04678nam 2200601Ia 450 991096088810332120200520144314.01-282-28924-197866122892480-08-095527-4(CKB)1000000000789985(EBL)452978(OCoLC)316568668(SSID)ssj0000336919(PQKBManifestationID)12061766(PQKBTitleCode)TC0000336919(PQKBWorkID)10301850(PQKB)10429428(MiAaPQ)EBC452978(BIP)46214154(EXLCZ)99100000000078998520090320d1965 uy 0engur|n|---|||||txtrdacontentcrdamediacrrdacarrierDynamic programming and the calculus of variations /Stuart E. DreyfusNew York Academic Press19651 online resource (xix, 248 pages) illustrationsMathematics in science and engineering ;210-12-221850-7 Includes bibliographical references and index.Front Cover; Dynamic Programming and the Calculus of Variations; Copyright Page; Contents; Preface; Chapter I. Discrete Dynamic Programming; 1. Introduction; 2. An Example of a Multistage Decision Process Problem; 3. The Dynamic Programming solution of the Example; 4. The Dynamic Programming Formalism; 5. Two Properties of the Optimal Value Function; 6. An Alternative Method of Solution; 7. Modified Properties of the Optimal Value Function; 8. A Property of Multistage Decision Processes; 9. Further Illustrative Examples; 10. Terminal Control Problems; 11. Example of a Terminal Control Problem12. Solution of the Example; 13. Properties of the Solution of a Terminal Control Problem; 14. Summary; Chapter II. The Classical Variational Theory; 1. Introduction; 2. A Problem; 3. Admissible Solutions; 4. Functions; 5. Functionals; 6. Minimization and Maximization; 7. Arc-Length; 8. The Simplest General Problem; 9. The Maximum-Value Functional; 10. The Nature of Necessary Conditions; 11. Example; 12. The Nature of Sufficient Conditions; 13. Necessary and Sufficient Conditions; 14. The Absolute Minimum of a Functional; 15. A Relative Minimum of a Function16. A Strong Relative Minimum of a Functional; 17. A Weak Relative Minimum of a Functional; 18. Weak Variations; 19. The First and Second Variations; 20. The Euler-Lagrange Equation; 21. Example; 22. The Legendre Condition; 23. The Second Variation and the Second Derivative; 24. The Jacobi Necessary Condition; 25. Example; 26. Focal Point; 27. Geometric Conjugate Points; 28. The Weierstrass Necessary Condition; 29. Example; 30. Discussion; 31. Transversality Conditions; 32. Corner Conditions; 33. Relative Summary; 34. Sufficient Conditions; 35. Hamilton-Jacobi Theory36. Other Problem Formulations; 37. Example of a Terminal Control Problem; 38. Necessary Conditions for the Problem of Mayer; 39. Analysis of the Example Problem; 40. Two-Point Boundary Value Problems; 41. A Well-Posed Problem; 42. Discussion; 43. Computational Solution; 44. Summary; References to Standard Texts; Chapter III. The Simplest Problem; 1. Introduction; 2. Notation; 3. The Fundamental Partial Differential Equation; 4. A Connection with Classical Variations; 5. A Partial Differential Equation of the Classical Type; 6. Two Kinds of Derivatives7. Discussion of the Fundamental Partial Differential Equation; 8. Characterization of the Optimal Policy Function; 9. Partial Derivatives along Optimal Curves; 10. Boundary Conditions for the Fundamental Equation: I; 11. Boundary Conditions: II; 12. An Illustrative Example-Variable End Point; 13. A Further Example-Fixed Terminal Point; 14. A Higher-Dimensional Example; 15. A Different Method of Analytic Solution; 16. An Example; 17. From Partial to Ordinary Differential Equations; 18. The Euler-Lagrange Equation; 19. A Second Derivation of the Euler-Lagrange Equation;20. The Legendre Necessary ConditionDynamic programming and the calculus of variationsMathematics in science and engineering ;v. 21.Calculus of variationsDynamic programmingCalculus of variations.Dynamic programming.519.92Dreyfus Stuart E151MiAaPQMiAaPQMiAaPQBOOK9910960888103321Dynamic programming and the calculus of variations346432UNINA03172oam 22004452 450 991095353430332120251116185023.01-000-04840-30-429-35260-31-000-04838-1(CKB)4100000010159245(MiAaPQ)EBC6036738(OCoLC)1128887802(OCoLC-P)1128887802(FlBoTFG)9780429352607(EXLCZ)99410000001015924520191122d2020 uy 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierA brief history of knowledge for social science researchers before method /Deborah Court1 Edition.New York :Routledge,2020.1 online resource (89 pages)0-367-37079-4 Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- 1 How Can We Think about Research? A Gallery of Heroes -- 2 Epistemology and its Relevance to Research -- 3 A Historical Sketch of knowledge in the Western world: the Greeks through the Middle Ages -- 4 A Historical Sketch of knowledge in the Western world: from the Middle Ages to the Enlightenment -- 5 A Historical Sketch of knowledge in the Western world: from the Enlightenment onward -- 6 Are we there yet? The birth and development of the social sciences -- 7 How Can We Think about theory? A gallery of heroes -- 8 A Brief History of knowledge, and the vistas beyond -- Index."A Brief History of Knowledge for Social Science Researchers outlines a history of knowledge from Ancient Greece to present day, in Europe and the Western world. This outline provides the basis for understanding where various research methods originate, and their epistemological, historical, political and social roots. This book provides social science researchers with an understanding of how research methods developed, and how their truth criteria, and what is accepted as knowledge, spring from human history. Research is often reduced to data collection, results and publication in the stressful, results-oriented academic environment. But research is a human enterprise, a product of both individual creativity and historical, political and social conditions. This book will focus on how shared research criteria (as we know them today) were developed through the work and thought of philosophers, social activists and researchers. This book will be useful for graduate and post-graduate students, particularly those studying Research Methods, and Philosophy of Science courses; and for experienced social science researchers who wish to understand how research methods have developed in human history"--Provided by publisher.Social sciencesHistorySocial sciencesHistory.300.9001.09Court Deborah1950-1882187OCoLC-POCoLC-PBOOK9910953534303321A brief history of knowledge for social science researchers4497272UNINA