differential coefficient of sin ??: 32
• Differential coefficient of cosx: 33
• Differential coefficient of cotx: 34
• Differential coefficient of cosecx: 35
• 45 Illustrative examples: 37
• 10: 39
• CHAPTER III: 44
• Change of the independent variable: 46
• Order of partial differentiations indifferent: 50
• Successive differentiation of an explicit function of two func tions of a single variable: 52
• Successive differentiation of an implicit function of a single variable: 55
• Successive total differentials: 57
• Successive differentiation of an explicit function of three vari ables one of which is a function of the other two а: 58
• Change of variables: 60
• Transformation of one system of independent variables into another: 61
• CHAPTER V: 84
• Failure of the method of differentials for the evaluatiou of: 92
• CHAPTER VI: 99
• Abbreviation of operation: 107
• CHAPTER VII: 128
• Another demonstration of Taylors theorem: 133
• Cauchys expression for R: 134
• Examples of Taylors theorem: 136
• Lagranges theory of Functions: 137
• Stirlings theorem: 140
• Examples of the application of Stirlings theorem: 141
• Extension of Taylors theorem to functions of two variables: 146
• Failure of the development of fx+h y+k by Taylors theorem: 149
• Limits and remainders of the development of f x + h y + k 95 Example of the application of Taylors theorem for two variables: 150
• Stirlings theorein applied to functions of two variables: 151
• Lagranges formula for the development of implicit functions: 152
• Laplaces formula for the development of implicit functions: 155
• SECOND PART CHAPTER I: 159
• Inclinations of the tangent and the normal at any point of a curve to the coordinate axes: 160
• Equations to the tangent and the normal at any point of a curve: 162
• Distance of the origin of coordinates from the tangent: 164
• Intercepts of the tangent: 165
• Length of the tangent: 166
• Oblique axes: 168
• Article: 170
• ölö lol: 177
• CHAPTER III: 178
• 12: 185
• Branches pointillées: 191
• Symmetrical investigation of points of inflection: 197
• CHAPTER V: 203
• Another method of finding the radius of curvature: 209
• Analytical Determination of the Centre of Curvature Theory of Evolutes: 210
• CHAPTER VII: 217
• CHAPTER VIII: 223
• Intersection of consecutive normals to a curve: 230
• 17: 233
• CHAPTER X: 235
• Differential of an area: 237
• Diagram of differentials: 238
• Chord of curvature through the pole: 239
• 22: 240
• Asymptotes: 241
• Asymptotic circles: 243
• CHAPTER XI: 245
• Homogeneous curves: 257
• The cycloid: 259
• Tangent and normal to the cycloid: 260
• Arc of the cycloid: 261
• Evolute of the cycloid: 262
• 18: 2

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Bibliographic information

• Title: A Treatise on the Differential Calculus; A Treatise on the Differential Calculus, William Walton
• Author: William Walton
• Publisher: Deightons, 1846
• Original from: the University of Michigan
• Digitized: Jun 20, 2007
• Length: 263 pages