Lectures on the Calculus of Variations by Harris Hancock

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About this book :-
This book is a comprehensive guide to the calculus of variations, with a focus on the Weierstrassian theory. The calculus of variations is a branch of mathematics that deals with finding the optimal solution to a functional problem. The book covers the basic concepts of the calculus of variations, including the Euler-Lagrange equation, the Hamiltonian, and the Jacobi equation. It also delves into the Weierstrassian theory, which is a more rigorous approach to the calculus of variations. The book is aimed at students and researchers in mathematics and physics who are interested in the calculus of variations. It is written in a clear and concise style, with numerous examples and exercises to help readers understand the concepts. Overall, "Lectures on the Calculus of Variations: The Weierstrassian Theory" is a valuable resource for anyone interested in this fascinating field of mathematics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

Book Detail :-
This book has following details information.
Title: Lectures on the Calculus of Variations by Harris Hancock by NA
Publisher: Cincinnati University Press
Series: eBooksDirectory
Year: 1904
Pages: 322
Type: PDF
Language: English
ISBN-10 #: 1429703113
ISBN-13 #: 978-1429703116
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
1. PHESENTATION OF THE PRINCIPAL PROBLEMS OF THE CALCULUS OF VARIATIONS. 2. EXAMPLES OF SPECIAL VARIATIONS OF CURVES. APPLICATIONS TO THE CATENARY. 3. PROPERTIES OF THE CATENARY. 4. PROPERTIES OF THE FUNCTION F{^X, y, X , y). 5. THE VARIATION OF CURVES EXPRESSED ANALYTICALLY. THE FIRST VARIATION. 6. THE FORM OF THE SOLUTION OF THE DIFFERENTIAL EQUATION G= 0. 7. REMOVAL OF CERTAIN LIMITATIONS THAT HAVE BEEN MADE. INTEGRATION OF THE DIFFERENTIAL EQUATION G=,0 8. THE SECOND VARIATION; ITS SIGN DETERMINED BY THAT OF THE FITNCTION F\. 9. CONJUGATE POINTS. 10. THE CRITERIA THAT HAVE BEEN DERIVED UNDER THE ASSUMPTION OF CERTAIN SPECIAL VARIATIONS ARE ALSO SUFFICIENT FOR THE ESTABLISHMENT OF THE FORMULA HITHERTO EMPLOYED. 11. THE NOTION OF A FIELD ABOUT THE CURVE WHICH OFFERS A MINIMUM OR A MAXIMUM VALUE OF THE INTEGRAL. THE GEOMETRICAL MEANING OF THE CONJUGATE POINTS. 12. A FOURTH AND FINAL CONDITION FOR THE EXISTENCE OF A MAXIMUM OR A MINIMUM, AND A PROOF THAT THE CONDITIONS WHICH HAVE BEEN GIVEN ARE SUFFICIENT. 13. STATEMENT OF THE PROBLEM. DERIVATION OF THE NECESSARY CONDITIONS. 14. THE ISOPERIMETRICAL PROBLEM. 15. RESTRICTED VARIATIONS. THE THEOREMS OF STEINER. 16. THE DETERMINATION OF THE CURVE OF GIVEN LENGTH AND GIVEN END-POINTS, WHOSE CENTER OF GRAVITY LIES LOWEST. 17. THE SUFFICIENT CONDITIONS. 18. PROOF OF TWO THEOREMS -WHICH HAVE BEEN ASSUMED IN THE PREVIOUS CHAPTER.

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