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辅助函数证题法,是高等数学中一种必要的而又高明的手法,让学生掌握它、运用它,是教法课的一个重要内容。这种方法思路独特与一般习惯推理顺序又不尽相同,使人总感玄奥、难以捉摸,是学习中的一个难点。因此很有必要对其规律作进一步的探讨。 辅助函数证题法又称构造法,它是先构造一个与所证结果有关的辅助函数、或者算式、或者命题,而后再运用已知条件及有关概念、推理得出所要证明的结果。 它的基本思路是常以一个目标出发,联想某些曾经学过的方法,而后用这种方法,去接近目标,或者再从这方法出发,又去联想到别的通向目标的方法。这样下去直至达到把问题归结到一个明显成立的结论为止。
Auxiliary function certificate method is a necessary and clever way in advanced mathematics. It is an important part of the teaching method for students to master it and use it. This method of thinking unique and general order of reasoning and not the same, people always feel mysterious and elusive, is a learning difficulty. Therefore, it is necessary to further explore the law. Auxiliary function certificate is also called construction method, it is to construct a auxiliary function, or formula, or proposition related to the result of the certificate, and then use the known conditions and related concepts to deduce the result to be proved. Its basic idea is often to set a goal, to associate some of the methods that have been learned, and then use this method to approach the target, or from this method, but also to think of other ways to reach the target. This continues until the problem is attributed to a clearly established conclusion.