Lectures on the Calculus of Variations (the Weierstrassian Theory)
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Book 1
Book 2
Book 3
Home > History and Archaeology > History > Lectures on the Calculus of Variations (the Weierstrassian Theory)
Lectures on the Calculus of Variations (the Weierstrassian Theory)

Lectures on the Calculus of Variations (the Weierstrassian Theory)


     0     
5
4
3
2
1



Out of Stock


Notify me when this book is in stock
X
About the Book

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1904 edition. Excerpt: ...123. In this connection a discovery made by Jacobi (Crelle's Journal, bd. 17, p. 68) is of great use. He showed that with the integration of the differential equation G=o, also that of the differential equation J = o is performed. We are then able to derive the general expression for, and may determine completely whether and when u--O. We shall next derive the general solution of the equation J = o, it being presupposed that the differential equation G=o admits of a general solution. We derived the first variation in the form We may form the second variation by causing in this expression G alone to vary, and then w alone, and by adding the results. It follows that Since the differential equation G=o is supposed satisfied, we dy dAdy'l and also Gi = y'G, G2=-x' G. When in the expression for Gx, the substitutions and if we take into consideration 3), 4), 6) and 7) of the last Chapter, we may write the above result in the form: In an analogous manner, we have When these values are substituted in (), we have Hence from (o) we have By the previous method we found the second variation to be see formula 8) of the last Chapter These two expressions should agree as to a constant term. The difference of the integrals is k to but since it is seen that f r-dw', D=rwF'-dtV The formula (&) is When we compare this with 12) of the preceding Chapter, the differential equation for u, viz.: it is seen that as soon as we find a quantity w for which 8(7=0, we have a corresponding integral of the differential equation for u. 125. The total variation of G is &G=G(x+eg1+, ?+Vi+-ih + + +..../ + Vi +.1h'+...' S'+r"+ Ts +..-.)-G (x, y, x', /,,"/') =e8G + #G+ where 8(7, as found in the preceding article, has the value...


Best Sellers


Product Details
  • ISBN-13: 9781154971262
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 60
  • Spine Width: 3 mm
  • Width: 189 mm
  • ISBN-10: 1154971260
  • Publisher Date: 01 Oct 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 127 gr

Related Categories

Similar Products

Add Photo
Add Photo

Customer Reviews

REVIEWS      0     
Click Here To Be The First to Review this Product
Lectures on the Calculus of Variations (the Weierstrassian Theory)
Rarebooksclub.com -
Lectures on the Calculus of Variations (the Weierstrassian Theory)
Writing guidlines
We want to publish your review, so please:
  • keep your review on the product. Review's that defame author's character will be rejected.
  • Keep your review focused on the product.
  • Avoid writing about customer service. contact us instead if you have issue requiring immediate attention.
  • Refrain from mentioning competitors or the specific price you paid for the product.
  • Do not include any personally identifiable information, such as full names.

Lectures on the Calculus of Variations (the Weierstrassian Theory)

Required fields are marked with *

Review Title*
Review
    Add Photo Add up to 6 photos
    Would you recommend this product to a friend?
    Tag this Book Read more
    Does your review contain spoilers?
    What type of reader best describes you?
    I agree to the terms & conditions
    You may receive emails regarding this submission. Any emails will include the ability to opt-out of future communications.

    CUSTOMER RATINGS AND REVIEWS AND QUESTIONS AND ANSWERS TERMS OF USE

    These Terms of Use govern your conduct associated with the Customer Ratings and Reviews and/or Questions and Answers service offered by Bookswagon (the "CRR Service").


    By submitting any content to Bookswagon, you guarantee that:
    • You are the sole author and owner of the intellectual property rights in the content;
    • All "moral rights" that you may have in such content have been voluntarily waived by you;
    • All content that you post is accurate;
    • You are at least 13 years old;
    • Use of the content you supply does not violate these Terms of Use and will not cause injury to any person or entity.
    You further agree that you may not submit any content:
    • That is known by you to be false, inaccurate or misleading;
    • That infringes any third party's copyright, patent, trademark, trade secret or other proprietary rights or rights of publicity or privacy;
    • That violates any law, statute, ordinance or regulation (including, but not limited to, those governing, consumer protection, unfair competition, anti-discrimination or false advertising);
    • That is, or may reasonably be considered to be, defamatory, libelous, hateful, racially or religiously biased or offensive, unlawfully threatening or unlawfully harassing to any individual, partnership or corporation;
    • For which you were compensated or granted any consideration by any unapproved third party;
    • That includes any information that references other websites, addresses, email addresses, contact information or phone numbers;
    • That contains any computer viruses, worms or other potentially damaging computer programs or files.
    You agree to indemnify and hold Bookswagon (and its officers, directors, agents, subsidiaries, joint ventures, employees and third-party service providers, including but not limited to Bazaarvoice, Inc.), harmless from all claims, demands, and damages (actual and consequential) of every kind and nature, known and unknown including reasonable attorneys' fees, arising out of a breach of your representations and warranties set forth above, or your violation of any law or the rights of a third party.


    For any content that you submit, you grant Bookswagon a perpetual, irrevocable, royalty-free, transferable right and license to use, copy, modify, delete in its entirety, adapt, publish, translate, create derivative works from and/or sell, transfer, and/or distribute such content and/or incorporate such content into any form, medium or technology throughout the world without compensation to you. Additionally,  Bookswagon may transfer or share any personal information that you submit with its third-party service providers, including but not limited to Bazaarvoice, Inc. in accordance with  Privacy Policy


    All content that you submit may be used at Bookswagon's sole discretion. Bookswagon reserves the right to change, condense, withhold publication, remove or delete any content on Bookswagon's website that Bookswagon deems, in its sole discretion, to violate the content guidelines or any other provision of these Terms of Use.  Bookswagon does not guarantee that you will have any recourse through Bookswagon to edit or delete any content you have submitted. Ratings and written comments are generally posted within two to four business days. However, Bookswagon reserves the right to remove or to refuse to post any submission to the extent authorized by law. You acknowledge that you, not Bookswagon, are responsible for the contents of your submission. None of the content that you submit shall be subject to any obligation of confidence on the part of Bookswagon, its agents, subsidiaries, affiliates, partners or third party service providers (including but not limited to Bazaarvoice, Inc.)and their respective directors, officers and employees.

    Accept

    Fresh on the Shelf


    Inspired by your browsing history


    Your review has been submitted!

    You've already reviewed this product!