18/08/25 20:37:22.75 RnpU6cYx.net
“The textbook of Zorich seems to me the most successful of the available comprehensive textbooks of
analysis for mathematicians and physicists. It differs from the traditional exposition in two major ways:
on the one hand in its closer relation to natural-science applications (primarily to physics and mechanics)
and on the other hand in a greater-than-usual use of the ideas and methods of modern mathematics, that is,
algebra, geometry, and topology. The course is unusually rich in ideas and shows clearly the power of the
ideas and methods of modern mathematics in the study of particular problems. Especially unusual is the
second volume, which includes vector analysis, the theory of differential forms on manifolds, an introduction
to the theory of generalized functions and potential theory, Fourier series and the Fourier transform, and
the elements of the theory of asymptotic expansions. At present such a way of structuring the course must
be considered innovative. It was normal in the time of Goursat, but the tendency toward specialized courses,
noticeable over the past half century, has emasculated the course of analysis, almost reducing it to mere
logical justifications. The need to return to more substantive courses of analysis now seems obvious,
especially in connection with the applied character of the future activity of the majority of students.
...In my opinion, this course is the best of the existing modern courses of analysis.”
From a review by V.I.Arnold