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 needed: *mirtitles*

4-shared link here

Password, if required, for 4shared files:

www.mirtitles.org

Facing problems while extracting? See *FAQs*

Table of Contents

**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

**ANSWERS AND HINTS 202**

**BIBLIOGRAPHY 215**

**INDEX 217**

WONDERFUL COLLECTION OF BOOKS. THANKS FOR UPLOADING THEM

LikeLike

thanks a lot, great effort

LikeLike

Some more books below

http://archive.org/search.php?query=mir%20publishers

LikeLike

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!

LikeLike

Jovan,

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

D

LikeLike

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

LikeLike

Book cover is missing here

LikeLike

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

LikeLike

normalin

Are you asking for a problem book in Calculus?

LikeLike

excuse me

the password doesn’t pass with the file

LikeLike

Does anybody has problem to download in MacBook Air computer

LikeLike

@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.

LikeLike

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

LikeLike

@Gordhan, did you provided the password for it when asked? Since the rar files are password protected (password provided in the page!). Provide the password and try to extract to a folder then you can access the pdf file. Let me know if you still face any issues.

LikeLike

pdf and djvu file available at

http://libgen.io/book/index.php?md5=886F22B5ED7572D36B0C6946384A1526 pdf and

http://libgen.io/book/index.php?md5=E4A1A290A519D020522E2576A6B22AE5 djvu

LikeLike