(完整版)數(shù)學(xué)分析講義

第一章函數(shù)1.1函數(shù)一、函數(shù)概念二、函數(shù)的四則運(yùn)算三、函數(shù)的圖象四、數(shù)列1.2四類具有特殊性質(zhì)的函數(shù)一、有界函數(shù)二、單調(diào)函數(shù)三、奇函數(shù)與偶函數(shù)四、周期函數(shù)1.3復(fù)合函數(shù)與反函數(shù)一、復(fù)合函數(shù)二、反函數(shù)三、初等函數(shù)§1.1函數(shù)

函數(shù)是整個(gè)高等數(shù)學(xué)中最基本的研究對(duì)象，可以說數(shù)學(xué)分析就是研究函數(shù)的，因此我們對(duì)函數(shù)的概念以及常見的一些函數(shù)有一個(gè)清楚的認(rèn)識(shí)。一、函數(shù)概念例1.真空中自由落體，物體下落的時(shí)間t與下落的距離s互相聯(lián)系著.如果物體距地面的高度為h，都對(duì)應(yīng)一個(gè)距離s.已知t與s之間的對(duì)應(yīng)關(guān)系是其中g(shù)是重力加速度，是常數(shù).§1.1函數(shù)

例2.在氣壓為101.325kPa

時(shí)，溫度T

與水的體積V

互相聯(lián)系著.實(shí)測(cè)如下表：T/100℃02468101214V/cm310099.9999.98799.9999.998100.012100.032100.057對(duì){0,2,4,6,8,10,12,14}中每個(gè)溫度T都對(duì)應(yīng)唯一一個(gè)體積V，已知T與V的對(duì)應(yīng)關(guān)系用上面的表格表示.§1.1函數(shù)函數(shù)的定義§1.1函數(shù)關(guān)于函數(shù)概念的幾點(diǎn)說名f()xf(x)Sin()xSin(x)§1.1函數(shù)§1.1函數(shù)二、函數(shù)的四則運(yùn)算§1.1函數(shù)三、函數(shù)的圖象符號(hào)函數(shù):1-1xyo有理數(shù)點(diǎn)無理數(shù)點(diǎn)?1xyo狄利克雷函數(shù):§1.1函數(shù)四、數(shù)列數(shù)列的定義:§1.2四類具有特殊性質(zhì)的函數(shù)一、有界函數(shù)

§1.2四類具有特殊性質(zhì)的函數(shù)

y=sin(x)§1.2四類具有特殊性質(zhì)的函數(shù)§1.2四類具有特殊性質(zhì)的函數(shù)-6-4-20246-1.5-1-0.500.511.5xatan(x)arctgx

圖像§1.2四類具有特殊性質(zhì)的函數(shù)§1.2四類具有特殊性質(zhì)的函數(shù)1234§1.2四類具有特殊性質(zhì)的函數(shù)二、單調(diào)函數(shù)xyo§1.2四類具有特殊性質(zhì)的函數(shù)xyo§1.2四類具有特殊性質(zhì)的函數(shù)三、奇函數(shù)與偶函數(shù)yxox-x§1.2四類具有特殊性質(zhì)的函數(shù)偶函數(shù)yxox-x§1.2四類具有特殊性質(zhì)的函數(shù)§1.2四類具有特殊性質(zhì)的函數(shù)四、周期函數(shù)§1.2四類具有特殊性質(zhì)的函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)一、復(fù)合函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)二、反函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)DWDW§1.3復(fù)合函數(shù)與反函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)三、初等函數(shù)1、冪函數(shù)§1.3復(fù)合函數(shù)與反函數(shù)2、指數(shù)函數(shù)1§1.