第七章-多元函數(shù)微積分初步

第七章

多元函數(shù)微積分初步7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與最值7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件1.正確理解空間直角坐標(biāo)系的概念及空間點(diǎn)的坐標(biāo)表示方法;會求空間兩點(diǎn)間的距離.2.理解空間曲面方程的概念,能求出空間動點(diǎn)的軌跡方程;了解幾種常見曲面的曲面方程.7.1空間曲面教學(xué)目標(biāo)講授法教學(xué)方法節(jié)菜單教學(xué)重點(diǎn)1.理解空間直角坐標(biāo)系的概念,會求空間兩點(diǎn)間的距離.2.理解空間曲面方程的概念,求出空間動點(diǎn)的軌跡方程.教學(xué)難點(diǎn)

理解空間曲面方程的概念,能求出空間動點(diǎn)的軌跡方程7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單在空間取三條相互垂直且相交于O點(diǎn)的數(shù)軸構(gòu)成空間直角坐標(biāo)系.這三條數(shù)軸依次稱為x

軸(橫軸)、y

軸(縱軸)、z

軸(豎軸),三條軸統(tǒng)稱為坐標(biāo)軸,點(diǎn)O稱為坐標(biāo)原點(diǎn).習(xí)慣上,我們把x

軸、y

軸置于水平面上,而z軸取垂直向上方向,如圖7—2所示.觀看圖7—3,我們可以想象,y

軸和z軸是落在紙面上的,而x

軸是垂直于紙面指向我們,它們的方向滿足右手法則.所謂右手法則,指的是:伸出右手,使拇指的指向與其他四指垂直,當(dāng)四指從x

軸的正向轉(zhuǎn)向y

軸正向時拇指的指向就是z

軸的正向.按右手法則確定的坐標(biāo)系稱為右手系.本章用的坐標(biāo)系都是右手系.7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件在平面解析幾何中,我們把平面曲線視作動點(diǎn)的軌跡.同樣,在空間解析幾何中,任何曲面(包括平面)都看作是動點(diǎn)的運(yùn)動軌跡(或點(diǎn)的集合),如圖7—8所示.在這個意義下,曲面所具有的性質(zhì)是它的一切點(diǎn)所共有的.設(shè)(x,y,z)是曲面上的任意一點(diǎn),我們用x,y,z

之間的一個方程F(x,y,z)=0來表達(dá)這曲面上所有點(diǎn)的共同性質(zhì).7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.1空間曲面節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件理解多元函數(shù)的概念,會求二元函數(shù)的定義域;了解二元函數(shù)的極限和連續(xù)的概念;了解閉區(qū)域上二元函數(shù)的性質(zhì).7.2多元函數(shù)的極值與連續(xù)教學(xué)目標(biāo)講授法教學(xué)方法節(jié)菜單教學(xué)重點(diǎn)理解多元函數(shù)的概念,會求二元函數(shù)的定義域.教學(xué)難點(diǎn)理解多元函數(shù)的概念,會求二元函數(shù)的定義域.7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.2多元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件1.理解偏導(dǎo)數(shù)概念;2.掌握偏導(dǎo)數(shù)的求法.7.3偏導(dǎo)數(shù)教學(xué)目標(biāo)講練結(jié)合法教學(xué)方法節(jié)菜單教學(xué)重點(diǎn)理解偏導(dǎo)數(shù)概念,掌握偏導(dǎo)數(shù)的求法.教學(xué)難點(diǎn)理解偏導(dǎo)數(shù)概念,掌握偏導(dǎo)數(shù)的求法.7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.3偏導(dǎo)數(shù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件1.理解二元函數(shù)極值與最值的概念,會判定并求出簡單二元函數(shù)的極值;2.會利用拉格朗日乘數(shù)法求簡單的條件極值.7.4二元函數(shù)的極值與連續(xù)教學(xué)目標(biāo)講練結(jié)合法教學(xué)方法節(jié)菜單教學(xué)重點(diǎn)理解二元函數(shù)極值與最值的概念,會判定并求出簡單二元函數(shù)的極值;會利用拉格朗日乘數(shù)法求簡單的條件極值.教學(xué)難點(diǎn)會判定并求出簡單二元函數(shù)的極值;會利用拉格朗日乘數(shù)法求簡單的條件極值.7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件前面所討論的極值問題,自變量的變化是在函數(shù)的定義域范圍內(nèi),除此之外沒有其他附加條件的限制,因此,這種極限有時又稱為無條件極值

.但在許多實(shí)際問題中,函數(shù)的自變量還要滿足某些附加條件,這種對自變量有附加條件的極值稱為條件極值.7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.4二元函數(shù)的極值與連續(xù)節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件理解二重積分的概念和性質(zhì);掌握二重積分在直角坐標(biāo)系中的計(jì)算方法,會計(jì)算一些簡單的二重積分。7.5二重積分與應(yīng)用教學(xué)目標(biāo)講練結(jié)合法教學(xué)方法節(jié)菜單教學(xué)重點(diǎn)

理解二重積分的概念和性質(zhì);掌握二重積分在直角坐標(biāo)系中的計(jì)算方法,會計(jì)算一些簡單的二重積分教學(xué)難點(diǎn)二重積分在直角坐標(biāo)系中的計(jì)算方法7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件第五章中,我們通過求曲邊梯形的面積和變速直線運(yùn)動的路程引入了定積分的概念.同樣,我們將通過求曲頂柱體的體積和平面薄片的質(zhì)量來引入二重積分的概念.7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用例題解析第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件7.5二重積分與應(yīng)用節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件附錄簡易積分表節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件附錄簡易積分表節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件附錄簡易積分表節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件附錄簡易積分表節(jié)菜單7.1空間曲面7.2多元函數(shù)的極值與連續(xù)7.3偏導(dǎo)數(shù)7.4二元函數(shù)的極值與連續(xù)7.5二重積分與應(yīng)用第七章多元函數(shù)微積分初步ppt課件附錄簡易積分表節(jié)菜單7.1空間曲面7.2多元函數(shù)的極