Calculus of One Variable

  • Keith E. Hirst

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 47-77
  3. Pages 79-92
  4. Pages 153-171
  5. Pages 173-183
  6. Back Matter
    Pages 241-267

About this book


Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering;

algebraic techniques

functions and graphs

an informal discussion of limits

techniques of differentiation and integration

Maclaurin and Taylor expansions

geometrical applications

Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.

The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.



Calculus of a single variable Integration Real functions calculus real analysis

Authors and affiliations

  • Keith E. Hirst
    • 1
  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK

Bibliographic information