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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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★★★★★ 5
My dog loves it
My 70 lb 1 year old dog plays his own soccer with this toy and he loves making it squeek but he is a toy destroyer and so far this has held up pretty well. It's made of a soft material so I don't have to worry about it harming his teeth. It's easy to clean. It can be used in the house or outside for fetch. It is unpredictable at times with its bouncing which makes it more interesting for my dog to chase after. This is his favorite toy and carries it everywhere including to bed.
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Reviewed in the United States on September 23, 2025
★★★★★ 5
Durable Enough for Strong Jaws
I’ve gone through many toys that my dog destroys in minutes. This one has held up way better. The material feels tough, yet safe for chewing. I use it both indoors and outside, and it’s easy to rinse off when dirty. It’s been a relief to find something that can last longer in daily play.
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Reviewed in the United States on September 23, 2025
★★★★★ 5
Durable Toy for Active Dogs
This ball is strong enough to handle daily play while keeping dogs entertained. It provides stimulation that helps reduce boredom and restlessness. The material feels tough but safe for dogs, and the interactive design makes it more exciting than a regular ball. It’s also lightweight enough for indoor or outdoor use. A smart choice for pet owners looking to keep dogs occupied.
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Reviewed in the United States on November 13, 2025
★★★★★ 5
Bright, easy to clean toy
This ball is a fun little addition for my big dog. The bright blue color really helps, it is easy to spot under the sofa or behind furniture. The outer shell feels durable, not soft rubber but springy enough to handle his chewing without marks. When switched on, it rolls around by itself and makes my dog chase it all over the living room, which is a good way to burn his energy on rainy days. The internal switch is hidden, which I like because my dog cannot open it with his teeth. It is simple to turn on and off, and so far, the movement works as described. The texture also resists hair sticking, and I can rinse it under water, and it looks clean again in seconds. For the price, it serves its purpose and gives my dog a short burst of excitement each day.
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Reviewed in the United States on October 10, 2025
★★★★★ 5
Fun and Tough Interactive Toy for My Big Dog
This interactive dog ball has been a great addition for my large dog. The ball’s material is very durable and holds up well even with heavy chewing. My dog usually destroys toys within days, but this one has lasted weeks and still looks great. The automatic play modes keep him active and entertained, especially when I’m busy. He loves chasing it both indoors and outdoors, and it helps release his energy. The battery life is decent, and the operation is simple. Overall, it’s a fun, sturdy, and smart toy that really keeps my dog busy and happy
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Reviewed in the United States on October 11, 2025