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Description
A First Course in Partial Differential Equations: With Complex Variables and Transform MethodsThis popular text was created for a one year undergraduate course or beginning graduate course in partial differential equations, including the elementary theory of complex variables. It employs a framework in which the general properties of partial differential equations, such as characteristics, domains of independence, and maximum principles, can be clearly seen. The only prerequisite is a good course in calculus. Incorporating many of the
This popular text was created for a one-year undergraduate course or beginning graduate course in partial differential equations, including the elementary theory of complex variables. It employs a framework in which the general properties of partial differential equations, such as characteristics, domains of independence, and maximum principles, can be clearly seen. The only prerequisite is a good course in calculus.Incorporating many of the techniques of applied mathematics, the book also contains most of the concepts of rigorous analysis usually found in a course in advanced calculus. These techniques and concepts are presented in a setting where their need is clear and their application immediate. Chapters I through IV cover the one-dimensional wave equation, linear second-order partial differential equations in two variables, some properties of elliptic and parabolic equations and separation of variables, and Fourier series. Chapters V through VIII address nonhomogeneous problems, problems in higher dimensions and multiple Fourier series, Sturm-Liouville theory, and general Fourier expansions and analytic functions of a complex variable.
The last four chapters are devoted to the evaluation of integrals by complex variable methods, solutions based on the Fourier and Laplace transforms, and numerical approximation methods. Numerous exercises are included throughout the text, with solutions at the back.
Binding Type: Paperback
Publisher: Dover Publications
Published: 09/11/1995
ISBN: 9780486686400
Pages: 480
Weight: 1.43lbs
Size: 9.21h x 6.48w x 0.91d
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★★★★★ 5
Works well when properly applied
Size: 3 Fl Oz (Pack of 1)
I try to always buy the highest SPF that I can find. This one fits the bill. If you apply it thoroughly all over and then reapply every few hours, you shouldn't get burned. I've worn it to the water park numerous times now. I have very sensitive skin, and it's given me no issues. I even put it on my face, just being careful not to get too close to my eye area. Once it absorbs into your skin, it doesn't feel too sticky like some other sunscreens can. Just be aware that it will leave a white residue on your bathing suit if you get it on there, but I've always been able to wash it out and that's a small price to pay for proper sun protection!
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Reviewed in the United States on April 9, 2026
★★★★★ 5
Protected Our Skin and Smells Good
Size: 6 Ounce (Pack of 1)
I love this stuff! My husband and I bought it as a last minute grab for our honeymoon and it was well worth it! I'm very sensitive to the sun AND to sunscreens, so I needed something with simple ingredients that would also protect my skin without breaking me out. This not only kept away the burning rash I get from the sun, but protected my husband and I from any sunburn at all. It worked not only in dry conditions, but it stayed on for hours after we swam in the ocean. We also liked the fact that it smelled herbal, almost like pizza/Italian seasoning. That didn't bother us because we both hate the smell of most sunscreens.
If you have sensitive skin or are looking for a more natural product, I highly recommend this!
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Reviewed in the United States on March 25, 2026
★★★★★ 5
Great reef-safe, easy-to-apply sunscreen (comparison of three ThinkSport products)
Size: 6 Ounce (Pack of 1)
I will start by saying that I am used to traditional non-mineral sunscreens and tend to only buy physical/mineral-based sunscreens when I'm going to be in a tropical ocean and need something reef-safe, though more and more kids sunscreens are shifting to mineral-based. After quite a bit of research I settled on ThinkSport for my family's recent trip to Hawaii, and I'm very pleased with it. I brought and used three types of Thinksport sunscreen: Thinksport Kids lotion (yellow/orange and teal squeeze bottle), Thinksport adult lotion (Black, white, and orange squeeze bottle), and Thinksport adult spray (black, white and orange spray bottle). All protected us from sunburn and rubbed in to be invisible as long as skin was dry and free of visible hair (visible whiteness persisted around my husbands facial stubble and chest hair). The only difference between the kids lotion versus the adult lotion is scent--the kids version has a fruitier, more tropical but not-too-strong scent (possibly coconut and something else? it was hard to identify) that I found unobjectionable (though one if my kids wasn't a fan), and the adult lotion had a lighter, less sweet, more citrus-y scent (my son though maybe lime and mint, but I'm not sure that's accurate) that I LOVE. The adult spray had no discernible scent, so I suspect the kids spray might be fairly unscented as well. The easiest to apply by far was the spray--it sprays on white, but feels very light, rubs in easily, and becomes invisible quickly. I was a little worried about whether it could possibly be effective given how light and thin it felt, but it was! The lotions weren't thick for a lotion (but much thicker than the spray) and went on easily, but took more rubbing in to disappear than the spray (this is consistent with my experience with lotion vs spray in traditional sunscreens as well). Invisibility was harder to get after a second or third application or when skin was damp, but all-in-all I found all three Thinksport products to be superior to other mineral-based sunscreens I have tried in the past. In the future I'll probably buy the adult thinksport spray for my kids and husband (who all much prefer a spray-on sunscreen) and the adult thinksport lotion for myself (because I love the scent and don't mind rubbing it in).
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Reviewed in the United States on April 17, 2023
★★★★★ 5
Dependable sun protection for active days outdoors
Size: 6 Ounce (Pack of 1)
I like how this sunscreen provides reliable broad-spectrum protection and holds up well during outdoor activities. The zinc oxide formula gives me peace of mind, and I appreciate that it's water resistant and reef-safe. It applies smoothly for a mineral sunscreen and stays on effectively during sports, swimming, and long days in the sun. Overall, it's a trustworthy option for anyone looking for strong sun protection.
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Reviewed in the United States on June 8, 2026
★★★★★ 4
Clean product
Size: 3 Ounce (Pack of 1)
I only gave it 4 stars because of the smell. Of course it’s sunscreen so it’s going to have a chemical smell but this smell is just too strong for me. Other then that, it’s a great sunscreen. Does take some more rubbing in and be carful to rub it in really good or you’ll have white streaks all over your face. Leaves a bit of a white cast. You don’t need much.
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Reviewed in the United States on April 12, 2026