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

新罕布什尔大学（UNH）正在开展一项为期一年的综合课程，围绕线性的基本概念和线性化过程进行研究。这个顺序的目标是：1)通过利用这三个学科领域之间丰富的相互联系，统一通常以独立方式学习的常微分方程、线性代数和多变量微积分的核心思想和技术的学习；2)最大限度地提高学生参与这些关键概念的上下文学习的机会。为了实现这些目标，数学科学学院正在与来自机械工程、电气工程和物理的同事合作，开发用于课堂的“工作台实验室实验”。这些实验是从学生同时注册的许多课程中研究的应用领域中提取的，并且能够利用“工作室”或实验室方法将通常静态的学习环境重组为动态的学习环境。基于一套“工作台-实验室”实验的教学材料正在开发中，以供商业出版。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。这种方法的全面实施预计将影响到UNH工程与物理科学学院的所有学生。

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.