18.04 1999秋季課程：複變與應用(Complex Variables with Applications, Fall 1999)
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在複數平面上的立方根之虛部。MATLAB®軟體所繪出的圖像 (感謝R.Rosales教授提供此圖。)
Image of imaginary part of the cube root on the complex plane. Image created with MATLAB® software. (Image courtesy of Prof. R. Rosales.)
Image of imaginary part of the cube root on the complex plane. Image created with MATLAB® software. (Image courtesy of Prof. R. Rosales.)
課程重點
本課程包含一系列完整的作業（含解答）和所有試題，此外學習素材包含許多MATLAB®軟體所繪的三維圖形，其中包含牛頓疊代法與多值函數，以及MATLAB®使用指南。This course features a complete set of assignments with solutions and all exams are available. In addition, the study materials section inclues MATLAB®-generated three-dimensional graphics (e.g., Newton Iterations and Multiple-Valued Functions) and a MATLAB® tutorial.
課程描述
本課程包含下列各項主題：複數代數與函數；可解析性；輪廓積分；柯西定理；奇異性，泰勒與羅倫茲級數，留數，積分的運算；多值函數，二維的勢能理論；傅立葉分析與拉普拉斯轉換。
The following topics are covered in the course: complex algebra and functions; analyticity; contour integration, Cauchy's theorem; singularities, Taylor and Laurent series; residues, evaluation of integrals; multivalued functions, potential theory in two dimensions; Fourier analysis and Laplace transforms.
