微積分と実解析（テキスト） A Course in Calculus and Real Analysis (Undergraduate Texts in Mathematics)

Ghorpade, Sudhir R./ Limaye, Balmohan V.

Springer（2006/06発売）

• 製本 Hardcover:ハードカバー版／ページ数 442 p.／サイズ 71 illus.
• 言語 ENG
• 商品コード 9780387305301

基本説明

Offers self-contained introduction to the calculus of functions of one variable; The text is sequenced to emphasize the structural development of calculus.

Full Description

This book provides a self-contained and rigorous introduction to calculus of functions of one variable, in a presentation which emphasizes the structural development of calculus. Throughout, the authors highlight the fact that calculus provides a firm foundation to concepts and results that are generally encountered in high school and accepted on faith; for example, the classical result that the ratio of circumference to diameter is the same for all circles. A number of topics are treated here in considerable detail that may be inadequately covered in calculus courses and glossed over in real analysis courses.

Contents

Numbers and Functions.- Sequences.- Continuity and Limits.- Differentiation.- Applications of Differentiation.- Integration.- Elementary Transcendental Functions.- Applications and Approximations of Riemann Integrals.- Infinite Series and Improper Integrals.