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.
Rezensionen / Stimmen
'The self-contained text, suitable for advanced undergraduates, provides an extensive introduction into mathematical analysis, from the fundamentals to more advanced material.' Zentralblatt fur Didaktik der Mathematik
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Illustrationen
Worked examples or Exercises; 11 Line drawings, unspecified
Maße
Höhe: 261 mm
Breite: 183 mm
Dicke: 19 mm
Gewicht
ISBN-13
978-0-521-84072-9 (9780521840729)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Richard Beals is James E. English Professor of Mathematics at Yale University. He has also served as Professor at the University of Chicago and visiting Professor at the University of Paris, Orsay. He is the author of over 100 research papers and monographs in partial differential equations, differential equations, functional analysis, inverse problems, mathematical physics, mathematical psychology and mathematical economics.
Autor*in
Yale University, Connecticut
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.
