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随着新课改的不断推进,参与高考命题的专家越来越重视初、高等数学知识的衔接,很多高考题、模拟题的命制都喜欢有着高等数学背景的定理,这些看起来抽象、高深的定理下放到中学试卷中,用初等数学方法来解答,往往蕴含着丰富的数学思想,对于训练思维非常有好处。下面我将从线性变换、不动点和凹凸函数三个方面给出例证。
With the continuous advancement of the new curriculum reform, experts participating in the college entrance examination propositions pay more and more attention to the connection of elementary and advanced mathematics knowledge. Many college entrance exam questions and simulation questions like the theorems of higher mathematics background. These seem abstract and profound Theorem into secondary school papers, using elementary mathematics to answer, often contains a wealth of mathematical thinking, for training thinking is very good. Below I will give an example from the three aspects of linear transformation, fixed point and bump function.