# A Treatise on the Differential and Integral Calculus: And on the Calculus of Variations

A. S. Barnes, 1855 - Calculus - 501 pages
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### Contents

 TAYLORS THEOREM 60 2D CASE when the Equation is Homogeneous with Respect to x and 65 To Differentiate u Fpq where pfx and qf₁x 70 MAXIMA AND MINIMA FUNCTIONS OF A SINGLE VARIABLE 90 To Determine whether any Proposed Combination of x and y is a Func 120 RECTIFICATION OF CURVES 135 CHAPTER XI 137 INTEGRATION OF DIFFERENTIAL EQUATIONS OF THE SECOND ORDER 141 CHAPTER IX 147 3D CASE the Form y 149 CHAPTER II 160 Examples 167 EVOLUTES AND INVOLUTES 176
 CHAPTER VII 291 CHAPTER VIII 298 CHAPTER IX 312 QUADRATURE OF CURVED SURFACES 337 CHAPTER IV 344 120 356 SINGULAR SOLUTIONS OF DIFFERENTIAL EQUATIONS 358 130 362 137 368 OBJECT AND FIRST PRINCIPLES 389 CHAPTER IV 403 Maxima and Minima of One Variable 412 434 466

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Page vii - ... processes, and far-reaching and profound in its general views. It was admirably adapted both to acquire and use knowledge.''t He was modest and unassuming in his manner, even to diffidence. He would never utter a harsh word to pupils or disparage their efforts. " His pleasant smile and kind voice, when he would say, ' Is that answer perfectly correct?
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