Phet Assisted Trigonometric Worksheet for Students’ Trigonometric Adaptive Thinking

Rearrangements of Trigonometric Series and Trigonometric Polynomials

Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...

Empirical Similarity Analysis Using Adaptive Trigonometric Functions

Similarity methods have been widely employed in engineering design and analysis to model and scale complex systems. The Empirical Similitude Method (ESM) is one such method based on the use of experimental data. Using a variant of the similitude process involving experimental data, we present in this paper, the use of advanced numerical approximations, trigonometric functions in particular to m...

Orthonormal shift-invariant adaptive local trigonometric decomposition

In this paper, an extended library of smooth local trigonometric bases is defined, and an appropriate fast “best-basis” search algorithm is introduced. When compared with the standard local cosine decomposition (LCD), the proposed algorithm is advantageous in three respects. First, it leads to a best-basis expansion that is shift-invariant. Second, the resulting representation is characterized ...

Shift-invariant adaptive local trigonometric decomposition

When Is a Trigonometric Polynomial Not a Trigonometric Polynomial?

for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why the term trigonometric polynomial is ...