Vector Calculus via Linearization: Visualization and ModernApplications

通过线性化进行向量微积分：可视化和现代应用

• 批准号: 9752453
• 负责人: Matthias Kawski
• 金额: $ 7.5万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-01-15 至 2000-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9752453&HistoricalAwards=false
• 关键词: Vector; Calculus; via; Linearization; Visualization

This project is developing a radically new approach to vector calculus that is completely aligned with recent reform efforts in other college entry-level math, science, and engineering (MSE) courses. As part of this larger MSE curriculum, it brings more coherence and consistency to it, emphasizing the common foundation for much of these courses. Sophisticated computer visualization is vigorously exploited as it has opened a completely new avenue to vector calculus, allowing to reconnect the concepts of vectorial derivatives back to their foundation, local linearity. Students now can see the curl by zooming. Connections to concepts of linear algebra and differential equations perspectives are omnipresent. The curriculum is ideally suited for cooperative learning environments where students are guided to make many key discoveries themselves via often dramatic computer experiments. The new course is also broadening the range of applications (beyond the traditional EM and fluid dynamics) by drawing on modern geometric control which has ubiquitous applications, even connecting to recent research achievements that fit into this sophomore course. The curriculum is being implemented in the form of interactive texts, and is using modern electronic media and the WWW for rapid dissemination. Assessment of the enhanced learning experiences is an integral part of the project. This curriculum is having a high impact on both MSE majors and future math and science teachers by conveying a coherent and modern view of advanced mathematics.

这个项目正在开发一种全新的矢量微积分方法，与最近其他大学入门级数学、科学和工程(MSE)课程的改革努力完全一致。作为这个更大的MSE课程的一部分，它带来了更多的连贯性和一致性，强调了这些课程的共同基础。复杂的计算机可视化被大力开发，因为它为矢量微积分开辟了一条全新的途径，允许将矢量导数的概念重新连接到它们的基础局部线性。现在，学生们可以通过缩放看到卷曲。与线性代数和微分方程式概念的联系无处不在。该课程非常适合于合作学习环境，在这种环境中，学生被引导通过通常是戏剧性的计算机实验自己做出许多关键发现。这门新课程还拓宽了应用范围(超越传统的电磁和流体动力学)，利用了应用无处不在的现代几何控制，甚至结合了这门二年级课程的最新研究成果。该课程正在以互动文本的形式实施，并利用现代电子媒体和万维网迅速传播。评估增强的学习体验是该项目的一个组成部分。这门课程传达了一种连贯而现代的高等数学观，对MSE专业的学生和未来的数学和科学教师都产生了很大的影响。