本書深入貫徹近年職業(yè)教育有關(guān)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(xué)要求,基于"數(shù)專結(jié)合”理念,以服務(wù)高職院校航空專業(yè)群(含通用航空航務(wù)技術(shù)、無人機應(yīng)用技術(shù)、通用航空器維修、空中乘務(wù)等專業(yè))教學(xué)需求為導(dǎo)向,內(nèi)容體現(xiàn)思想性、科學(xué)性、基礎(chǔ)性、職業(yè)性、時代性,體現(xiàn)學(xué)科知識與航空行業(yè)應(yīng)用場景的融合,對數(shù)學(xué)概念、性質(zhì)等內(nèi)容提供直觀、通俗的說明和解釋,契合高職生數(shù)學(xué)基礎(chǔ)和學(xué)習(xí)特點。本書作為高職院校航空專業(yè)學(xué)生必修的一門專業(yè)基礎(chǔ)課教材,分為兩個部分:一是基礎(chǔ)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(chǔ),同時結(jié)合課程思政,提高學(xué)生數(shù)學(xué)核心素養(yǎng)。二是應(yīng)用部分。以航空專業(yè)球面幾何知識和數(shù)學(xué)模型為主要教學(xué)內(nèi)容,注重使學(xué)生掌握航空專業(yè)知識相關(guān)的數(shù)學(xué)技能,服務(wù)專業(yè)課學(xué)習(xí)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(xué)院通識教育學(xué)院副院長、黨總支副書記,擔(dān)任校數(shù)學(xué)學(xué)科專業(yè)帶頭人、校級教學(xué)名師,福建省職業(yè)教育教科研組數(shù)學(xué)組副組長。結(jié)合學(xué)院雙高項目牽頭開展了基于專業(yè)能力模型的數(shù)學(xué)課程模塊化數(shù)學(xué)課程改革,修訂數(shù)學(xué)課程標(biāo)準(zhǔn)。主持《高等數(shù)學(xué)(模塊A)》校級精品課程建設(shè)。作為團隊負責(zé)人獲2022年全國職業(yè)院校技能大賽教學(xué)能力比賽二等獎。
目 錄
基礎(chǔ)模塊
第一章 基礎(chǔ)知識 ···························································································.1
第一節(jié) 代數(shù)基礎(chǔ) ····················································································2
第二節(jié) 等式與不等式 ··············································································9
第三節(jié) 函數(shù)及其性質(zhì) ···········································································.19
第四節(jié) 幾何基礎(chǔ) ·················································································.39
復(fù)習(xí)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(fù)習(xí)題二 ·····························································································.91
第三章 導(dǎo)數(shù)與微分 ·····················································································.100
第一節(jié) 導(dǎo)數(shù)的概念 ··············································································101
第二節(jié) 直接求導(dǎo)法 ··············································································110
第三節(jié) 復(fù)合函數(shù)求導(dǎo)法 ········································································114
第四節(jié) 隱函數(shù)求導(dǎo)法和參數(shù)方程求導(dǎo)法 ···················································120
第五節(jié) 高階導(dǎo)數(shù) ·················································································124
第六節(jié) 函數(shù)的微分 ··············································································127
復(fù)習(xí)題三 ·····························································································131
第四章 導(dǎo)數(shù)的應(yīng)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(diào)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(fù)習(xí)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(xué)(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(fù)習(xí)題五 ·····························································································198
第六章 定積分 ···························································································.206
第一節(jié) 定積分的概念與性質(zhì) ··································································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(yīng)用 ·······························································225
復(fù)習(xí)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(yīng)用 ········································································251
復(fù)習(xí)題七 ·····························································································254
職業(yè)模塊
第八章 多元函數(shù)微積分及其應(yīng)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(dǎo)數(shù)及全微分 ········································································262
第三節(jié) 多元函數(shù)的極值及其應(yīng)用 ····························································268
第四節(jié) 二重積分 ·················································································272
復(fù)習(xí)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(biāo)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(fù)習(xí)題九 ·····························································································305
第十章 航空工程測量誤差理論基礎(chǔ) ································································.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(biāo)準(zhǔn) ······················································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(fù)習(xí)題十 ·····························································································326
附錄 積分表 ······························································································.327