Aimed at the public college course advanced mathematics, a few cases which derived from the practical application background can be applied in research-oriented teaching. It helps the student grasp the essence and understand the profound idea with efifciency. It can help the student improve the interest and ability of research at the same time.%结合大学公共基础课高等数学，建构若干具有实际背景的、适合于教师实施课堂教学或学生自主实验的研究型教学案例，让学生在知识的发现过程中抓住其本质，加深对概念的理解和掌握，同时培养学生研究问题的兴趣和能力。
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