• 高等数学(航空类)
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高等数学(航空类)

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作者金晶晶

出版社电子工业出版社

ISBN9787121464881

出版时间2023-09

装帧平装

开本其他

定价69.9元

货号1203113044

上书时间2024-07-02

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目录
目 录

基础模块

第一章 基础知识 ···························································································.1

第一节 代数基础 ····················································································2

第二节 等式与不等式 ··············································································9

第三节 函数及其性质 ···········································································.19

第四节 几何基础 ·················································································.39

复习题一 ·····························································································.47

第二章 极限与连续 ························································································52

第一节 函数的极限 ··············································································.53

第二节 极限的运算 ··············································································.65

第三节 函数的连续性 ···········································································.81

复习题二 ·····························································································.91

第三章 导数与微分 ·····················································································.100

第一节 导数的概念 ··············································································101

第二节 直接求导法 ··············································································110

第三节 复合函数求导法 ········································································114

第四节 隐函数求导法和参数方程求导法 ···················································120

第五节 高阶导数 ·················································································124

第六节 函数的微分 ··············································································127

复习题三 ·····························································································131

第四章 导数的应用 ·····················································································.137

第一节 微分中值定理 ···········································································138

第二节 洛必达法则 ··············································································141

第三节 函数的单调性和极值 ··································································147

第四节 函数的最值 ··············································································153

第五节 曲线的凸凹与拐点 ·····································································156

复习题四 ·····························································································165

第五章 不定积分 ························································································.170

第一节 原函数与不定积分 ·····································································170

V

高等数学(航空类)

第二节 不定积分的第一换元积分法 ·························································179

第三节 不定积分的第二换元积分法 ·························································186

第四节 不定积分的分部积分法 ·······························································191

第五节 积分表的使用 ···········································································197

复习题五 ·····························································································198

第六章 定积分 ···························································································.206

第一节 定积分的概念与性质 ··································································207

第二节 定积分的计算 ···········································································217

第三节 定积分在几何上的应用 ·······························································225

复习题六 ·····························································································230

第七章 微分方程 ························································································.234

第一节 微分方程的基本概念 ··································································235

第二节 一阶微分方程 ···········································································237

第三节 二阶微分方程 ···········································································243

第四节 微分方程的应用 ········································································251

复习题七 ·····························································································254

职业模块

第八章 多元函数微积分及其应用 ···································································.257

第一节 多元函数极限与连续性 ·······························································258

第二节 偏导数及全微分 ········································································262

第三节 多元函数的极值及其应用 ····························································268

第四节 二重积分 ·················································································272

复习题八 ·····························································································281

第九章 空间解析几何 ··················································································.284

第一节 向量的几何表示 ········································································284

第二节 向量的坐标表示 ········································································287

第三节 平面及其方程 ···········································································295

第四节 空间直线及其方程 ·····································································299

复习题九 ·····························································································305

第十章 航空工程测量误差理论基础 ································································.308

第一节 测量误差概述 ···········································································309

第二节 航空工程中的测量精度的标准 ······················································313

第三节 误差传播定律 ···········································································316

第四节 最或是值及其残差 ·····································································321

第五节 等精度直接观测平差 ··································································322

复习题十 ·····························································································326

附录 积分表 ······························································································.327

内容摘要
本书深入贯彻近年职业教育有关指示批示和重要文件精神,基于高职教育的实际情况和本课程教学要求,基于"数专结合”理念,以服务高职院校航空专业群(含通用航空航务技术、无人机应用技术、通用航空器维修、空中乘务等专业)教学需求为导向,内容体现思想性、科学性、基础性、职业性、时代性,体现学科知识与航空行业应用场景的融合,对数学概念、性质等内容提供直观、通俗的说明和解释,契合高职生数学基础和学习特点。本书作为高职院校航空专业学生必修的一门专业基础课教材,分为两个部分:一是基础部分。以一元函数微积分的基本知识和计算技能为主线,夯实基础,同时结合课程思政,提高学生数学核心素养。二是应用部分。以航空专业球面几何知识和数学模型为主要教学内容,注重使学生掌握航空专业知识相关的数学技能,服务专业课学习需求和未来职业发展需要。

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