《普通高等教育十五国家级规划教材微分几何》是北京大学微分几何课程教材，并为普通高等教育“十五”国家级规划教材，其前身《微分几何初步》曾于1995年获教育部优秀教材一等奖。《普通高等教育十五国家级规划教材微分几何》主要讲述三维欧氏空间中曲线和曲面的理论。全书共七章，内容包括：预备知识、曲线论、曲面的第一基本形式、曲面的第二基本形式、曲面论基本定理、测地曲率和测地线，以及活动标架和外微分法。《普通高等教育十五国家级规划教材微分几何》的取材和体例仍同于《微分几何初步》，但在内容上吸取了近几年教学改革和教学实践的新鲜经验，作了较多的增改；并增添了一定数量的习题。附录也有增删，例如为便于读者自学，增加了用MATHEMATICA做的课件；书末并附有习题解答和提示，便于读者使用。《普通高等教育十五国家级规划教材微分几何》力图与近代微分几何的语言和方法靠近，突出标架场的功用，介绍活动标架和外微分法。《普通高等教育十五国家级规划教材微分几何》阐述深入浅出，条理清楚，突显几何思想，便于读者理解和掌握。

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