Mathematica Laboratory for Upper-Level Science and Engineering Students

在过去的六年中，机械工程系开设了一套六门应用数学本科课程。这些课程将传统数学训练与工程和科学问题紧密联系起来。这些课程满足了学生的主要需求，每年的学生总数约为265人。这些课程可以满足机械工程、地质力学、物理、光学等专业的学位要求，也可以作为电气工程、化学工程、数学等专业的选修课。该项目的目标是在所有这些课程中增加一个Mathematica计算实验室。这个实验也可以用于机械系统课程和其他传统的工程课程，这些课程具有很强的数学成分。Mathematica中的数值和图形功能允许每周分配更有趣的问题和更实际的学期项目。Mathematica的符号功能允许传统分析技术的扩展。笔记本界面可以为每组学生提供完全正确水平的材料。初学者可以简单地执行带有各种参数选择的笔记本，而更高级的学生可以要求扩展给定的笔记本来处理更复杂的问题。这个数学实验室每年可供几百名学生使用。这些学生可以更深入地了解数学在可视化和分析物理过程中的应用。学生们还可以掌握数学软件的技能，这是一种在科学和工程中必不可少的计算模式。

In the past 6 years, the Department of Mechanical Engineering has developed a set of six upper-division undergraduate courses in applied mathematics. These courses combine training in traditional mathematics with strong and frequent connections to engineering and scientific problems. The courses meet a major need and have grown to a combined yearly enrollment of about 265 students. They are taken to satisfy degree requirements in Mechanical Engineering, Geomechanics, Physics, and Optics and as electives for some majors in Electrical Engineering, Chemical Engineering, and Mathematics. The objective of this project is to add a Mathematica Computational Laboratory to all of these courses. This laboratory can also be used in the Mechanical Systems course and other traditional engineering courses that feature a strong mathematical component. The numerical and graphical capabilities in Mathematica allow for the weekly assigning of more interesting problems and more realistic term projects. The symbolic capabilities of Mathematica allow extensions of traditional analytical techniques. The notebook interface makes it possible to supply each group of students with material of exactly the right level. Beginning students can simply execute notebooks with various parameter choices, whereas more advanced students can be asked to extend the given notebooks to handle more complex problems. This Mathematica Laboratory can be used by several hundred students a year. These students can gain greater insight into the use of mathematics in visualizing and analyzing physical processes. The students can also acquire skills in Mathematica, a mode of computing now essential in science and engineering.