| Calculus of One Variable 2006 Edition Contributor(s): Hirst, K. E. (Author) |
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ISBN: 1852339403 ISBN-13: 9781852339401 Publisher: Springer OUR PRICE: $36.09 Product Type: Paperback - Other Formats Published: October 2005 Annotation: 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:
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. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Functional Analysis - Mathematics | Calculus |
| Dewey: 515.83 |
| LCCN: 2005925984 |
| Series: Springer Undergraduate Mathematics |
| Physical Information: 0.56" H x 7.08" W x 9.28" (0.99 lbs) 268 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The development of the di?erential calculus was one of the major achievements of seventeenth century European mathematics, originating in the work of N- ton, Leibniz and others. Integral calculus can be traced back to the work of Archimedes in the third century B. C. Since its inception, calculus has dev- oped in two main directions. One is the growth of applications and associated techniques, indiverse?eldssuchasphysics, engineering, economics, probability and biology. The other direction is that of analytical foundations, where the intuitive and largely geometrical approach is replaced by an emphasis on logic and the development of an axiomatic basis for the real number system whose properties underpin many of the results of calculus. This approach occupied many mathematicians through the eighteenth and nineteenth centuries, c- minating in the work of Dedekind and Cantor, leading into twentieth century developments in Analysis and Topology. We can learn much about calculus by studying its history, and a good starting point is the St Andrews' History of Mathematics website www-history. mcs. st-and. ac. uk/history/ Thisbookisdesignedforbeginninguniversitystudents, boththosestudying mathematics as a major subject, and those whose main specialism requires the use and understanding of calculus. In the latter case we would expect that lecturers would customise the treatment with applications from the relevant subject area. Thepre-universityschoolmathematicscurriculaofmostEuropeancountries all include some calculus, and this book is intended to provide, among other things, a transition between school and university calculus. In some countries suchastheU. K. |