本書深入貫徹近年職業(yè)教育有關指示批示和重要文件精神，基于高職教育的實際情況和本課程教學要求，基于"數(shù)專結合”理念，以服務高職院校航空專業(yè)群（含通用航空航務技術、無人機應用技術、通用航空器維修、空中乘務等專業(yè)）教學需求為導向，內容體現(xiàn)思想性、科學性、基礎性、職業(yè)性、時代性，體現(xiàn)學科知識與航空行業(yè)應用場景的融合，對數(shù)學概念、性質等內容提供直觀、通俗的說明和解釋，契合高職生數(shù)學基礎和學習特點。本書作為高職院校航空專業(yè)學生必修的一門專業(yè)基礎課教材，分為兩個部分：一是基礎部分。以一元函數(shù)微積分的基本知識和計算技能為主線，夯實基礎，同時結合課程思政，提高學生數(shù)學核心素養(yǎng)。二是應用部分。以航空專業(yè)球面幾何知識和數(shù)學模型為主要教學內容，注重使學生掌握航空專業(yè)知識相關的數(shù)學技能，服務專業(yè)課學習需求和未來職業(yè)發(fā)展需要。
金晶晶，1983年8月出生，中共黨員，福建船政交通職業(yè)學院通識教育學院副院長、黨總支副書記，擔任校數(shù)學學科專業(yè)帶頭人、校級教學名師，福建省職業(yè)教育教科研組數(shù)學組副組長。結合學院雙高項目牽頭開展了基于專業(yè)能力模型的數(shù)學課程模塊化數(shù)學課程改革，修訂數(shù)學課程標準。主持《高等數(shù)學（模塊A）》校級精品課程建設。作為團隊負責人獲2022年全國職業(yè)院校技能大賽教學能力比賽二等獎。
目 錄
基礎模塊
第一章 基礎知識 ···························································································.1
第一節(jié) 代數(shù)基礎 ····················································································2
第二節(jié) 等式與不等式 ··············································································9
第三節(jié) 函數(shù)及其性質 ···········································································.19
第四節(jié) 幾何基礎 ·················································································.39
復習題一 ·····························································································.47
第二章 極限與連續(xù) ························································································52
第一節(jié) 函數(shù)的極限 ··············································································.53
第二節(jié) 極限的運算 ··············································································.65
第三節(jié) 函數(shù)的連續(xù)性 ···········································································.81
復習題二 ·····························································································.91
第三章 導數(shù)與微分 ·····················································································.100
第一節(jié) 導數(shù)的概念 ··············································································101
第二節(jié) 直接求導法 ··············································································110
第三節(jié) 復合函數(shù)求導法 ········································································114
第四節(jié) 隱函數(shù)求導法和參數(shù)方程求導法 ···················································120
第五節(jié) 高階導數(shù) ·················································································124
第六節(jié) 函數(shù)的微分 ··············································································127
復習題三 ·····························································································131
第四章 導數(shù)的應用 ·····················································································.137
第一節(jié) 微分中值定理 ···········································································138
第二節(jié) 洛必達法則 ··············································································141
第三節(jié) 函數(shù)的單調性和極值 ··································································147
第四節(jié) 函數(shù)的最值 ··············································································153
第五節(jié) 曲線的凸凹與拐點 ·····································································156
復習題四 ·····························································································165
第五章 不定積分 ························································································.170
第一節(jié) 原函數(shù)與不定積分 ·····································································170
V
高等數(shù)學（航空類）
第二節(jié) 不定積分的第一換元積分法 ·························································179
第三節(jié) 不定積分的第二換元積分法 ·························································186
第四節(jié) 不定積分的分部積分法 ·······························································191
第五節(jié) 積分表的使用 ···········································································197
復習題五 ·····························································································198
第六章 定積分 ···························································································.206
第一節(jié) 定積分的概念與性質 ··································································207
第二節(jié) 定積分的計算 ···········································································217
第三節(jié) 定積分在幾何上的應用 ·······························································225
復習題六 ·····························································································230
第七章 微分方程 ························································································.234
第一節(jié) 微分方程的基本概念 ··································································235
第二節(jié) 一階微分方程 ···········································································237
第三節(jié) 二階微分方程 ···········································································243
第四節(jié) 微分方程的應用 ········································································251
復習題七 ·····························································································254
職業(yè)模塊
第八章 多元函數(shù)微積分及其應用 ···································································.257
第一節(jié) 多元函數(shù)極限與連續(xù)性 ·······························································258
第二節(jié) 偏導數(shù)及全微分 ········································································262
第三節(jié) 多元函數(shù)的極值及其應用 ····························································268
第四節(jié) 二重積分 ·················································································272
復習題八 ·····························································································281
第九章 空間解析幾何 ··················································································.284
第一節(jié) 向量的幾何表示 ········································································284
第二節(jié) 向量的坐標表示 ········································································287
第三節(jié) 平面及其方程 ···········································································295
第四節(jié) 空間直線及其方程 ·····································································299
復習題九 ·····························································································305
第十章 航空工程測量誤差理論基礎 ································································.308
第一節(jié) 測量誤差概述 ···········································································309
第二節(jié) 航空工程中的測量精度的標準 ······················································313
第三節(jié) 誤差傳播定律 ···········································································316
第四節(jié) 最或是值及其殘差 ·····································································321
第五節(jié) 等精度直接觀測平差 ··································································322
復習題十 ·····························································································326
附錄 積分表 ······························································································.327
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