Introductory Explorations of the Fourier Series
نویسندگان
چکیده
منابع مشابه
Determination of a jump by Fourier and Fourier-Chebyshev series
By observing the equivalence of assertions on determining the jump of a function by its differentiated or integrated Fourier series, we generalize a previous result of Kvernadze, Hagstrom and Shapiro to the whole class of functions of harmonic bounded variation. This is achieved without the finiteness assumption on the number of discontinuities. Two results on determination of ...
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15 صفحه اولApplications of the Fourier Series
The Fourier Series, the founding principle behind the field of Fourier Analysis, is an infinite expansion of a function in terms of sines and cosines. In physics and engineering, expanding functions in terms of sines and cosines is useful because it allows one to more easily manipulate functions that are, for example, discontinuous or simply difficult to represent analytically. In particular, t...
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for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...
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Here are some facts about Fourier Series — useful for pde and elsewhere. Proofs of Lemmas are easy exercises, and not given. On the other hand, proofs of LEMMAS are harder; their proofs are indicated, or a reference is given.
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ژورنال
عنوان ژورنال: Journal of Chemical Education
سال: 2008
ISSN: 0021-9584,1938-1328
DOI: 10.1021/ed085p1708.1