Books like A First Course in Mathematical Analysis by David A. Brannan

James Stewart's CALCULUS texts are renowned for their precision, clarity, and effectiveness in teaching calculus to students worldwide.

A clear, self‑contained calculus text that emphasizes physical applications and introduces differential equations and linear algebra early, complete with over 1,600 worked problems and detailed solutions.

A comprehensive bridge from elementary calculus to advanced real and complex function theory, this textbook introduces the abstract reasoning characteristic of modern mathematical analysis.

As the title implies, this is an introductory text on mathematical analysis. It focuses on the logical basis of particular math topics which nowadays (as of 2012) are typically featured in a pre-calculus text. The 1967 teacher's edition is accessible to anyone who understands basic algebra. It is designed to prepare students to approach math in a methodical and rigorous manner from an elementary level. Some of the topics are outdated--it includes log and other tables. Although it is an elementary text, the approach used by the authors was meant to introduce logical rigor into high-school mathematics. The lessons are concerned with structure; some of the methods are quite out of favor now that electronic calculators are ubiquitous. This is the sort of math that a student ought to be able to appreciate without a calculator, i.e., it is more concerned with logical structure and proof (at least by the authors' standards) than with memorization of axioms without proof, backed by blind faith in calculators. At the time the text was first written there were no handheld calculators, so elegant algorithms were in demand. The text was designed to teach students how to construct algorithms based on mathematical reasoning. The one exception would be the inclusion of various log, trig, and other tables in the back that were probably computer generated, the algorithms for which were slightly beyond the scope of the text.

A Beginners choice for learning Real Analysis.

A classic compilation of challenging analysis problems and theorems drawn from leading mathematicians between 1850 and 1925.