Lectures on the Calculus of Variations by Oskar Bolza
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About this book :-
Calculus variation is a field concerned with finding functions that minimize or maximize certain quantities. This book provides a rigorous and detailed introduction to the classical theory of the calculus of variations. It provides clear definitions of the fundamental concepts, sharp formulations of the problems, and rigorous demonstrations of their solutions.
The book also covers foundational topics like the Euler–Lagrange equation, conditions for extrema, and isoperimetric problems, as well as more advanced ideas like Weierstrass’s sufficiency conditions and existence theorems. It gives clear explanations and lots of examples. While the style is old-fashioned and doesn’t use modern functional analysis tools, the book remains valuable for understanding the roots of variational calculus.
Book Detail :-
This book has following details information.
Title:
Lectures on the Calculus of Variations by Oskar Bolza
Publisher:
The University of Chicago press
Year:
1904
Pages:
304
Type:
PDF
Language:
English
ISBN-10 #:
141818201X
ISBN-13 #:
N/A
License:
N\A
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About Author :-
The author NA
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Book Contents :-
This book has following table of contents.
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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