微分方程：Mathematica®简介

English | PDF | 2004 | 445 Pages | ISBN : 0387212841 | 28.9 MB

Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex­ plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat­ ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory.

英文|PDF|2004|445页|ISBN:0387212841|28.9 MB《数学家》一书的目标和重点已经开始找到将计算能力纳入数学课程的有效方法。这里没有试图使用计算来避免做微分方程和线性代数。目标是让已经学过一年微积分的学生能够接触到这门学科的一些初步探索。一些科学现在正在利用Mathematica的符号操纵能力，使更多的学科变得触手可及。这本书是微分方程和线性代数的一种方法。我相信，如果一个学生第一次接触一门学科是愉快和令人兴奋的，那么这个学生就会寻找继续学习这门学科的方法。微分方程和线性代数理论渗透在讨论中。每个主题都有一个理论陈述作为支撑。但这里的主要推动力是获得解和关于解的信息，而不是证明定理。在其他课程中，证明定理是核心。本文的目标是建立对解决方案概念的扎实理解，并欣赏该理论在寻求解决方案过程中给予的信心。后来，学生在个人发展理论的同时也可以有同样的信心。

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