This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics asdifferential forms on manifolds, asymptotic methods, integral transforms, anddistributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books. The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions. The thoroughness of the coverage, from elementary to very advanced The clarity of the exposition The originality and variety of the exercises and examplesEspecially good for physics students INDICE: Prefaces.- 9. Continuous Mappings (General Theory).- 10. Differential Calculus from a General Viewpoint.- 11. Multiple Integrals.- 12. Surfaces and Differential Forms in Rn.- 13. Line and Surface Integrals.- 14. The Elements of Vector Analysis and Field Theory.- 15. Integration of Differential Formson Manifolds.- 16. Uniform Convergence and the Basic Operations of Analysis.-17. Integrals Depending on a Parameter.- 18. Fourier Series and the Fourier Transform.- 19. Asymptotic Expansions.- Some Problems from the Midterm Examinations.- Examination Topics.- References.- Subject Index.- Name Index.
- ISBN: 978-3-540-87453-9
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 681
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés