Development of an Innovative Elementary Course in Fourier Analysis

为数学、物理和工程科学的学生准备的傅里叶分析低年级课程的文本和相关的讲座材料正在SIUC和其他一些学院和大学进行课堂测试。由于FOURIER最近的发展，这门课程变得可行，傅里叶是一个软件包，它使学生能够用一堆“函数”进行计算，就像他们在RPN计算器上用一堆数字进行计算一样。学生将使用傅里叶来探索通常用傅里叶级数、傅里叶变换或离散傅里叶变换分析的经典和当代现象，从而认识到数学分析和计算机模拟在现代科学和工程中的重要作用。

A text and related lecture materials for a lower division course in Fourier analysis for students in the mathematical, physical, and engineering sciences are being prepared and class tested at SIUC and a number of other colleges and universities. This course has become feasible due to the recent development of FOURIER, a software package that enables students to do calculations with a stack of `functions' in much the same way that they would do calculations with a stack of numbers on an RPN calculator. Students will use FOURIER to explore classic and contemporary phenomena commonly analyzed with Fourier series, Fourier transforms, or the discrete Fourier transform and thereby come to appreciate the essential roles of mathematical analysis and computer simulation in modern science and engineering.