MATLAB在数学物理方法中的应用
摘 要：《数学物理方法》作为众多理工科专业的必修课和重要基础课程之一，课程内容复杂，是一门公认的难度较大的课程。尽管数学物理方法中的习题都有其明确的物理意义，但是如何从这些繁杂的数学表达式中看出其中所表示的物理图像，却常常使教师在教学中感到棘手，学生在学习中感觉困惑。通过介绍MATLAB在复变函数，特殊函数以及傅里叶级数中的应用，复变函数的生成与运算，并利用MATLAB编程解决《数学物理方法》中的一些问题，使复杂繁琐的计算变的简便，以图像的形式将一些特殊函数及数理方程的解显现出来，便于学生对数理问题的物理意义有一个更深刻的理解。将MATLAB应用于数学物理方法中可以改变用公式符号教学的模式，对教学效果会有很大的提高。
关键词：MATLAB；复变函数；特殊函数；傅里叶级数
Application of MATLAB on Method of Mathematical Physics
Abstract: As a required course for many science and engineering professionals and an important foundation for one of the courses，Methods of Mathematical Physics is so complex and difficult that it is hard to master. Although the exercises of Methods of Mathematical Physics have its clear physical meaning, how to find the reprehensive physical image from these complicated mathematical expressions often makes teachers feel difficult to teach and makes students feel confused in learning as well. For students, it will be easily and deeply understood about the physical meaning of the mathematical problems through introducing Complex functions, Special functions and Fourier series problem applications and Complex functions of generation and operation process of MATLAB. The calculation will become from complicated to simple, some special functions and mathematical equations will be demonstrated in the form of images by using MATLAB programming to solve some of the problems in Methods of Mathematical Physics, it will be helpful for the improvement of the learning effectiveness of students consequently. With the changed teaching mode by using MATLAB in Methods of Mathematical Physics, the effectiveness of teaching would be greatly improved.
Keywords: MATLAB; Complex functions; Special functions; Fourier series
目 录
摘要 1
引言 1
1. MATLAB在复变函数的应用 2
1.1 复数的生成 3
1.2 复数的运算 3
1.3 复变函数的图形画法 3
1.4 复变函数的图形示例 4
2. MATLAB在特殊函数的应用 5
2.1 函数 6
2.2 函数的函数命令 6
2.3 函数的图形示例 6
3. MATLAB在傅里叶级数中的应用 7
3.1傅里叶级数 8
3.2平面波展开为球面波的叠加的图形示例 8
4.结论 13
5.结束语 14
参考文献 14
附录 14
致谢 16,3325