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Distribution Theory and Transform Analysis: An Introduction to Generalized Functions, with ApplicationsDistribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with
Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems.Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems.
After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions.
Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Binding Type: Paperback
Publisher: Dover Publications
Published: 11/18/2010
ISBN: 9780486654799
Pages: 400
Weight: 0.89lbs
Size: 8.44h x 5.39w x 0.78d
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★★★★★ 5
Great for Budgeting – Instant Balance and Easy to Use
Reload type: One Time Reload
I use Amazon’s gift card reload feature to plan my spending. It’s perfect when I know I want to make a purchase but prefer to set the funds aside first.
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Overall, it’s a convenient and reliable way to manage spending on Amazon, especially if you like having control over your purchases.
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Reviewed in the United States on May 1, 2026
★★★★★ 5
EASY TO MANAGE AND HIGH QUALITY
Style: Ballistic, Size: 75 FT
I love this pocket Hose. Bought a cheaper retractable hose when I saw the pocket Hose advertised because I thought it was little expensive. Well, it didn't last and it did not retract to smaller size like the pocket hose does, just not made as well. Love love love the light weight rather than the heavy plastic hose that crimps, twist, etc. I'm a smaller older person so dragging that around was a chore. So, when the other hose decided to leak in two more spots after one repair I didn't think twice about the price for the 75 foot that I wanted. So much invested in my yard, need tool to keep it watered. LOVE IT!!
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Reviewed in the United States on June 8, 2026
★★★★★ 5
A lightweight hose that performs like a heavyweight!
The Copper Head Expandable Garden Hose is my favorite hose to use when doing garden wastering chores. I am an avid gardener and need a sturdy hose that is portable. We have many gardens on our rural property, but no irrigation, so watering is essential in the summer droughts we’ve had lately. I like that the water drains out quickly and completely, which allows me to fill up containers until the hose is empty so we don’t waste the water. The outer cover is extremely durable, feels quite thick, so even if it catches on a branch, I don’t worry about the cover getting ruined. Also, the spray head and swivel connection make moving around while using the hose very easy. I can turn off the spray head with one finger and easily select another spray pattern as needed with the easy to use dial design. The hose does not tangle or kink, which also makes it easy to use. Even when the hose is filled with water, I am able to move around the gardens with ease. When I am done using the hose, I can put it in a reusable grocery bag to carry it in the garage and store it. I would not leave the hose full when done using it, nor leave it in the sun. When I am finished for the day, I drain it, put it in the bag, fold over the top, and leave it in the shade or put it in the garage so that it will not deteriorate. It’s my second year using it and it’s still like new. I love this hose! I recently bought two more 50 ft. ones!
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Reviewed in the United States on May 18, 2026
★★★★★ 5
BEST HOSE I EVER BOUGHT
I sure hope this thing lasts because it is simply the best garden hose I EVER bought! I’ve used it a lot in the 2 months since buying it, watering my plants, filling grow boxes, attaching to my pressure washer, etc. It does not kink, not even once.
The pocket pivot connector is a nice touch, and the spray nozzle works great without the usual dripping of cheaper models. The hose expands as soon as you turn it on, so be ready. I bought the 100’ and got a $30 discount at the time. $69 "all in" is still a lot of money for a garden hose, but I am super pleased thus far.
When you turn the water supply off, the hose will continue to spray for a couple minutes while it contracts, but again, it does so without tangles or kinks.
Super lightweight and very easy to handle with a strong water flow.
Only time will tell on durability, but thus far there’s been no “fraying” or signs of wear from dragging it across my driveway or rock landscape. I’ll re-evaluate after a season but I’m ready to replace my other hose with one of these.
For now, I love it and highly recommend.
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Reviewed in the United States on May 27, 2026
★★★★★ 4
I am hopeful this new version of Pocket Hose is better built than earlier versions!
I have not had great luck with earlier versions of Pocket Hose products! I have had leaks, hose blowout holes, leaks at the facet connector and sprayer difficulty! BUT, I wanted to give the new Copper Head Hose a try. I like all the new features and feel they have made good enhancements to the hose quality! I have had the new hose for a week or so and it appears to be of better quality than previous versions. The hose is working great and I am hopeful it will last longer than the last ones. However the product is expensive and this will be my last purchase of Pocket Hose if I have ANY issues in the future. I will update my review in the future!
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Reviewed in the United States on April 15, 2026