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AuthorHilton, P. J. author
TitleDifferential Calculus [electronic resource] / by P. J. Hilton
ImprintDordrecht : Springer Netherlands : Imprint: Springer, 1958
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Descript VII, 57 p. online resource


THIS book is intended to provide the university student in the physical sciences with information about the differential calculus which he is likely to need. The techniques described are presented with due regard for their theoretical basis; but the emphasis is on detailed discussion of the ideas of the differยญ ential calculus and on the avoidance of false statements rather than on complete proofs of all results. It is a frequent experiยญ ence of the university lecturer that science students 'know how to differentiate', but are less confident when asked to say 'what ix means'. It is with the conviction that a proper understandยญ ing of the calculus is actually useful in scientific work and not merely the preoccupation of pedantic mathematicians that this book has been written. The author wishes to thank his colleague and friend, Dr. W. Ledermann, for his invaluable suggestions during the preparaยญ tion of this book. P. J. HILTON The University. Manchester . . . Contents PAGE Preface V CHAPTER I Introduction to Coordinate Geometry I 6 2 Rate of Change and Differentiation I. The meaning of 'rate of change' 6 2. Limits 9 3. Rules for differentiating IS 4. Formulae for differentiating 21 Exerc-bses 2 3 3 Maxima and Minima and Taylor's Theorem 34 I. Mean Value Theorem 34 2. Taylor's Theorem 41 3. Maxima and minima 45 4


1 Introduction to Coordinate Geometry -- 2 Rate of Change and Differentiation -- 3 Maxima and Minima and Taylorโ{128}{153}s Theorem -- Answer to Exercises

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