常微分方程解的延拓定理教学研究

On Teaching of Continuation Theorem of Solutions in Ordinary Differential Equations

探讨了解的延拓定理的教学策略.针对学生在理解和应用定理时遇到的困难,从分析学的角度补充证明了定理,并给出了两个可以进行条件验证的推论.在此基础上,结合三个具体例子,提供了不同于教材的求最大存在区间的新途径.

This paper discusses the teaching strategy of continuation theorem of solutions which is one of important theories in Ordinary Differential Equations. In order to help students to understand and apply this theorem, its proof has been added from an analytical point of view. Moreover, two corollaries whose conditions can be verified directly have been deduced. Based on these results, new methods, being different from that of textbook, have been applied for three examples to obtain the corresponding maximum existing interval of solutions.