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

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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

thanks a lot, great effort

Some more books below

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

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!

Jovan,

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

D

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

Book cover is missing here

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

normalin

Are you asking for a problem book in Calculus?

excuse me

the password doesn’t pass with the file