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Description
Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and ManagementAn excellent financial research tool, this classic focuses on the methods of solving continuous time problems. The two part treatment covers closely related approaches to the calculus of variations and optimal control. In the two decades since its initial publication, the text has defined dynamic optimization for courses in economics and management science. Simply, clearly, and succinctly written chapters introduce new developments, expound upon
An excellent financial research tool, this classic focuses on the methods of solving continuous time problems. The two-part treatment covers closely related approaches to the calculus of variations and optimal control. In the two decades since its initial publication, the text has defined dynamic optimization for courses in economics and management science.Simply, clearly, and succinctly written chapters introduce new developments, expound upon underlying theories, and cite examples. Exercises extend the development of theories, provide working examples, and indicate further uses of the methods. Geared toward management science and economics PhD students in dynamic optimization courses as well as economics professionals, this volume requires a familiarity with microeconomics and nonlinear programming. Extensive appendices provide introductions to calculus optimization and differential equations.
Binding Type: Paperback
Publisher: Dover Publications
Published: 11/21/2012
ISBN: 9780486488561
Pages: 377
Weight: 1.05lbs
Size: 8.90h x 5.90w x 0.80d
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4.8 ★★★★★
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Product Reviews
★★★★★ 5
Great Value Toy
Color: Crinkle Duck (Blue), Size: Large, Color: Crinkle Duck (Blue), Size: Large
This toy has been one of my dog’s absolute favorites. He gets excited every time he sees it and will carry it around the house, toss it in the air, and keep himself entertained for a long time. The shape and texture seem perfect for him, and it quickly became one of his go-to toys over everything else in his basket.
What I really like is that it holds up reasonably well for the price. It’s definitely not indestructible, and after a lot of play, it will sometimes start to rip—usually around the feet first since that’s where my dog tends to grab and chew the most. But honestly, considering how affordable it is, I don’t mind replacing it when needed. It’s inexpensive enough that rebuying feels worth it because he genuinely loves it that much.
I’d rather keep buying a toy he is obsessed with than spend more on something that just sits untouched. It’s fun, cute, and keeps him happy, which is what matters most. Overall, I’d definitely recommend it for dogs who love plush toys and playful chewing.
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Reviewed in the United States on April 28, 2026
★★★★★ 5
Best affordable squeaker toy
Color: Crinkle Chicken (Brown), Size: Large, Color: Crinkle Chicken (Brown), Size: Large
my dog is obsessed with this toy, this has became his new comfort toy and after having this for about four months the legs are falling off but it’s very durable. The squeaker also moved from the head of the chicken to the body of the chicken but that’s after it was played with every single day. I love that it has two squeakers and it’s the perfect toy for my dog.
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Reviewed in the United States on May 6, 2026
★★★★★ 5
My dogs favorite toy EVER
Color: Crinkle Chicken (Brown), Size: Large
I have a Belgian Malinois who loves any and every toy, but this one is definitely her favorite. She will walk around the house constantly carrying it in her mouth, which is honestly adorable to watch.
The squeakers only lasted a couple of months, but I don’t really consider that a downside—I’m kind of grateful they didn’t last forever given how much she plays with it. It still remains one of her most-loved toys even without them.
My only word of caution is that if you work from home, this toy makes a lot of crinkling noise. And I mean A LOT. It’s great for keeping the dog entertained, but it can definitely get a little frustrating for humans trying to focus or take calls.
Overall, it’s been a big hit in our house and easily one of her favorite toys.
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Reviewed in the United States on June 8, 2026
★★★★★ 5
Super cute
Color: Bunny (Mauve), Size: Small
Super cute and fuzzy. Definitely perfect size for a puppy and not too loud. The fur is very soft and the nose is sown on not a hard piece that can be chewed on. Very good quality too.
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Reviewed in the United States on June 3, 2026
★★★★★ 4
Normally amazing
Color: Spiky Ball (Blue, Orange), Size: Medium
We have purchased these slightly spiky dog balls several times for our very strong jaw heavy chewer dogs and they’ve been amazing. They don’t break down they don’t get torn apart the squeakers don’t even pop out of them.
So we ordered another package because we’ve lost a few outside to the lawnmower… oops and the package that got delivered today had only one ball that squeaks and the other does not. THIS IS A PROBLEM ! Unfortunately my female dog got to the new squeaking ball first and my male got to the non-squeaking ball and he was NOT happy. Basically once they claim a ball it’s theirs and the other dogs don’t go near the ball they claimed. So he’s following my female around and every time she squeaks the ball and I’m just waiting for him to attempt to take it from her causing damage to her. Normally… These are amazingly fun, tough, durable but also squeaking balls (that’s rare in a tough ball) that my dogs absolutely love.
This time just got a bad batch I guess. When they squeak the dogs LOVE them. After several months of play the squeaker might break inside of the ball but the ball never comes apart or gets damaged. And we as the owners love that they don’t break down are not able to be ripped or torn even by our very strong jawed and big jaw muscle dogs.
They are also great for in the house play because they’re small enough that they fit completely inside our dog‘s mouth but obviously not small enough to get swallowed so when we throw them in the house for fetch the dogs can jump up and catch them fully in their mouth so they don’t cause any damage to the walls when they hit the walls. They’re not super heavy but they’re incredibly durable.
Definitely worth the price especially if you have heavy chewers or big jaw muscle dogs.
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Reviewed in the United States on April 28, 2026
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