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Differential Calculus

  • Authors
  • P. J. Hilton

Part of the Library of Mathematics book series (LIMA)

Table of contents

  1. Front Matter
    Pages N1-vii
  2. P. J. Hilton
    Pages 1-5
  3. P. J. Hilton
    Pages 6-33
  4. P. J. Hilton
    Pages 34-51
  5. Back Matter
    Pages 52-57

About this book

Introduction

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 differ­ ential calculus and on the avoidance of false statements rather than on complete proofs of all results. It is a frequent experi­ 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 understand­ 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 prepara­ 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.

Keywords

differential calculus differential equation maximum minimum

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-011-6087-2
  • Copyright Information Springer Science+Business Media B.V. 1958
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-7100-4341-2
  • Online ISBN 978-94-011-6087-2
  • Buy this book on publisher's site