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There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Variational principles. --- Science --- Engineering --- Construction --- Industrial arts --- Technology --- Scientific method --- Logic, Symbolic and mathematical --- Extremum principles --- Minimal principles --- Variation principles --- Calculus of variations --- Methodology.

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Structure of Solutions of Variational Problems is devoted to recent progress made in the studies of the structure of approximate solutions of variational problems considered on subintervals of a real line.  Results on properties of approximate solutions which are independent of the length of the interval, for all sufficiently large intervals are presented in a clear manner. Solutions, new approaches, techniques and methods to a number of difficult problems in the calculus of variations  are illustrated throughout this book. This book also contains significant results and information about the turnpike property of the variational problems. This well-known property is a general phenomenon which holds for large classes of variational problems. The author examines the following in relation to the turnpike property  in individual  (non-generic) turnpike results, sufficient and necessary conditions for the turnpike phenomenon as well as in the non-intersection property for extremals of variational problems. This book appeals to mathematicians  working in optimal control and the calculus as  well as with graduate students.

Boundary value problems -- Numerical solutions. --- Geometry, Differential -- Congresses. --- Variational principles. --- Calculus of variations --- Mathematical optimization --- Civil & Environmental Engineering --- Mathematics --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Calculus of variations. --- Isoperimetrical problems --- Variations, Calculus of --- Mathematics. --- Algorithms. --- Mathematical analysis. --- Analysis (Mathematics). --- Difference equations. --- Functional equations. --- Calculus of Variations and Optimal Control; Optimization. --- Difference and Functional Equations. --- Algorithm Analysis and Problem Complexity. --- Analysis. --- Maxima and minima --- Mathematical optimization. --- Computer software. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Software, Computer --- Computer systems --- Equations, Functional --- Functional analysis --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Operations research --- Simulation methods --- System analysis --- 517.1 Mathematical analysis --- Algorism --- Algebra --- Arithmetic --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Foundations