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題 名 | 傅利葉級數在三角函數微分問題上的應用=Application of Fourier Series on the Differential Problem of Trigonometric Functions |
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作 者 | 余啟輝; | 書刊名 | 遠東學報 |
卷 期 | 29:3 2012.09[民101.09] |
頁 次 | 頁271-279 |
分類號 | 314.55 |
關鍵詞 | 傅利葉級數; 三角函數; 高階微分值; 無窮級數; Fourier series; Trigonometric functions; Higher order derivative values; Infinite series; |
語 文 | 中文(Chinese) |
中文摘要 | 本篇論文利用傅利葉級數的方法來求解兩種類型三角函數的高階微分值。我們的方法可以求出這兩種三角函數的任意階導函數,因此大大降低了求解它們高階微分值的困難度。事實上這些高階微分值求出來的答案都是以無窮級數呈現的。同時我們舉出四個例子實際的來做計算,並且利用數學軟體Maple算出這些高階微分值以及它們無窮級數解的近似值。 |
英文摘要 | This paper uses the Fourier series method to evaluate the higher order derivative values of two types of trigonometric functions. Our method can obtain any order derivatives of the two types of trigonometric functions, and hence reducing the difficulty of evaluating their higher order derivative values greatly. In fact, the answers of these higher order derivative values are presented in infinite series. Simultaneously, we propose four examples to do calculation practically, and using the mathematical software Maple to calculate the approximations of these higher order derivative values and their infinite series solutions. |
本系統中英文摘要資訊取自各篇刊載內容。