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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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4.1 ★★★★★
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★★★★★ 5
Very pleasant nano hydroxyapatite toothpaste.
Color: A - Magic Mint (Pack of 3)
Bought this new nano hydroxyapatite toothpaste free of fluoride. This is a new technology toothpaste that reinforces enamel. The Mint taste is very pleasant.
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 20, 2026
★★★★★ 4
Pineapple and papaya
Color: A - Magic Mint (Pack of 3), Color: A - Magic Mint (Pack of 3)
I like it okay. I will use all of it but I am unsure if I will buy it again. It foams very little. I feel like I use more than I do with other pastes/gels. My mouth feels clean without having that too minty/medicinal taste from traditional flouride pastes. It comes out of the tube easy and sticks to my brush. I didn’t know until after I purchased it that there is papaya and pineapple extracts. There IS a photo in the product description that says this and I neglected to click through them all. I have two members in my household that are allergic to those ingredients so I have not had them try it. The only taste is a mild mint though. I think the whitening effects of nanohydroxyapatite pastes is much better than other popular brands that boast “whitening.” My teeth simply look whiter and shiny.
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Reviewed in the United States on September 22, 2025
★★★★★ 5
GREAT CHOICE !!!
Color: A - Magic Mint (Pack of 1)
Definitely works as discribed helped with tooth sensitivity active ingredients help whiten and strengthen tooth enamel. I alternate 3 X a week woth normal Fluoride toothpastes and use this 2X a week. Total game changer
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 21, 2026
★★★★★ 5
Perfect
Color: A - Magic Mint (Pack of 3)
This is the only toothpaste I use now. It makes my teeth look great, tastes great & does exactly as intended.
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Reviewed in the United States on June 2, 2026
★★★★★ 3
And alternative to floride toothpaste.
Color: A - Magic Mint (Pack of 1)
I've been using this alternative toothpaste for a couple months now. It's expensive compared to regular toothpaste, but some suggest that it's healthier for your teeth. Nano hydroxyapatite is supposedly the same molecule that our teeth are made of. So perhaps it may be better for hardening teeth than fluoride. Of course, I can tell if it is doing that or not. Do your own research.
It's a bit more fluid than standard paste, so it sits more flat on the toothbrush. I've discovered that if it dribbles from your mouth onto your shirt, it leaves a white stain on the fabric! So don't use it while wearing your good work shirt. The taste is more mild than the usual minty toothpaste. Not bad at all. At my next dental exam we'll see if it's cleaning my teeth effectively.
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Reviewed in the United States on November 24, 2025
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