Calculus
著者
書誌事項
Calculus
Cambridge University Press, 2001
- : pbk
- タイトル別名
-
Calculus : concepts and methods
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注記
Includes index
内容説明・目次
内容説明
The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.
目次
- Preface
- Preliminaries
- 1. Matrices and vectors
- 2. Functions of one variable
- 3. Functions of several variables
- 4. Stationary points
- 5. Vector-valued functions
- 6. Optimization of scalar-valued functions
- 7. Inverse functions
- 8. Implicit functions
- 9. Differentials
- 10. Sums and integrals
- 11. Multiple integrals
- 12. Differential and difference equations of order one
- 13. Complex numbers
- 14. Higher order differential and difference equations.
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