Explore the frontiers of mathematical analysis with “Variational Analysis: Critical Extremals and Sturmian Extensions.” This essential text by renowned mathematician Marston Morse revisits classical variational theory, offering powerful extended separation, comparison, and oscillation theorems that provide crucial insights into mathematical physics and global analysis. Delve into the analysis of quadratic functionals, understanding how critical extremals can expertly replace minimizing extremals. Morse theory, a cornerstone of modern mathematics, is presented with a deep dive into critical extremals, quadratic index forms, focal conditions, and Sturm-like theorems. Ideal for researchers and students in advanced mathematics, this book offers a comprehensive treatment of fundamental concepts and their applications, enhanced by supplementary appendixes on free linear conditions and quadratic forms. Discover the advanced mathematical tools that shape our understanding of equilibrium problems and complex systems.