四川省普通高校在校生专升本高等数学

前 言

本书是普通高等学校专升本专用教材，是根据四川省普通高等学校专升本考试大纲，深入分析近年来“高等数学”专升本考试试题特点，尤其是针对学生在考前复习时遇到的问题，综合相关“高等数学”专升本教材和参考资料，由长期在高等院校担任“高等数学”教学和研究的专家和老师们合力编写而成的. 

专升本考试为有志于继续学习深造的学生创造了机会，是学生提高学历层次的有效途径. 目前，参加专升本考试的学生逐年增加，竞争日趋激烈，但学生常常苦于选不出适合自己的教材或参考书，进而无法较为准确地衡量自己的学习状况和知识水平. 为了减轻学生的心理压力，为学生排忧解难，本书从知识内容、考点分布、试题类型等角度进行了合理安排，有利于学生合理分配学习“高等数学”的时间、精力并把握学习的节奏，*终顺利通过专升本考试. 

本书的编写，遵从高等数学的知识体系，在比较系统地概括高等数学的基本概念和基本理论的基础上，紧扣《四川省普通高等学校专升本考试大纲》主线，对不同章节的知识点进行取舍，删繁就简，去粗取精，力求知识结构严谨，脉络清晰，避免考生在复习时面面俱到，花费不必要的时间和精力. 同时，在深入分析研究近年来普通高等学校专升本考试试题的基础上，归纳考试范围，把握重点和难点，使学生做到心中有数，沉着应对，起到事半功倍的效果. 

全书共分八章，主要内容包括函数、极限和连续、一元函数微分学、一元函数积分学、向量代数和空间解析几何、多元函数微积分学、无穷级数、常微分方程和线性代数. 每章由基本知识点、考点解析、题型训练和参考答案四部分组成，考点解析和题型训练中的大部分试题选自近年来的考试真题，具有很强的代表性. 

我们将这本极具针对性的教材谨献给准备参加专升本的学生，祝愿梦想成真. 

限于编者水平，书中难免存在不妥之处，恳请读者批评指正. 

编 者 

2018年9月 

目 录

*章 函数、极限和连续···································································································· 1

*节 函数················································································································ 1

第二节 极限················································································································ 7

第三节 函数的连续与间断··························································································· 17

考点解析···················································································································· 24

题型训练···················································································································· 33

参考答案···················································································································· 35

第二章 一元函数微分学····································································································· 38

*节 导数与微分···································································································· 38

第二节 中值定理········································································································ 48

第三节 导数的应用···································································································· 53

考点解析····················································································································· 59

题型训练···················································································································· 70

参考答案····················································································································· 73

第三章 一元函数积分学····································································································· 77

*节 不定积分········································································································ 77

第二节 定积分··········································································································· 85

第三节 定积分的应用································································································· 94

考点解析···················································································································· 98

考点解析··················································································································· 250

题型训练··················································································································· 263

参考答案··················································································································· 266

参考文献·························································································································· 269