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

多元微积分、线性代数和微分方程的图形和定性研究

• 批准号: 9651374
• 负责人: David Arnold
• 金额: $ 3.59万
• 依托单位: College of the Redwoods
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1998-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9651374&HistoricalAwards=false
• 关键词: Graphical; Qualitative; Investigations; Multivariable; Calculus

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.

本计画的目的在于改变多元微积分、线性代数、微分方程式的教学模式。目前，这些课程是使用传统的讲座形式教授的。虽然应用程序经常被引用，但学生很少有实际应用的实践经验。通过只使用传统的铅笔和纸的方法来解决方程，学生的经验最小的洞察力的图形和定性性质的解决方案。 在过去的10年中，技术的变化在数学教育领域打开了新的和令人兴奋的大门。新的图形技术允许通过检查解决方案的图形在几秒钟内吸收大量信息。解决方案的图形提供了令人信服的视觉证据的理论推导，以及理解的定性性质的解决方案。 该项目中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，鼓励学生在教育中发挥更积极的作用。实验活动使用Matlab软件包。使用德州仪器的基于计算器的实验室单元的实验使学生能够观察物理系统如何通过微分方程建模。所有开发的材料都与同事分享，因为他们通过将它们张贴在万维网上的学院主页上来开发。 这个项目意义重大，因为它可以极大地改变大学数学课程的教学方式。新的课程可以激发学生对这些科目的热情和更好的理解，从而提高学生的保留率和入学率。