一道高等数学题的多种解法

Several Solutions to One Problem of Higher Mathematic

高等数学是理工科院校一门十分重要的公共基础课,在培养和训练学生的创新能力方面起着重要的作用.在高等数学的教学中应注重学生数学思维能力的培养和发散思维的训练.发散思维是创新思维的主要形式之一,而一题多解是发散思维的具体表现.利用导数求极值法,变量代换法,等价变换法,不等式法等给出一道高等数学题的九种解法,以此引导学生去深入探索问题,培养学生的创新思维能力.

Higher Mathematics is a highly fundamental basic course in Institutes of Technology. It plays a crucial rolein developing and training students＇ innovation skill. In the teaching of higher mathematics, it is essential to pay attentionto the cultivation of students＇ mathematical thinking skill and the training of divergent thinking. Divergent thinking is oneof the main forms of creative thinking, and multiple solutions for one problem are the manifestation of divergent thinking.Nine kinds of solutions to a problem of higher mathematics can be provided by varied methods, such as Derivativeextremum method , variable substitution method, the equivalent transformation method, inequality method, etc. In suchway, students are guided to deeply explore problems and to develop their innovative thinking skill.