## Problems and Exercises in the Calculus of Variations – Krasnov, Makarenko, Kiselev

In this post we will see Problems and Exercises in the Calculus of
Variations by M. L. Krasnov, G. I. Makarenko, A. I. Kiselev .

The calculus of variations is one of the most important divisions of
classical mathematical analysis as regards applications.The authors’
aim was to supply the reader with a certain minimum of problems
covering the basic divisions of the classical calculus of variations,
and they deliberately avoided questions pertaining to the theory of
optimal control.

This book was translated from the Russian by George Yankovsky. The book was published by first Mir Publishers in 1975.

All credits to the original uploader.

DJVU | 3.1 MB | Pages: 221 | Bookmarked | OCR
You can get the book here.
For magnet / torrent links go here.

Password, if required, for 4shared files:

`www.mirtitles.org`

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CONTENTS
Introduction 6
Preliminary Remarks 7

CHAPTER I.
THE EXTREMUM OF A FUNCTION OF MANY VARIABLES

1. Absolute Extremum 9
2. Conditional Extremum 19

CHAPTER II.
EXTREMA OF FUNCTIONALS

3. The Functional. The Variation of a Functional and Its Properties 27
4. An Elementary Problem in the Calculus of Variations. Euler’s Equation 54
5. Generalizations of the Elementary Problem of the Calculus of Variations 75
6. Invariance of Euler’s Equation 85
7. Field of Extremals 88
8. Sufficient Conditions for the Extremum of a Functional 102
9. Conditional Extremum 118
10. Moving Boundary Problems 137
11. Discontinuous Problems. One-Sided Variations  151
12. The Hamilton-Jacobi Theory. The Variational Principles of Mechanics

CHAPTER III.
DIRECT METHODS IN THE CALCULUS OF VARIATIONS

13. Euler’s Finite-Difference Method 177
14. Ritz Method. Kantorovich Method 179
15. Variational Methods for Finding Eigenvalues and Eigenfunctions 188

BIBLIOGRAPHY 215

INDEX 217

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### 15 Responses to Problems and Exercises in the Calculus of Variations – Krasnov, Makarenko, Kiselev

1. ANIL says:

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2. m95 says:

thanks a lot, great effort

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3. kantikiranKanti Kiran says:
4. Jovan says:

I was wondering if there is a chance of you uploading books from the Mathematical Analysis for Engineers series by M. Krasnov, A. Kiselev, G. Makarenko and I E. Shikin… It is a much needed literature for me and many of my fellow students, and I would be very grateful if you did such a thing. I, of course, supposed that you are in possession of the titles. In case I am wrong, please let me know. Thank you for a tremendous web site, all of the books that are here are an inheritance of colossal value!

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• The Mitr says:

Jovan,

We might see these books in the future, please wait.

D

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• Jovan says:

In case you do get a hold on them, please write a response in this part of the website. Thank you once again!

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5. Siddharth says:

Book cover is missing here

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6. normalin says:

please, a book with the ALL problems solved step by step, please, i need this, anyone????

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• Siddharth says:

normalin
Are you asking for a problem book in Calculus?

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excuse me
the password doesn’t pass with the file

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8. Gordhan says:

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@gordhan, What issue you are facing? Any error message or error code? I believe only 4 shared link is working. Try that. Remember you should log in to download the file.

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9. Gordhan says:

Thanks for reply @ desperadomar, I was using was using wrong link. However, when I use 4 shared link I am facing rar file conversion problem. I just double click rar file, After log in again, read ERROR as “The archive is incomplete”.
How do you convert rar file to pdf.
Thanks

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