Applied Mathematics and Linear Algebra in an Electronic Classroom Environment

9451557 Lawson杜兰大学数学系正在将计算机应用纳入其核心应用数学和线性代数课程。这些课程是科学和工程课程的基础。应用数学课程是所有工程和大多数理科生的必修课程，线性代数课程是数学专业的必修课程，也是许多工程和理科生的必修课程。在这两门课程中，软件的作用都是增强对基本概念的理解。学生将能够在随后的科学和工程课程以及工作场所使用该软件。应用数学课程使用相平面分析来帮助学生理解由各种模型产生的非线性系统的定性行为。它还使用Mathematica对微分方程进行符号和数值分析。线性代数课程使用Mathematica和Matlab实现对LU、QR和奇异值二分等关键算法的掌握，并提供激励示例的数值和符号探索。这两门课都会在每次的课堂上把计算作为一种基本的工具，让学生更积极地参与到课程中来。小组活动将在这两门课中发挥关键作用。将通过出版物和在会议上的介绍进行传播。

9451557 Lawson The Mathematics Department at Tulane University is integrating computer use into its core applied mathematics and linear algebra courses. These courses are fundamental to the science and engineering curriculum. The applied math course is required for all engineering and most science students, and the linear algebra course is required for math majors and taken by many engineering and science students. In both courses the role of the software is to enhance understanding of the basic concepts. Students will be able to use the software in subsequent science and engineering courses and in the workplace. The applied math course uses phase plane analysis to help students understand the qualitative behavior of nonlinear systems arising from a variety of models. It also uses Mathematica to allow symbolic and numerical analysis of differential equations. The linear algebra course uses Mathematica and Matlab to achieve mastery of crucial algorithms such as LU, QR, and singular value dicompositions as well as provide numerical and symbolic exploration of motivating examples. Both classes will make fundamental use of computing as an integral tool in each class meeting, involving the students more actively in the course. Group activities will play a key role in both classes. Dissemination will occur through publications as well as presentations at conferences.