دانلود کتاب Introduction to Analysis

This text is the outgrowth of a course given at Berkeley since 1960.
The object is to redo calculus correctly in a setting of sufficient generality
to provide a reasonable foundation for advanced work in various branches
of analysis. The emphasis is on abstraction, concreteness, and simplicity.
A few abstract ideas are introduced, almost minimal in number. Such
important concepts as metric space, compactness, and uniform convergence
are discussed in such a manner that they will not need to be redone later.
They are given concrete illustration and their worth is demonstrated by
using them to prove the results of calculus, generalized in ways that are
obviously meaningful and practical.

The background recommended is any first course in calculus, through
partial differentiation and multiple integrals (although, as a matter of fact,
nothing is assumed except for the axioms of the real number system). A
person completing most of the material in this book should not only have
a respectable comprehension of basic real analysis but should also be ready
to take serious courses in such subjects as integration theory, complex
variable, differential equations, other topics in analysis, and general
topology. Experience indicates that this material is accessible to a wide
range of students, including many with primary interests outside mathe-
matics, provided there is a stress on the easier problems.