Linearity I & II: Connected Learning of Differential Equations, Linear Algebra and Multi-variable Calculus

新汉普郡大学(UNH)正在围绕线性的基本概念和线性化过程组织一个为期一年的综合课程。这个系列的目标是：1)统一学习常微分方程式、线性代数和多元微积分中通常以单独方式学习的核心思想和技术，通过大写这三个学科领域之间的丰富相互联系，以及2)最大限度地增加学生参与这些关键概念的背景学习的机会。为了实现这些目标，数学科学系正在与机械工程、电气工程和物理的同事合作，开发用于课堂的“实验台实验”。这些实验取材于同时招收学生的许多课程所研究的应用领域，能够将通常静态的学习环境重组为采用“工作室”或实验室方法的动态学习环境。目前正在为商业出版而开发基于这套“实验台”实验的教学材料。试点测试将从一组机械工程、电气和计算机工程以及应用数学科学的学生开始。这一方法的全面实施预计将对UNH工程和物理科学学院的所有学生产生影响。

A year-long integrated course of study organized around the fundamental concept of linearity and the process of linearization is being developed at the University of New Hampshire (UNH). The goals of this sequence are: 1) to unify the learning of the core ideas and techniques normally studied in a separate fashion in ordinary differential equations, linear algebra, and multivariable calculus, by captitalizing on the rich interconnections among the three subject areas, and 2) to maximize student opportunities to engage in contextual learning of these key concepts. To achieve these goals, mathematical sciences faculty are collaborating with colleagues from mechanical engineering, electrical engineering, and physics, to develop "bench-lab experiments" for use in the classroom. These experiments are drawn from the application areas studied in many of the courses in which students are concurrently enrolled, and enable the restructuring of the normally static learning environment into a dynamic one employing a "studio" or laboratory approach. Teaching and learning materials based on the set of "bench-lab" experiments are being developed for commercial publication. Pilot testing will begin with a group of mechanical engineering, electrical and computer engineering, and applied mathematical sciences students. Full implementation of this approach is expected to impact all students in the UNH College of Engineering and Physical Sciences.