Graphical and Qualitative Investigations In Multivariable Calculus, Linear Algebra, and Differential Equations

这个项目的目的是改变多变量微积分、线性代数和微分方程的教学模式。目前，这些课程采用传统的授课形式。虽然应用程序经常被引用，但学生很少有实际应用程序的实践经验。通过使用传统的纸笔方法来解方程，学生对解的图形和定性本质的了解很少。在过去的十年里，技术的变化为数学教育领域打开了新的、令人兴奋的大门。新的绘图技术可以在几秒钟内通过检查解决方案的图形来吸收大量的信息。解的图形提供了令人信服的理论推导的视觉证据，以及对解的定性性质的理解。本项目使用的硬件和软件支持课堂演示和互动课程计划的开发和实施，鼓励学生在他们的教育中发挥更积极的作用。实验室活动采用Matlab软件包进行。实验使用德州仪器的基于计算器的实验室单元，使学生能够观察物理系统是如何用微分方程建模的。所有开发的材料都在开发过程中通过在万维网上发布在学院的主页上与同事共享。这个项目意义重大，因为它可以极大地改变大学水平数学课程的教学方式。新课程既能激发学生的热情，又能让他们更好地理解这些学科，从而提高学生的保留率和入学率。

The purpose of this project is to change the mode of instruction in multivariable calculus, linear algebra, and differential equations. Currently, these courses are taught using the traditional lecture format. Although applications are often cited, students have very little hands-on experience with real-world applications. By using only traditional pencil and paper methods to solve equations, students experience minimal insight into the graphical and qualitative nature of solutions. Changes in technology over the past 10 years have opened new and exciting doors in the field of mathematics education. New graphing technology allows huge amounts of information to be assimilated in a matter of seconds by examining the graph of a solution. The graphs of solutions provide compelling visual evidence of theoretical deductions as well as an understanding of the qualitative properties of solutions. The hardware and software utilized in this project support the development and implementation of classroom demonstrations and interactive lesson plans that encourage students to take a more active role in their education. Laboratory activities make use of the Matlab software package. Experiments using the Calculator Based Laboratory units from Texas Instruments enable students to observe how physical systems are modeled by differential equations. All developed materials are shared with colleagues as they develop by posting them on the college's home page on the World Wide Web. This project is significant because it can dramatically change the way college-level mathematics courses are taught. The new curriculum can generate both enthusiasm and a better understanding of these subjects, resulting in increased retention and enrollment.