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Field name	Details
Dewey Class	515
Title	Variational Calculus with Elementary Convexity ([EBook] /) / by John L. Troutman.
Author	Troutman, John L.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1983.
Physical Details	XIV, 365 p. : online resource.
Series	Undergraduate texts in mathematics 0172-6056
ISBN	9781468401585
Summary Note	The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.:
Contents note	0 Review of Optimization in ?d -- Problems -- One Basic Theory -- 1 Standard Optimization Problems -- 2 Linear Spaces and Gâteaux Variations -- 3 Minimization of Convex Functions -- 4 The Lemmas of Lagrange and Du Bois-Reymond -- 5 Local Extrema in Normed Linear Spaces -- 6 The Euler-Lagrange Equations -- Two Advanced Topics -- 7 Piecewise C1 Extremal Functions -- 8 Variational Principles in Mechanics -- 9* Sufficient Conditions for a Minimum -- A.1. The Intermediate and Mean Value Theorems -- A.2. The Fundamental Theorem of Calculus -- A.3. Partial Integrals: Leibniz’ Formula -- A.4. An Open Mapping Theorem -- A.5. Families of Solutions to a System of Differential Equations -- A.6. The Rayleigh Ratio -- Answers to Selected Problems.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-0158-5
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Troutman, John L. . Corporate Authors: SpringerLink (Online service) . Series: Undergraduate texts in mathematics . Classification: 515 .

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Variational Calculus with Elementary Convexity

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