Engineering Mathematics

工程數學

課程基本資料

課程摘要

(一)教材：Advanced Engineering Mathematics Erwing Kreyszig, John Wiley & Sons, Inc.

(二)參考書：

        •Advanced Engineering Mathematics Michael D. Greenberg Prentice Hall

        •Advanced Engineering Mathematics Peter V. O’eil PWS Publishing Company

(三)課程大綱：

•Periodic Functions. Trigonometric Series.

•Fourier Series. Euler Formulas

•Functions Having Arbitrary Period

•Even and Odd Functions

•Half-Range Expansions

•Determination of Fourier Coefficients without Integration.

•Forced Oscillations.

•Approximation by Trigonometric Polynomails. Square Error.

•The Fourier Integral.

(四)課程內容：

  Periodic functions occur frequently in engineering problems. Their representation in terms of simple periodic functions, such as sine and cosine, is a matter of great practical importance, which leads to Fourier series.  These series are a very powerful tool in connection with various problems involving ordinary and partial differential equations.

    In the present course we shall discuss basic concepts, facts and techniques in connection with Fourier series.  Illustrative examples and some important engineering applications will be included.  The theory of Fourier series is rather complicated, but the application of these series is simple.  Fourier series are, in a certain sense, more universal than Taylor series, because many discontinuous periodic functions of practical interest can be developed in Fourier Series, but, of-course, do not have Taylor series representations.

    The last section of this course is devoted to Fourier integrals. Applications to partial differential equations will also be introduced.

(五)成績評定：

平時 40% 期中30% 期末30%