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“Variational Principles” books focus on formulating and solving problems by finding functions or configurations that minimize, maximize, or make stationary a functional—capturing ideas like least action and minimal energy. Core topics include the calculus of variations, Euler–Lagrange and Hamiltonian formalisms, variational inequalities, and optimal control, often paired with numerical methods such as finite element techniques and convex optimization. The category spans rigorous mathematical foundations (functional analysis, PDEs, geometric mechanics) and wide-ranging applications in mechanics, optics, materials, fluid dynamics, general relativity, and increasingly in data science and machine learning (e.g., variational inference). It serves advanced students and researchers in mathematics, physics, engineering, and the applied sciences seeking both theory and practical tools for modeling and solving complex systems.

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