Variational Calculus and Optimal Control

Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.