The title is a trifle awkward. What would we call a later book that goes beyond postmodern analysis? The "post" is meant by Jost to differentiate this text from the generally labelled "modern analysis" of the late 19th century and continuing into the 20th century.

Labels aside, the book is a rigorous continuation of analysis. Beyond the level in Marsden's "Elementary Classical Analysis". Jost develops crucial ideas, like metric spaces, normed spaces, and what happens when we have completeness in both types, yielding Hilbert and Banach spaces. The former should be quite well known in mathematical physics, as the underlying space for quantum mechanics.

The book also explains the Lebesgue integral and topological spaces. Much of this is for the pure mathematician. But scientists can also use the sections devoted to solving partial differential equations. Though I imagine that the abstractness of the treatment might be beyond the background of many scientists.