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MATLAB是一个编程和数值计算平台，被数百万工程师和科学家用来分析数据、开发算法和创建模型。

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写matlab方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写matlab代写方面经验极为丰富，各种代写matlab相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

Ablowitz, M. J., and A. S. Fokas, 2003: Complex Variables: Introduction and Applications. Cambridge University Press, $660 \mathrm{pp}$. Covers a wide variety of topics, including complex numbers, analytic functions, singularities, conformal mapping and the Riemann-Hilbert problem.

Carrier, G. F., M. Krook, and C. E. Pearson, 1966: Functions of a Complex Variable: Theory and Technique. McGraw-Hill Book Co., 438 pp. Graduate-level textbook.

Churchill, R. V., 1960: Complex Variables and Applications. McGraw-Hill Book Co., 297 pp. Classic textbook.

Flanigan, F. J., 1983: Complex Variables. Dover, 364 pp. A crystal clear exposition and emphasis on an intuitive understanding of complex analysis.

In their course work, most engineering students are introduced to the concept of the Fourier and Laplace transforms. The presentations are limited because the student has not studied complex variables. Having presented this topic in the previous chapter, the reader is ready to deepen his/her ability to use these transform methods.

This chapter deals with two important aspects of transform methods. In the past you may have inverted Fourier and Laplace transforms using partial fractions, tables and some general properties of the transform. Often these techniques fail and here we show how the power of complex variables can overcome these difficulties.

Thé réason that Laplácé transforms aree taught to engineeers is théir ability to solvé ordinary differential equations. When it comes to partial differential equations the student is only taught one method: separation of variables. In Sections $2.4$ through $2.6$ we show how Laplace transforms can be used to solve the wave, heat, and Laplace equations.

## 数学代写|matlab代写|INVERSION OF FOURIER TRANSFORMS BY CONTOUR INTEGRATION

Although we may find the inverse by direct integration or partial fractions, in many instances the Fourier transform does not lend itself to these techniques. On the other hand, if we view the inverse Fourier transform as a line integral along the real axis in the complex $\omega$-plane, then some of the techniques that we developed in Chapter 1 can be applied to this problem. To this end, we rewrite the inversion integral for the Fourier transform as
$$f(t)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i t \omega} d \omega=\frac{1}{2 \pi} \oint_{C} F(z) e^{i t z} d z-\frac{1}{2 \pi} \int_{C_{R}} F(z) e^{i t z} d z$$

where $C$ denotes a closed contour consisting of the entire real axis plus a new contour $C_{R}$ that joins the point $(\infty, 0)$ to $(-\infty, 0)$. There are countless possibilities for $C_{R}$. For example, it could be the loop $(\infty, 0)$ to $(\infty, R)$ to $(-\infty, R)$ to $(-\infty, 0)$ with $R>0$. However, any choice of $C_{R}$ must be such that we can compute $\int_{C_{R}} F(z) e^{i t z} d z$. When we take that constraint into account, the number of acceptable contours decreases to just a few. The best is given by Jordan’s lemma. ${ }^{1}$

Jordan’s lemma: Suppose that, on a circular arc $C_{R}$ with radius $R$ and center at the origin, $f(z) \rightarrow 0$ uniformly as $R \rightarrow \infty$. Then
$$\lim {R \rightarrow \infty} \int{C_{R}} f(z) e^{i m z} d z=0, \quad(m>0)$$
if $C_{R}$ lies in the first and/or second quadrant;
$$\lim {R \rightarrow \infty} \int{C_{R}} f(z) e^{-i m z} d z=0, \quad(m>0)$$
if $C_{R}$ lies in the third and/or fourth quadrant;
$$\lim {R \rightarrow \infty} \int{C_{R}} f(z) e^{m z} d z=0, \quad(m>0)$$
if $C_{R}$ lies in the second and/or third quadrant; and
$$\lim {R \rightarrow \infty} \int{C_{R}} f(z) e^{-m z} d z=0, \quad(m>0)$$
if $C_{R}$ lies in the first and/or fourth quadrant.

# matlab代写

Ablowitz、MJ 和 AS Fokas，2003 年：复杂变量：介绍和应用。剑桥大学出版社，660pp. 涵盖了广泛的主题，包括复数、解析函数、奇点、保角映射和黎曼-希尔伯特问题。

Carrier, GF, M. Krook 和 CE Pearson，1966 年：复变量的函数：理论和技术。McGraw-Hill Book Co.，438 页。研究生水平的教科书。

Churchill, RV, 1960：复变量和应用。McGraw-Hill Book Co.，297 页。经典教科书。

## 数学代写|matlab代写|INVERSION OF FOURIER TRANSFORMS BY CONTOUR INTEGRATION

$$f(t)=\frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i t \omega} d \omega=\frac{1}{2 \pi} \oint_{C} F(z) e^{i t z} d z-\frac{1}{2 \pi} \int_{C_{R}} F(z) e^{i t z} d z$$

$$\lim R \rightarrow \infty \int C_{R} f(z) e^{i m z} d z=0, \quad(m>0)$$

$$\lim R \rightarrow \infty \int C_{R} f(z) e^{-i m z} d z=0, \quad(m>0)$$

$$\lim R \rightarrow \infty \int C_{R} f(z) e^{m z} d z=0, \quad(m>0)$$

$$\lim R \rightarrow \infty \int C_{R} f(z) e^{-m z} d z=0, \quad(m>0)$$

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师