Mathematical Analysis I

This two-volume work by V.A.Zorich on Mathematical Analysis constitutes a thorough first course in real analysis. The text leads from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions. With masterful exposition, the author provides a smooth, gradual transition from each topic to the next, so that the slope never feels too steep for the reader. The clarity of the exposition is matched by a wealth of instructive exercises and fresh applications to areas seldom touched on in real analysis books, many of which are taken from physics and technology.

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
Some General Mathematical Concepts and Notation.- The Real Numbers.- Limits.- Continuous Functions.- Differential Calculus.- Integration.- Functions of Several Variables: their Limits and Continuity.- The Differential Calculus of Functions of Several Variables.- Some Problems from the Midterm Examinations.- Examination Topics.