An entire generation of mathematicians has grown up during the time - tween the appearance of the ?rst edition of this textbook and the publication of the fourth edition, a translation of which is before you. The book is fam- iar to many people, who either attended the lectures on which it is based or studied out of it, and who now teach others in universities all over the world. I am glad that it has become accessible to English-speaking readers. This textbook consists of two parts. It is aimed primarily at university students and teachers specializing in mathematics and natural sciences, and at all those who wish to see both the rigorous mathematical theory and examplesofitse?ectiveuseinthesolutionofrealproblemsofnaturalscience. The textbook exposes classical analysis as it is today, as an integral part of Mathematics in its interrelations with other modern mathematical courses such as algebra, di?erential geometry, di?erential equations, complex and functional analysis.

The thoroughness of the coverage, from elementary to very advanced The clarity of the exposition The originality and variety of the exercises and examples Especially good for physics students Includes supplementary material: sn.pub/extras

Inhalt
Continuous Mappings (General Theory).- Differential Calculus from a more General Point of View.- Multiple Integrals.- Surfaces and Differential Forms in ?n.- Line and Surface Integrals.- Elements of Vector Analysis and Field Theory.- Integration of Differential Forms on Manifolds.- Uniform Convergence and the Basic Operations of Analysis on Series and Families of Functions.- Integrals Depending on a Parameter.- Fourier Series and the Fourier Transform.- Asymptotic Expansions.- Topics and Questions for Midterm Examinations.- Examination Topics.