SKU: 58803866949

Lecture Notes on Calculus of Variations

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Lecture Notes on Calculus of VariationsThis is based on the course "Calculus of Variations" taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1 8 focus on the classical theory of calculus of variations. Lectures 9 14 introduce direct methods along with their theoretical foundations.

This is based on the course "Calculus of Variations" taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.

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SKU: 58803866949

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LC
Louisville, US
★★★★★ 3
Our dog loves it but it wasn’t durable enough to last
Color: Dogwood Jack, Size: Large, Color: Dogwood Jack, Size: Large
Our lab took to it as soon as we gave it to her. Perfect size for our 80 lb yellow lab. However, now that it’s in about 10 days, she’s able to break off chunks from this bone that are dime size or larger, and we have to throw it away
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Reviewed in the United States on May 1, 2026
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Matthew Anderson
Belleville, US
★★★★★ 5
No problems after a year and a half
Color: Dogwood & Calming, Size: Medium
Have been regularly buying these for my corgi for about a year and a half. The 2 pack lasts about a month or 2 each time. Pieces break off in small enough pieces that they safely pass through his digestive system. He gnaws each one down to about 1/4 the original size before we take it away and give him a new one. He continues to have regular bowel movements and has a healthy appetite so I can’t imagine any problems arising after so long. I have tried other alternatives and every other similar chew breaks off in larger pieces and didn’t feel comfortable letting him chew/eat them. I noticed there are a few 1 star reviews saying their dogs got sick off these but after a year and a half I have had 0 issues with this product. I guess it depends on the dog and how big of pieces they are swallowing. My dog ingests pieces about the size of a grain of rice so just pay attention and you should be fine.
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Reviewed in the United States on February 18, 2026
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terlynn4
Lowell, US
★★★★★ 5
Long lasting and safer alternative to sticks
Color: Dogwood & Calming, Size: Medium
These are great, very durable, and have lasted a very long time. Much safer for my dogs than the random sticks they find in the yard. They do get shorter with chewing eventually, but they don't break off in little chunks like I've seen with some nylon chews, and they don't splinter like wood. Medium size works well for both my 16 lb Cavalier and my 60 lb Pyrenees/Golden mix. They're both moderate-to-aggressive chewers, though size obviously affects how much damage they can do. I wish you could buy the hemp chew separately because that one is very much a favorite in my house, so after 2 years and 2 purchases, I have barely any left of the remaining hemp chew, but still 2 of the dogwood chews that neither dog is as interested in anymore. I'd love to buy a couple more of just the hemp one.
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Reviewed in the United States on April 30, 2026
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Shannon Brace
Louisville, US
★★★★★ 5
Your dog will thank you.
Color: Dogwood & Fresh Breath, Size: Large
My dogs loves to chew on these. They make a small mess but not as bad as other chews. They are food for keeping teeth clean.
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Reviewed in the United States on May 31, 2026
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Anna
Louisville, US
★★★★★ 5
Nice chew toy
Color: Dogwood Mushroom, Size: Medium, Color: Dogwood Mushroom, Size: Medium
Super durable and puppy loves it. It was a bit hard for her at first but now at 5 months it’s one of her favorite things to gnaw on! It is heavy for the size but seems to be great quality and has given many hours of chew time with minimal wear.
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Reviewed in the United States on March 12, 2026

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