Lesson plan
Transform theory
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory. Main examples of transforms that are both well known and widely applicable include integral transforms such as the Fourier transform, the fractional Fourier Transform, the Laplace transform, and linear canonical transformations. These transformations are used in signal processing, optics, and quantum mechanics.
Article summary
In mathematics, transform theory is the study of transforms, which relate a function in one domain to another function in a second domain. The essence of transform theory is that by a suitable choice of basis for a vector space a problem may be simplified—or diagonalized as in spectral theory. Main examples of transforms that are both well known and widely applicable include integral transforms such as the Fourier transform, the fractional Fourier Transform, the Laplace transform, and linear canonical transformations. These transformations are used in signal processing, optics, and quantum mechanics.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.