Vector Calculus via Linearization: Visualization and ModernApplications

该项目正在开发一种全新的向量微积分方法，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，因为它为向量微积分开辟了一条全新的途径，允许将向量导数的概念重新连接到它们的基础，局部线性。学生们现在可以通过缩放看到卷曲。与线性代数和微分方程概念的联系是无所不在的。该课程非常适合合作学习环境，在这种环境中，学生被引导通过经常引人注目的计算机实验来自己做出许多关键的发现。新课程还通过借鉴无处不在的现代几何控制，拓宽了应用范围（超越了传统的EM和流体动力学），甚至将最新的研究成果与本大二课程相结合。课程以互动式教材的形式实施，并利用现代电子媒介和万维网迅速传播。加强学习经验的评估是项目的一个组成部分。该课程通过传达连贯和现代的高等数学观点，对MSE专业和未来的数学和科学教师产生了很大的影响。

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.