Loomis, Lynn H.; Sternberg, Shlomo Advanced calculus. Rev. ed. (English) Zbl 0782.46041 Boston, MA: Jones and Bartlett Publishers. 580 p. (1990). The first edition of this textbook on real analysis appeared in 1968 (cf. Zbl 0162.35301). On account of the modern treatment of the subject, the wealth of material that is covered and the huge variety of applications included in the text, this book very quickly established itself as one of the standard works for students and teachers worldwide. Still now, after about one quarter of a century, this outstanding character of the textbook is unrestrictedly persisting. Its main features, namely the thorough combination of the aspects of multivariable calculus in \(\mathbb R^n\), analysis on manifolds, differential geometry and mathematical physics, on the one hand, as well as the systematic use of the ubiquitous, efficient algebraic framework, on the other hand, reflect the global tendencies in mathematics in a protruding manner, now as before, and therefore it remains as one of the most significant, progressive and sophisticated textbooks on topics in advanced calculus.For this reason, the present new edition should be very welcome to the younger generations of students, teachers and researchers in mathematics and natural sciences, not only as a standard text but also as a reference work. The original text has not been changed, but just revised for misprints. Reviewer: Werner Kleinert (Berlin) Cited in 1 ReviewCited in 20 Documents MSC: 46G05 Derivatives of functions in infinite-dimensional spaces 46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis 26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions 58A05 Differentiable manifolds, foundations 70Hxx Hamiltonian and Lagrangian mechanics Keywords:differential calculus; differentiable manifolds; integral calculus on manifolds; potential theory; Hamiltonian and Lagrangian mechanics; multivariable calculus; analysis on manifolds; differential geometry; mathematical physics Citations:Zbl 0162.35301 PDFBibTeX XMLCite \textit{L. H. Loomis} and \textit{S. Sternberg}, Advanced calculus. Rev. ed. Boston, MA: Jones and Bartlett Publishers (1990; Zbl 0782.46041)