Purely mathematical treatment covers Rayleigh-Ritz method, Weinstein method, Weinstein-Aronszajn method and others. Little math needed beyond elements of calculus. First 9 chapters discuss general theory of variational methods with special reference to the vibrating plate. Last chapter extends to more general cases. Includes exercises. 1957 edition.
Introduction to the Calculus of Variations by Hans Sagan Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Variational Analysis: Critical Extremals and Sturmian Extensions by Marston Morse This text presents extended separation, comparison, and oscillation theorems that replace classical analysis. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals. 1973 edition.
Gauge Theory and Variational Principles by David Bleecker Covers principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition
Variational Principles by B. L. Moiseiwitsch This text shows how variational principles are used to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities that arise in the theory of scattering. 1966 edition.