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 Lao, Dazhong.
 Singapore : Springer, [2021]
 Description
 Book — 1 online resource (1006 pages)
 Summary

 Preliminaries. Variational Problems with Fixed Boundaries. Sufficient Conditions of Extrema of Functionals. Problems with Variable Boundaries. Variational Problems of Conditional Extrema. Variational Problems in Parametric Forms. Variational Principles. Methods of Variational Problems. Variational Principles in Mechanics and Their Applications. Variational Problems of Functionals with Vector, Tensor and Hamiltonian Operators.
 .
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2. Lectures on the calculus of variations [1904]
 Bolza, O. (Oskar), 18571942.
 Dover edition, [2018 edition].  Mineola, New York : Dover Publications, Inc., 2018.
 Description
 Book — 1 online resource.
 Noguchi, Junjirō, 1948 author.
 Singapore : Springer, 2016.
 Description
 Book — 1 online resource (xvi, 397 pages) : illustrations (some color) Digital: text file.PDF.
 Summary

 Holomorphic Functions. Oka's First Coherence Theorem. Sheaf Cohomology. Holomorphically Convex Domains and OkaCartan's Fundamental Theorem. Domains of Holomorphy. Analytic Sets and Complex Spaces. Pseudoconvex Domains and Oka's Theorem. Cohomology of Coherent Sheaves and Kodaira's Embedding Theorem. On Coherence. Appendix. References. Index. Symbols.
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 Freguglia, Paolo, author.
 Switzerland : Birkhäuser, [2016]
 Description
 Book — xii, 293 pages : illustrations ; 24 cm
 Summary

 Preface. Some Introductory Material. The Brachystochrone Problem: Johann and Jakob Bernoulli. Isoperimetrical Problems: Jakob and Johann Bernoulli. Shortest Lines and Geodesics. Euler's Memoirs of 1738 and 1741. Euler's Method us Inveniendi. Lagrange's deltaCalculus. Bibliography. Index of Names. Subject Index.
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QA315 .F74 2016  CHECKEDOUT Request 
 Burns, John A. (John Allen), 1945
 Boca Raton : CRC Press, c2014.
 Description
 Book — xvii, 544 p. : ill. ; 24 cm.
 Summary

 Calculus of Variations Historical Notes on the Calculus of Variations Some Typical Problems Some Important Dates and People
 Introduction and Preliminaries Motivating Problems Mathematical Background Function Spaces Mathematical Formulation of Problems
 The Simplest Problem in the Calculus of Variations The Mathematical Formulation of the SPCV The Fundamental Lemma of the Calculus of Variations The First Necessary Condition for a Global Minimizer Implications and Applications of the FLCV
 Necessary Conditions for Local Minima Weak and Strong Local Minimizers The Euler Necessary Condition  (I) The Legendre Necessary Condition  (III) Jacobi Necessary Condition  (IV) Weierstrass Necessary Condition  (II) Applying the Four Necessary Conditions
 Sufficient Conditions for the Simplest Problem A Field of Extremals The Hilbert Integral Fundamental Sufficient Results
 Summary for the Simplest Problem
 Extensions and Generalizations Properties of the First Variation The Free Endpoint Problem The Simplest Point to Curve Problem Vector Formulations and Higher Order Problems Problems with Constraints: Isoperimetric Problem Problems with Constraints: Finite Constraints An Introduction to Abstract Optimization Problems
 Applications Solution of the Brachistochrone Problem Classical Mechanics and Hamilton's Principle A Finite Element Method for the Heat Equation Optimal Control Optimal Control Problems An Introduction to Optimal Control Problems The Rocket Sled Problem Problems in the Calculus of Variations Time Optimal Control
 Simplest Problem in Optimal Control SPOC: Problem Formulation The Fundamental Maximum Principle Application of the Maximum Principle to Some Simple Problems
 Extensions of the Fundamental Maximum Principle A FixedTime Optimal Control Problem Application to Problems in the Calculus of Variations Application to the Farmer's Allocation Problem Application to a Forced Oscillator Control Problem Application to the Linear Quadratic Control Problem The Maximum Principle for a Problem of Bolza The Maximum Principle for Nonautonomous Systems Application to the Nonautonomous LQ Control Problem
 Linear Control Systems Introduction to Linear Control Systems Linear Control Systems Arising from Nonlinear Problems Linear Quadratic Optimal Control The Riccati Differential Equation for a Problem of Bolza Estimation and Observers The Time Invariant Infinite Interval Problem The Time Invariant MinMax Controller
 Problems appear at the end of each chapter.
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QA315 .B85 2014  Unknown 
 Kristály, Alexandru.
 Cambridge, UK ; New York : Cambridge University Press, 2010.
 Description
 Book — xv, 368 p. : ill. ; 24 cm.
 Summary

 Foreword Jean Mawhin
 Preface
 Part I. Variational Principles in Mathematical Physics: 1. Variational principles
 2. Variational inequalities
 3. Nonlinear eigenvalue problems
 4. Elliptic systems of gradient type
 5. Systems with arbitrary growth nonlinearities
 6. Scalar field systems
 7. Competition phenomena in Dirichlet problems
 8. Problems to Part I
 Part II. Variational Principles in Geometry: 9. Sublinear problems on Riemannian manifolds
 10. Asymptotically critical problems on spheres
 11. Equations with critical exponent
 12. Problems to Part II
 Part III. Variational Principles in Economics: 13. Mathematical preliminaries
 14. Minimization of costfunctions on manifolds
 15. Best approximation problems on manifolds
 16. A variational approach to Nash equilibria
 17. Problems to Part III
 Appendix A. Elements of convex analysis
 Appendix B. Function spaces
 Appendix C. Category and genus
 Appendix D. Clarke and Degiovanni gradients
 Appendix E. Elements of setvalued analysis
 References
 Index.
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QA315 .K75 2010  Unknown 
 Introduction au calcul des variations. English
 Dacorogna, Bernard, 1953
 2nd ed.  London : Imperial College Press ; Hackensack, NJ : Distributed by World Scientific Pub., c2009.
 Description
 Book — xii, 285 p. : ill. ; 24 cm.
 Summary

 Preliminaries
 Classical Methods
 Direct Methods: Existence
 Direct Methods: Regularity
 Minimal Surfaces
 Isoperimetric Inequality
 Solutions to the Exercises.
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QA315 .D34313 2009  Available 
 Dacorogna, Bernard, 1953
 2nd ed.  New York : Springer, c2008.
 Description
 Book — xii, 619 p. : ill. ; 25 cm.
 Summary

 Introduction. Convex Analysis and the Scalar Case. Convex Sets and Convex Functions. Lower Semicontinuity and Existence Theorems. The one Dimensional Case. Quasiconvex Analysis and the Vectorial Case. Polyconvex, Quasiconvex and Rank one Convex Functions. Polyconvex, Quasiconvex and Rank one Convex Envelopes. Polyconvex, Quasiconvex and Rank one Convex Sets. Lower Semi Continuity and Existence Theorems in the Vectorial Case. Relaxation and Non Convex Problems. Relaxation Theorems. Implicit Partial Differential Equations. Existence of Minima for Non Quasiconvex Integrands. Miscellaneous. Function Spaces. Singular Values. Some Underdetermined Partial Differential Equations. Extension of Lipschitz Functions on Banach Spaces. Bibliography. Index. Notations.
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QA315 .D34 2008  Available 
 Dacorogna, Bernard, 1953
 2nd ed.  New York, N.Y. : Springer, c2008.
 Description
 Book — xii, 619 p. : ill.
 Borwein, Jonathan M.
 New York : Springer, c2005.
 Description
 Book — vi, 362 p. : ill.
11. The calculus of variations [2004]
 Van Brunt, B. (Bruce)
 New York : SpringerVerlag, c2004.
 Description
 Book — xiii, 290 p. : ill. ; 25 cm.
 Summary

 The First Variation. Some Generalizations. Isoperimetric Problems. Applications to Eigenvalue Problems. Holonomic and Nonholonomic Constraints. Problems with Variable Endpoints. The Hamiltonian Formulation. Noether's Theorem. The Second Variation.
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QA315 .V35 2004  Unknown 
12. Introduction to the calculus of variations [2004]
 Introduction au calcul des variations. English
 Dacorogna, Bernard, 1953
 London : Imperial College Press ; Singapore ; Hackensack, N.J. : Distributed by World Scientific, c2004.
 Description
 Book — xii, 228 p. : ill. ; 24 cm.
 Summary

 Preliminaries
 Classical Methods
 Direct Methods
 Regularity
 Minimal Surfaces
 Isoperimetric Inequality
 Solutions to the Exercises.
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The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology. This book serves both as a guide to the expansive existing literature and as an aid to the nonspecialist  mathematicians, physicists, engineers, students or researchers  in discovering the subjects most important problems, results and techniques. Despite the aim of addressing nonspecialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions. The book, containing more than seventy exercises with detailed solutions, is well designed for a course both at the undergraduate and graduate levels.
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QA315 .D34313 2004  Available 
13. Six themes on variation [2004]
 Providence, RI : American Mathematical Society, c2004.
 Description
 Book — xi, 153 p. : ill. ; 22 cm.
 Summary

 Calculus of variations: What does "variations" mean? by F. Jones How many equilibria are there? An introduction to Morse theory by R. Forman Aye, there's the rub. An inquiry into why a plucked string comes to rest by S. J. Cox Proof of the double bubble conjecture by F. Morgan Minimal surfaces, flat cone spheres and moduli spaces of staircases by M. Wolf Hold that light! Modeling of traffic flow by differential equations by B. L. Keyfitz.
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QA315 .S59 2004  Available 
 Giusti, Enrico.
 Singapore ; Hackensack, N.J. : World Scientific Pub. Co., c2003.
 Description
 Book — vii, 403 p.
 Summary

 SemiClassical Theory
 Integrable Functions
 Sobolev Spaces
 Semicontinuity
 QuasiConvex Functionals
 QuasiMinima
 Regularity of QuasiMinima
 First Derivatives
 Partial Regularity
 Higher Derivatives.
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15. Calculus of variations [1998]
 Jost, Jürgen, 1956
 Cambridge, UK ; New York : Cambridge University Press, c1998.
 Description
 Book — xvi, 323 p. ; 24 cm.
 Summary

 Part I. OneDimensional Variational Problems: 1. The classical theory
 2. Geodesic curves
 3. Saddle point constructions
 4. The theory of Hamilton and Jacobi
 5. Dynamic optimization
 Part II. Multiple Integrals in the Calculus of Variations: 6. Lebesgue integration theory
 7. Banach spaces
 8. Lp and Sobolev spaces
 9. The direct methods
 10. Nonconvex functionals: relaxation
 11. Gconvergence
 12. BVfunctionals and Gconvergence: the example of Modica and Mortola
 Appendix A. The coarea formula
 Appendix B. The distance function from smooth hypersurfaces
 13. Bifurcation theory
 14. The PalaisSmale condition and unstable critical points of variational problems.
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QA315 .J67 1998  Unknown 
 Giaquinta, Mariano, 1947
 New York : Springer, 1998.
 Description
 Book — 2 v.
 Summary

 Part I: General Measure Theory. Integer Rectifiable Currents. Cartesian Maps. Cartesian Currents in Euclidean Spaces. Cartesian Currents in Riemannian Manifolds. Part II: Regular Variational Integrals. Finite Elasticity and Weak Diffeomorphisms. The Dirichlet Integral in Sobolev Spaces. The Dirichlet Energy for Maps into S2. Regular and Non Regular Integrals. The Non Parametric Area Functional.
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QA316 .G53 1998 V.1  Available 
QA316 .G53 1998 V.2  Available 
 Buttazzo, Giuseppe.
 Oxford : Clarendon Press, 1998.
 Description
 Book — viii, 262 p. : ill. ; 24 cm.
 Summary

 Introduction
 1. Classical problems and indirect methods
 2. Absolutely continuous functions and Sobolev spaces
 3. Semicontinuity and existence results
 4. Regularity of minimizers
 5. Some applications
 6. Scholia.
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QA315 .B867 1998  Available 
18. Variational analysis [1998]
 Rockafellar, R. Tyrrell, 1935
 Berlin ; New York : Springer, c1998.
 Description
 Book — xiii, 733 p. : ill. ; 25 cm.
 Summary

 Max and Min. Convexity. Cones and Cosmic Closure. Set Convergence. SetValued Mappings. Variational Geometry. Epigraphical Limits. Subderivatives and Subgradients. Lipschitzian Properties. Subdifferential Calculus. Dualization. Monotone Mappings. SecondOrder Theory. Measurability. References. Index of Statements. Index of Notation. Index of Topics.
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QA315 .R63 1998  Unknown 
19. Calculus of variations [1996]
 Giaquinta, Mariano, 1947
 Berlin ; New York : SpringerVerlag, 1996.
 Description
 Book — 2 v. : ill. ; 24 cm.
 Summary

 1. The Lagrangian formalism
 2. The Hamiltonian formalism.
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This longawaited book by two of the foremost researchers and writers in the field is the first part of a treatise that covers the subject in breadth and depth, paying special attention to the historical origins, partly in applications, e. g. from geometrical optics, of parts of the theory. A variety of aids to the reader is provided: besides the very detailed table of contents, an introduction to each chapter, section and subsection, an overview of the relevant literature (in Vol. 2) plus the references in the Scholia to each chapter, in the (historical) footnotes, and in the bibliography, and finally an index of the examples used throughout the book. Both individually and collectively these volumes have already become standard references.
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QA315 .G46 1996 V.1  CHECKEDOUT Request 
QA315 .G46 1996 V.2  Unknown 
20. Metodi diretti nel calcolo delle variazioni [1994]
 Giusti, Enrico.
 Bologna : Unione matematica italiana, 1994.
 Description
 Book — v, 422 p. ; 25 cm.
 Online
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QA315 .G48 1994  Available 
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