首页 > 教育 > 高职高专 > 其他

高等数学习题解答及考研辅导（上册）

作译者：王玲娜

出版时间：2025-07 千字数：302 版次：01-01 页数：180

开本：16开装帧： I S B N ：9787121512681

换版：

纸质书定价：￥49.0

库存:无

分享到：

共有图书评论0条【查看评论摘要】

看了又看

{{data.bookName}}

￥{{data.price}}

内容简介

前言

上架建议

作者简介

编辑推荐

音视频专区

第一章 函数与极限 ·······················································································.1 
第一节 映射与函数··················································································.1 
一、考研典型例题解析··································································.2
二、考研自测习题········································································.2
第二节 数列的极限··················································································.3 
一、典型习题解析········································································.4
二、考研典型例题解析··································································.4
三、考研自测习题········································································.5
第三节 函数的极限··················································································.7 
一、典型习题解析········································································.7 
二、考研典型例题解析··································································.8 
三、考研自测习题········································································.9 
第四节 无穷小与无穷大 ··········································································.10 
一、典型习题解析·······································································.11 
二、考研典型例题解析·································································.11 
三、考研自测习题·······································································.13 
第五节 极限运算法则··············································································.13 
一、典型习题解析·······································································.14 
二、考研典型例题解析·································································.14 
三、考研自测习题·······································································.16 
第六节 极限存在准则及两个重要极限 ························································.17 
一、典型习题解析·······································································.18 
二、考研典型例题解析·································································.18 
三、考研自测习题·······································································.21 
第七节 无穷小的比较··············································································.23 
一、典型习题解析·······································································.23 
二、考研典型例题解析·································································.25 
三、考研自测习题·······································································.28 
第八节 函数的连续性与间断点 ·································································.30 
一、典型习题解析·······································································.31 
二、考研典型例题解析·································································.31 
三、考研自测习题·······································································.33 
第九节 连续函数的运算与初等函数的连续性 ···············································.35 
一、典型习题解析·······································································.35 
高等数学习题解答及考研辅导（上册） VI 
二、考研典型例题解析·································································.36 
三、考研自测习题·······································································.37 
第十节 闭区间上连续函数的性质 ······························································.38 
一、典型习题解析·······································································.38 
二、考研典型例题解析·································································.39 
三、考研自测习题·······································································.40 
第二章 导数与微分 ······················································································.42 
第一节 导数概念····················································································.42 
一、典型习题解析·······································································.42 
二、考研典型例题解析·································································.45 
三、考研自测习题·······································································.49 
第二节 函数的求导法则 ··········································································.51 
一、典型习题解析·······································································.52 
二、考研典型例题解析·································································.53 
三、考研自测习题·······································································.55 
第三节 高阶导数····················································································.56 
一、典型习题解析·······································································.56 
二、考研典型例题解析·································································.57 
三、考研自测习题·······································································.59 
第四节 隐函数及参数方程所确定的函数的导数相关变化率 ·····························.60 
一、典型习题解析·······································································.60 
二、考研典型例题解析·································································.62 
三、考研自测习题·······································································.65 
第五节 函数的微分·················································································.67 
一、考研典型例题解析·································································.67 
二、考研自测习题·······································································.68 
第三章 微分中值定理与导数应用····································································.70 
第一节 微分中值定理··············································································.70 
一、典型习题解析·······································································.70 
二、考研典型例题解析·································································.71 
三、考研自测习题·······································································.74 
第二节 洛必达法则·················································································.77 
一、典型习题解析·······································································.77 
二、考研典型例题解析·································································.79 
三、考研自测习题·······································································.81 
第三节 泰勒公式····················································································.83 
一、典型习题解析·······································································.83 
二、考研典型例题解析·································································.84 
目 录 VII 
三、考研自测习题·······································································.87 
第四节 函数的单调性与曲线的凹凸性 ························································.89 
一、典型习题解析·······································································.90 
二、考研典型例题解析·································································.90 
三、考研自测习题·······································································.94 
第五节 函数的极值与最大值最小值 ···························································.96 
一、典型习题解析·······································································.97 
二、考研典型例题解析·································································.97 
三、考研自测习题·····································································.101 
第四章 不定积分 ·······················································································.103 
第一节 不定积分的概念与性质 ·······························································.103 
一、典型习题解析·····································································.103 
二、考研典型例题解析·······························································.104 
三、考研自测习题·····································································.105 
第二节 换元积分法···············································································.107 
一、典型习题解析·····································································.107 
二、考研典型例题解析·································································110 
三、考研自测习题·······································································112 
第三节 分部积分法·················································································114 
一、典型习题解析·······································································114 
二、考研典型例题解析·································································115 
三、考研自测习题·······································································117 
第四节 有理函数的积分 ········································································.120 
一、典型习题解析·····································································.120 
二、考研典型例题解析·······························································.122 
三、考研自测习题·····································································.125 
第五章 定积分 ··························································································.128 
第一节 定积分的概念和性质 ··································································.128 
一、考研典型例题解析·······························································.128 
二、考研自测习题·····································································.130 
第二节 微积分基本公式 ········································································.132 
一、典型习题解析·····································································.132 
二、考研典型例题解析·······························································.133 
三、考研自测习题·····································································.136 
第三节 定积分换元法和分部积分法 ·························································.137 
一、典型习题解析·····································································.138 
二、考研典型例题解析·······························································.138 
三、考研自测习题·····································································.141 
高等数学习题解答及考研辅导（上册） VIII 
第四节 反常积分··················································································.143 
一、典型习题解析·····································································.144 
二、考研典型例题解析·······························································.144 
三、考研自测习题·····································································.147 
第六章 定积分的应用 ·················································································.150 
第一节 定积分在几何学上的应用 ····························································.150 
一、典型习题解析·····································································.150 
二、考研典型例题解析·······························································.152 
三、考研自测习题·····································································.154 
第二节 定积分在物理学上的应用 ····························································.155 
一、考研典型例题解析·······························································.156 
二、考研自测习题·····································································.158 
第七章 微分方程 ·······················································································.159 
第一节 微分方程的基本概念 ··································································.159 
一、考研典型例题解析·······························································.159 
二、考研自测习题·····································································.159 
第二节 可分离变量的微分方程 ·······························································.160 
一、考研典型例题解析·······························································.160 
二、考研自测习题·····································································.161 
第三节 齐次方程··················································································.162 
一、考研典型例题解析·······························································.162 
二、考研自测习题·····································································.163 
第四节 一阶线性微分方程 ·····································································.164 
一、考研典型例题解析·······························································.164 
二、考研自测习题·····································································.165 
第五节 可降阶的高阶微分方程（仅数学一、数学二要求） ···························.166 
一、考研典型例题解析·······························································.166 
二、考研自测习题·····································································.167 
第六节 高阶线性微分方程 ·····································································.168 
一、考研典型例题解析·······························································.168 
二、考研自测习题·····································································.169 
第七节 常系数齐次线性微分方程 ····························································.169 
一、考研典型例题解析·······························································.170 
二、考研自测习题·····································································.170 
第八节 常系数非齐次线性微分方程 ·························································.171 
一、考研典型例题解析·······························································.171 
二、考研自测习题·····································································.172

本书可作为同济大学数学系编写的《高等数学》（上册）的配套考研辅导教材，以“巩
固基础、考研启蒙、能力进阶”为核心理念，创新性地构建了国内首套面向大一学生的高
等数学同步考研辅导体系。本书以课程标准为根基，以考研要求为导向，旨在帮助学生在
夯实数学基础的同时，系统培养数学思维能力与解题创新能力，为后续学习及考研深造奠
定坚实基础。
本书严格遵循同济版《高等数学》的知识逻辑体系，与课程章节完全同步。每章精心
设计五大特色模块：知识结构以可视化思维导图梳理知识脉络，精准标注重点；知识点讲
解结合典型例题，深化概念理解与应用；考研大纲要求明确能力层级，指引学习方向；典
型习题与考研典型例题解析既巩固课程知识，又前瞻性地训练考研解题思维；考研自测习
题助力学生系统排查知识盲点，促进基础巩固与综合运用能力提升。
本书特色鲜明：其一，精选典型考研例题与自测习题，科学设置难度梯度，既契合大
一学生认知规律，又逐步对接考研要求；其二，所有知识点均配套浙江省线上线下混合式
一流课程《高等数学》教学视频，扫描二维码实现优质资源即时获取，构建立体化学习场
景；其三，知识结构及典型例题凝聚了编者团队多年教学经验的原创成果，助力学生精准
把握学习要点；其四，考研典型例题解析附考点解析与解题思路，培养学生自主学习能力
与创新思维。
本书既适用于高等院校理工类、经济类专业学生同步学习与考研启蒙，亦可供高校数
学教师教学参考，力求为高等数学教学提供兼具实用性与启发性的资源支持。

查看更多 > 图书评论

暂无评论

发表图书评论

评论标题：
评论内容：
验证码：: 看不清楚
点击刷新
: 您还没有登录，请登录后再评论。
点击“登录”

购买过本书的顾客还买过

{{data.bookName}}

￥{{data.price}}