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普通高等教育“十一五”国家级规划教材·辅导教材
普通高等院校大学数学“十三五”规划教材
高等院校精品教材系列
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主 编 常桂娟 副主编 曹秀梅 王述香 吴 伟 孙春薇 姜兆英 参 编 姜德民 孙宝山 赵 静 吴春妹
内 容 简 介 《高等数学（同济第七版 下册）》包括五章内容，因此《高等数学（同济第七版 下册）习题辅导书》相应地包含五章的习题及其解答，每章内容包括基本内容、基本要求和习题解答。此外，书中还提供历年考研部分试题及解答、《高等数学（下册）》期末考试试卷选编及参考答案。全书习题丰富，解答详细完整，图表清晰，是学好高等数学课程的首选练习册和优秀的考研指导书。 本书可作为大学工科学生高等数学课程的复习指导和练习册，也可作为考研人员的参考书。 未经许可，不得以任何方式复制或抄袭本书之部分或全部内容。 版权所有，侵权必究。
图书在版编目(CIP)数据 高等数学（同济第七版）习题辅导书. 下册/常桂娟主编. —北京：电子工业出版社，2015.7 ISBN 978-7-121-26305-7 I．①高… II．①常… III．①高等数学－高等学校－题解 IV．①O13-44 中国版本图书馆CIP数据核字(2015)第127824号
策划编辑：王羽佳 责任编辑：王羽佳 特约编辑：王 崧 印 刷： 装 订： 出版发行：电子工业出版社 北京市海淀区万寿路173信箱 邮编：100036 开 本：787×1092 1/16 印张：16.75 字数：435千字 版 次：2015年7月第1版 印 次：2015年7月第1次印刷 定 价：35.00元 凡所购买电子工业出版社图书有缺损问题，请向购买书店调换。若书店售缺，请与本社发行部联系，联系及邮购电话：(010)88254888。 质量投诉请发邮件至zlts@phei.com.cn，盗版侵权举报请发邮件至dbqq@phei.com.cn。 服务热线：(010)88258888。
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本书是与同济大学数学系编写的教材《高等数学（第七版）》相配套的辅导教材. 同济大学数学系编写的《高等数学》是本科生学习高等数学的经典之作。因此，本书也力求成为更适合大学生学习《高等数学》的指导书, 可作为报考硕士研究生入学考试的复习参考书, 还可为高等数学教师批改作业或备课提供参考. 为方便读者使用, 本书在内容上严格按照同济大学《高等数学（第七版）》的各章顺序对应编写, 其内容包括三篇. 第一篇是《高等数学（下册）》习题解答, 内容包括: ① 基本内容, 列出各章节的基本理论知识; ② 基本要求, 提出学生对各章节知识点需要掌握的程度; ③ 习题解答, 给出《高等数学（下册）》教材各章节习题、总习题的解答. 第二篇是历年考研部分试题及解答, 内容涵盖向量代数与空间解析几何、多元函数微分学、多元函数积分学、无穷级数, 给出了每道试题的年份及类别, 学生可以根据自己的具体情况进行选做. 第三篇是《高等数学（下册）》期末考试试卷选编及参考答案. 本书由青岛农业大学理学与信息科学学院数学教师编写. 其中, 第一篇内容的第8章由曹秀梅编写, 第9章由姜兆英、赵静编写, 第10章由王述香、孙春薇编写, 第11章由吴春妹编写, 第12章由吴伟、孙宝山编写. 第二篇历年考研部分试题及解答由姜德民编写; 第三篇及最终的统稿、定稿由常桂娟完成. 由于时间仓促, 在编写上难免会有错误, 敬请同行、专家、读者批评指正. 编 者 2015年
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第8章 空间解析几何与向量代数 ··············································································································· 2 一、基本内容 ············································································································································ 2 二、基本要求 ············································································································································ 2 三、习题解答 ············································································································································ 3 总习题八 ·················································································································································· 19 第9章 多元函数微分法及其应用 ············································································································· 26 一、基本内容 ·········································································································································· 26 二、基本要求 ·········································································································································· 27 三、习题解答 ·········································································································································· 27 总习题九 ·················································································································································· 61 第10章 重积分 ·········································································································································· 69 一、基本内容 ·········································································································································· 69 二、基本要求 ·········································································································································· 69 三、习题解答 ·········································································································································· 69 总习题十 ················································································································································ 104 第11章 曲线积分与曲面积分 ················································································································ 114 一、基本内容 ········································································································································ 114 二、基本要求 ········································································································································ 115 三、习题解答 ········································································································································ 115 总习题十一 ············································································································································ 154 第12章 无穷级数 ······················································································
普通高等院校大学数学“十三五”规划教材
高等院校精品教材系列
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主 编 常桂娟 副主编 曹秀梅 王述香 吴 伟 孙春薇 姜兆英 参 编 姜德民 孙宝山 赵 静 吴春妹
内 容 简 介 《高等数学（同济第七版 下册）》包括五章内容，因此《高等数学（同济第七版 下册）习题辅导书》相应地包含五章的习题及其解答，每章内容包括基本内容、基本要求和习题解答。此外，书中还提供历年考研部分试题及解答、《高等数学（下册）》期末考试试卷选编及参考答案。全书习题丰富，解答详细完整，图表清晰，是学好高等数学课程的首选练习册和优秀的考研指导书。 本书可作为大学工科学生高等数学课程的复习指导和练习册，也可作为考研人员的参考书。 未经许可，不得以任何方式复制或抄袭本书之部分或全部内容。 版权所有，侵权必究。
图书在版编目(CIP)数据 高等数学（同济第七版）习题辅导书. 下册/常桂娟主编. —北京：电子工业出版社，2015.7 ISBN 978-7-121-26305-7 I．①高… II．①常… III．①高等数学－高等学校－题解 IV．①O13-44 中国版本图书馆CIP数据核字(2015)第127824号
策划编辑：王羽佳 责任编辑：王羽佳 特约编辑：王 崧 印 刷： 装 订： 出版发行：电子工业出版社 北京市海淀区万寿路173信箱 邮编：100036 开 本：787×1092 1/16 印张：16.75 字数：435千字 版 次：2015年7月第1版 印 次：2015年7月第1次印刷 定 价：35.00元 凡所购买电子工业出版社图书有缺损问题，请向购买书店调换。若书店售缺，请与本社发行部联系，联系及邮购电话：(010)88254888。 质量投诉请发邮件至zlts@phei.com.cn，盗版侵权举报请发邮件至dbqq@phei.com.cn。 服务热线：(010)88258888。
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本书是与同济大学数学系编写的教材《高等数学（第七版）》相配套的辅导教材. 同济大学数学系编写的《高等数学》是本科生学习高等数学的经典之作。因此，本书也力求成为更适合大学生学习《高等数学》的指导书, 可作为报考硕士研究生入学考试的复习参考书, 还可为高等数学教师批改作业或备课提供参考. 为方便读者使用, 本书在内容上严格按照同济大学《高等数学（第七版）》的各章顺序对应编写, 其内容包括三篇. 第一篇是《高等数学（下册）》习题解答, 内容包括: ① 基本内容, 列出各章节的基本理论知识; ② 基本要求, 提出学生对各章节知识点需要掌握的程度; ③ 习题解答, 给出《高等数学（下册）》教材各章节习题、总习题的解答. 第二篇是历年考研部分试题及解答, 内容涵盖向量代数与空间解析几何、多元函数微分学、多元函数积分学、无穷级数, 给出了每道试题的年份及类别, 学生可以根据自己的具体情况进行选做. 第三篇是《高等数学（下册）》期末考试试卷选编及参考答案. 本书由青岛农业大学理学与信息科学学院数学教师编写. 其中, 第一篇内容的第8章由曹秀梅编写, 第9章由姜兆英、赵静编写, 第10章由王述香、孙春薇编写, 第11章由吴春妹编写, 第12章由吴伟、孙宝山编写. 第二篇历年考研部分试题及解答由姜德民编写; 第三篇及最终的统稿、定稿由常桂娟完成. 由于时间仓促, 在编写上难免会有错误, 敬请同行、专家、读者批评指正. 编 者 2015年
4月
前 言3
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第8章 空间解析几何与向量代数 ··············································································································· 2 一、基本内容 ············································································································································ 2 二、基本要求 ············································································································································ 2 三、习题解答 ············································································································································ 3 总习题八 ·················································································································································· 19 第9章 多元函数微分法及其应用 ············································································································· 26 一、基本内容 ·········································································································································· 26 二、基本要求 ·········································································································································· 27 三、习题解答 ·········································································································································· 27 总习题九 ·················································································································································· 61 第10章 重积分 ·········································································································································· 69 一、基本内容 ·········································································································································· 69 二、基本要求 ·········································································································································· 69 三、习题解答 ·········································································································································· 69 总习题十 ················································································································································ 104 第11章 曲线积分与曲面积分 ················································································································ 114 一、基本内容 ········································································································································ 114 二、基本要求 ········································································································································ 115 三、习题解答 ········································································································································ 115 总习题十一 ············································································································································ 154 第12章 无穷级数 ······················································································
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