Analysis : an introduction

Richard Beals

This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.

「Nielsen BookData」より

This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.

「Nielsen BookData」より

[目次]

  • 1. Introduction
  • 2. The real and complex numbers
  • 3. Real and complex sequences
  • 4. Series
  • 5. Power series
  • 6. Metric spaces
  • 7. Continuous functions
  • 8. Calculus
  • 9. Some special functions
  • 10. Lebesgue measure on the line
  • 11. Lebesgue integration on the line
  • 12. Function spaces
  • 13. Fourier series
  • 14. Applications of Fourier series
  • 15. Ordinary differential equations
  • Appendix: the Banach-Tarski paradox
  • Hints for some exercises.

「Nielsen BookData」より

[目次]

  • 1. Introduction
  • 2. The real and complex numbers
  • 3. Real and complex sequences
  • 4. Series
  • 5. Power series
  • 6. Metric spaces
  • 7. Continuous functions
  • 8. Calculus
  • 9. Some special functions
  • 10. Lebesgue measure on the line
  • 11. Lebesgue integration on the line
  • 12. Function spaces
  • 13. Fourier series
  • 14. Applications of Fourier series
  • 15. Ordinary differential equations
  • Appendix: the Banach-Tarski paradox
  • Hints for some exercises.

「Nielsen BookData」より

この本の情報

書名 Analysis : an introduction
著作者等 Beals, Richard
出版元 Cambridge University Press
刊行年月 2004
ページ数 ix, 261 p.
大きさ 27 cm
ISBN 0521600472
0521840724
NCID BA69651134
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言語 英語
出版国 イギリス
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