課程大綱及進度表
開課系所
工科系開課學年
95開課學期
2課程名稱(中文)
微積分(二)課程名稱（英文）
CALCULUS (2)課程碼
E915620分班碼
先修科目或先備能力
微積分(一)學分數
3開課教師
林 牛電話
65140Office Hours
課程概述
這是一個學年介紹應用微積分的 課程的下學期。課程主要是為工學 院的學生而設計，我們將注重實際 例子的計算和應用，並有一些定理 的證明。詳細內容請見指定教材的 目錄。下學期我們教授多變數微積 分。即指定教材第九章、第十二章 到第十七章的部份。教學目標
授課課程大綱明細
下學期我們教授多變數微積分。講授內容如 下﹕1. POLAR COORDINATES; PARAMETRIC EQUATIONS
Conic sections, polar coordinates, area in polar coordinates, parametrized curves, tangents to curves, arc length.
2. VECTOR CALCULUS Differentiation, vector calculus.
3. FUNCTIONS OF SEVERAL VARIABLES Graphs, level curves and level surfaces, partial derivatives, limits and continuity.
4 GRADIENTS; EXTREME VALUES
Differentiability and Gradient, directional derivatives, Mean-Value Theorem; chain rules, gradient as a normal;
tangent lines and tangent planes, maximum and minimum values, maxima and minima with side conditions.
5. DOUBLE AND TRIPLE INTEGRALS
Double Integrals, repeated integrals, double integral as the limit of Riemann sums; polar coordinates, triple integrals, reduction to repeated integrals,
cylindrical coordinates, triple integral, spherical coordinates,
Jacobians; changing variables in multiple integration.
6. LINE INTEGRALS and SURFACE INTEGRALS
Line integrals , fundamental theorem for line integrals, Green’s
theorem, parametrized surfaces, surface integrals, divergence
theorem and Stroke’s theorem.
