The classical subject of calculus of variations provides the underlying mathematical foundation for a surprisingly diverse set of fields in science and engineering. In addition, its generality facilitates utilization in a wide variety of modern topics in optimization and control. This text provides an up-to-date treatment of the mathematics from a general point of view that highlights its generality and breadth of applications. Following such a treatment of the calculus of variations, the majority of the text consists of applications of variational methods in various fields in science and engineering with an emphasis on illustrating the wide range of applications from a unified variational point of view.
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YouTube Videos: Chapter 1 - Preliminaries
YouTube Videos: Chapter 2 - Calculus of Variations
YouTube Videos: Chapter 3 - Rayleigh-Ritz, Galerkin, and Finite-Element Methods
YouTube Videos: Chapter 4 - Hamilton's Principle
YouTube Videos: Chapter 5 - Classical Mechanics
YouTube Videos: Chapter 6 - Stability of Dynamical Systems
YouTube Videos: Chapter 7 - Optics and Electromagnetics
YouTube Videos: Chapter 8 - Modern Physics
YouTube Videos: Chapter 9 - Fluid Mechanics
YouTube Videos: Chapter 10 - Optimization and Control
YouTube Videos: Chapter 11 - Image Processing and Data Analysis
YouTube Videos: Chapter 12 - Numerical Grid Generation