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| 类型/形式： | Textbooks |
|---|---|
| 文件类型： | 书 |
| 所有的著者/提供者： |
Sudhir Ghorpade; Balmohan Vishnu Limaye |
| ISBN: | 0387305300 9780387305301 1441921451 9781441921451 |
| OCLC号码： | 70254725 |
| 描述： | x, 432 p. : ill. ; 24 cm. |
| 内容： | 1 Numbers and Functions 1 -- 1.1 Properties of Real Numbers 2 -- 1.2 Inequalities 10 -- 1.3 Functions and Their Geometric Properties 13 -- 2 Sequences 43 -- 2.1 Convergence of Sequences 43 -- 2.2 Subsequences and Cauchy Sequences 55 -- 3 Continuity and Limits 67 -- 3.1 Continuity of Functions 67 -- 3.2 Basic Properties of Continuous Functions 72 -- 3.3 Limits of Functions of a Real Variable 81 -- 4 Differentiation 103 -- 4.1 The Derivative and Its Basic Properties 104 -- 4.2 The Mean Value and Taylor Theorems 117 -- 4.3 Monotonicity, Convexity, and Concavity 125 -- 4.4 L'Hopital's Rule 131 -- 5 Applications of Differentiation 147 -- 5.1 Absolute Minimum and Maximum 147 -- 5.2 Local Extrema and Points of Inflection 150 -- 5.3 Linear and Quadratic Approximations 157 -- 5.4 The Picard and Newton Methods 161 -- 6 Integration 179 -- 6.1 The Riemann Integral 179 -- 6.2 Integrable Functions 189 -- 6.3 The Fundamental Theorem of Calculus 200 -- 6.4 Riemann Sums 211 -- 7 Elementary Transcendental Functions 227 -- 7.1 Logarithmic and Exponential Functions 228 -- 7.2 Trigonometric Functions 240 -- 7.3 Sine of the Reciprocal 253 -- 7.4 Polar Coordinates 260 -- 7.5 Transcendence 269 -- 8 Applications and Approximations of Riemann Integrals 291 -- 8.1 Area of a Region Between Curves 291 -- 8.2 Volume of a Solid 298 -- 8.3 Arc Length of a Curve 311 -- 8.4 Area of a Surface of Revolution 318 -- 8.5 Centroids 324 -- 8.6 Quadrature Rules 336 -- 9 Infinite Series and Improper Integrals 361 -- 9.1 Convergence of Series 361 -- 9.2 Convergence Tests for Series 367 -- 9.3 Power Series 376 -- 9.4 Convergence of Improper Integrals 384 -- 9.5 Convergence Tests for Improper Integrals 392 -- 9.6 Related Integrals 398. |
| 丛书名： | Undergraduate texts in mathematics. |
| 责任： | Sudhir R. Ghorpade, Balmohan V. Limaye. |
| 更多信息： |
摘要：
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. Contains examples and a large selection of exercises, as well as Notes and Comments.
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From the reviews: "The book is a self-contained and rigorous introduction to calculus of one variable. It covers the programme of the first-year in mathematical analysis. The main goal of the book is a clear and successful presentation of the basic ideas of analysis. The reader can see an attention of the authors to help students in understanding and further developing of the basic notions of the subject. ! are illustrated by a number of interesting examples and remarks. In some sense it is a book for self-education." (Sergi V. Rogosin, Zentralblatt MATH, Vol. 1100 (2), 2007) 再读一些...
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添加标签 目的是为 "A course in calculus and real analysis".
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