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Lectures on the Calculus of Variations by Oskar Bolza



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About this book :-
The text addresses basic problems with sufficient generality and rigor to offer a sound introduction for serious study. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions. Many examples are solved completely, and systematic references are given for each theorem upon its first appearance. Initial chapters address the first and second variation of the integral, and succeeding chapters cover the sufficient conditions for an extremum of the integral and Weierstrass's theory of the problem in parameter-representation; Kneser's extension of Weierstrass's theory to cover the case of variable end-points; and Weierstrass's theory of the isoperimetric problems. The final chapter presents a thorough proof of Hilbert's existence theorem.

Book Detail :-
This book has following details information.
Title: Lectures on the Calculus of Variations by Oskar Bolza by NA
Publisher: The University of Chicago press
Series: eBooksDirectory
Year: 1904
Pages: 304
Type: PDF
Language: English
ISBN-10 #: 141818201X
ISBN-13 #: N/A
Country: Pakistan
License: N\A
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About Author :-
The author NA NA

Book Contents :-
conver the following topics.
1. THE FIRST VARIATION OF THE INTEGRAL F(x, y,y')dx from x1 to x0 2. THE SECOND VARIATION OF THE INTEGRAL F(x y y')dx from x1 to x0 3. SUFFICIENT CONDITIONS FOR AN EXTREMUM OF THE INTEGRAL F(x y y')dx from x1 to x0 4. WEIERSTRASS'S THEORY OF THE PROBLEM IN PARAMETER-REPRESENTATION 5. KNESER'S THEORY 6. WEIERSTRASS'S THEORY OF THE ISOPERIMETRIC PROBLEMS 7. HILBERT'S EXISTENCE THEOREM

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