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Mathematical Analysis II

Mathematical Analysis II

This is a free, online textbook that is part of a series.  According to the author, it "completes the material on Real Analysis that is the foundation for later courses in functional analysis, harmonic analysis, probability theory, etc. The first chapter extends calculus to n-dimensional Euclidean space and, more generally, Banach spaces, covering the inverse function theorem, the implicit function theorem, Taylor expansions, etc. Some basic theorems in functional analysis, including the open mapping theorem and the Banach-Steinhaus uniform boundedness principle, are also proved. The text then moves to measure theory, with a complete discussion of outer measures, Lebesgue measure, Lebesgue-Stieltjes measures, and differentiation of set functions. The discussion of measurable functions and... Show More


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Bradley Lucier
Bradley Lucier (Faculty)
7 years ago

I'm the publisher of the book.  It should be classified as

Mathematics and Statistics/Mathematics/Analysis


Mathematics and Statistics/Mathematics/Numerical Analysis

The primary audience is definitely not Lower Division College, it's Upper Division College and probably mainly Graduate Courses in Mathematics