18.04 1999秋季课程：复变与应用(Complex Variables with Applications, Fall 1999)
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在复数平面上的立方根之虚部。MATLAB®软件所绘出的图像 (感谢R.Rosales教授提供此图。)
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.)
课程重点
本课程包含一整套作业（含解答）并提供所有测验题。此外，学习资料包含许多MATLAB软件所绘的三维图形，例如牛顿迭代法与多值函数，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.
课程描述
本课程包含下列各项主题：复数代数与函数；可解析性；路径积分；柯西定理；奇异性，泰勒与罗伦兹级数，留数，积分的运算；多值函数，二维的势能理论；傅立叶分析与拉普拉斯转换。
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.
