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Description
Calculus of VariationsThis concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems. Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency
This concise text offers both professionals and students an introduction to the fundamentals and standard methods of the calculus of variations. In addition to surveys of problems with fixed and movable boundaries, it explores highly practical direct methods for the solution of variational problems.Topics include the method of variation in problems with fixed boundaries; variational problems with movable boundaries and other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter features numerous illustrative problems, and solutions appear at the end.
Binding Type: Paperback
Publisher: Dover Publications
Published: 01/15/2007
ISBN: 9780486457994
Pages: 178
Weight: 0.33lbs
Size: 8.42h x 5.50w x 0.52d
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★★★★★ 5
Caution can cause addiction
Style: Sport, Size: 12in
My dog has become addicted to tennis balls because of this! She sees the blue handle and she immediately loses her mind! I love it because I don't have to bend down as far to pick up the ball, which is amazing after 2 back surgeries.
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Reviewed in the United States on February 25, 2026
★★★★★ 3
12 " too short, no direction.
Style: Sport, Size: 12in
I got the twelve inch handle. It is too short and does not flex enough to release ball in right direction. Its almost impossible to aim and doesn't sent the ball far enough.
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Reviewed in the United States on April 22, 2026
★★★★★ 5
Highly recommend for pet owners looking to keep their dogs busy and happy!
Color: Grid Pattern
These interactive dog toys were a great surprise! My dog was instantly interested in the bouncing and vibrating movement, and it kept him entertained much longer than regular toys. I like that the balls are rechargeable and washable, which makes them easy to maintain after outdoor play. The automatic motion is fun and unpredictable enough to keep pets curious and active. Great value for a 2-pack, especially for energetic dogs that need extra stimulation during the day. Highly recommend for pet owners looking to keep their dogs busy and happy!
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Reviewed in the United States on May 20, 2026
★★★★★ 5
Must have for your doggy!
Color: Grid Pattern
This interactive dog toy ball is amazing! It moves and jumps automatically, which keeps my dog constantly engaged and excited. My dog loves chasing it around the house and never seems to get bored. The material feels very durable and holds up well even with strong chewing. It’s a great way to keep pets active and entertained. Definitely a fun and high-quality toy I would recommend!
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Reviewed in the United States on April 12, 2026
★★★★★ 3
Not a Tough Chew Toy for Large Dogs
Color: Grid Pattern
While these were quite entertaining for our golden retrievers, they lasted only about 30 minutes before they were destroyed. This is NOT a tough toy item.
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Reviewed in the United States on April 11, 2026