Real analysis
著者
書誌事項
Real analysis
（Springer undergraduate mathematics series）
Springer, c2001
- : pbk
大学図書館所蔵 件 / 全20件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references and index
内容説明・目次
内容説明
Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, the book covers all the key topics with fully worked examples and exercises with solutions. All the concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject. This book offers a fresh approach to a core subject and manages to provide a gentle and clear introduction without sacrificing rigour or accuracy.
目次
- 1. Introductory Ideas.- 1.1 Foreword for the Student: Is Analysis Necessary?.- 1.2 The Concept of Number.- 1.3 The Language of Set Theory.- 1.4 Real Numbers.- 1.5 Induction.- 1.6 Inequalities.- 2. Sequences and Series.- 2.1 Sequences.- 2.2 Sums, Products and Quotients.- 2.3 Monotonie Sequences.- 2.4 Cauchy Sequences.- 2.5 Series.- 2.6 The Comparison Test.- 2.7 Series of Positive and Negative Terms.- 3. Functions and Continuity.- 3.1 Functions, Graphs.- 3.2 Sums, Products, Compositions
- Polynomial and Rational Functions.- 3.3 Circular Functions.- 3.4 Limits.- 3.5 Continuity.- 3.6 Uniform Continuity.- 3.7 Inverse Functions.- 4. Differentiation.- 4.1 The Derivative.- 4.2 The Mean Value Theorems.- 4.3 Inverse Functions.- 4.4 Higher Derivatives.- 4.5 Taylor's Theorem.- 5. Integration.- 5.1 The Riemann Integral.- 5.2 Classes of Integrable Functions.- 5.3 Properties of Integrals.- 5.4 The Fundamental Theorem.- 5.5 Techniques of Integration.- 5.6 Improper Integrals of the First Kind.- 5.7 Improper Integrals of the Second Kind.- 6. The Logarithmic and Exponential Functions.- 6.1 A Function Defined by an Integral.- 6.2 The Inverse Function.- 6.3 Further Properties of the Exponential and Logarithmic Functions.- Sequences and Series of Functions.- 7.1 Uniform Convergence.- 7.2 Uniform Convergence of Series.- 7.3 Power Series.- 8. The Circular Functions.- 8.1 Definitions and Elementary Properties.- 8.2 Length.- 9. Miscellaneous Examples.- 9.1 Wallis's Formula.- 9.2 Stirling's Formula.- 9.3 A Continuous, Nowhere Differentiable Function.- Solutions to Exercises.- The Greek Alphabet.
「Nielsen BookData」 より