Calculus : an introduction
著者
書誌事項
Calculus : an introduction
Springer, c1997
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注記
Includes index
内容説明・目次
内容説明
This book aims to be a straightforward, no-fuss introduction to calculus. Little formal reliance is made on the reader's previous mathematical background and great care has been taken to make the book as self-contained as possible. The topics are presented in a logical sequence with continuity of flow of ideas, with definitions given as succinctly as possible. Examples are given after definitions and theorems, and the more difficult proofs of these are relegated to the end of the chapter so as to allow for continuity of flow of ideas. The book includes an elementary treatment of ordinary differential equations with emphasis on first and second order differential equations. Exercises with complete solutions have also been carefully selected to supplement the text as well as to provide guidance to the correct way of writing mathematics.
目次
- Sets
- functions
- inequalities
- continuity
- differentiation
- the mean value theorem
- monotone functions and graph sketching
- anti-differentiation
- definite integrals
- inverse functions, logarithmic and exponential functions
- inverse trigonometric functions and hyperbolic functions
- integration by parts and techniques of integration
- L'Hopital's rule
- improper integrals and Taylor's formula
- ordinary differential equations
- solutions to exercises.
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