一 教學目標 1.激發學生們學習微積分的興趣。 2.使學生們熟悉微積分的基本性質及其應用。 3.能學習微分及積分技巧，以解決相關物理問題。 4.培養學生體會應用微積分解析問題之能力。 5.建立未來工程數學應用之基礎。 1.To arouse students' interest in learning Calculus. 2.To familiarize students’with the basic properties and application of Calculus. 3.Can study the differential and total mark skill, in order to solve the relevant physics problem. 4.Cultivate students to realize the ability that use calculus to analyze the question. 5.Establish future on the foundation that project mathematics uses. 二 科目概要 第六章不定積分 6-1 不定積分及其基本公式 6-2 變數變換法 6-3 分部積分法 6-4 三角函數的積分 6-5 三角代換積分法 6-6 部分分式法 第七章定積分及其應用 7-1 定積分定義與基本性質 7-2 瑕積分 7-3 平面區域面積 7-4 旋轉體體積 7-5 弧長;旋轉曲面面積 第八章多變數函數的導函數 8-1 多變數函 8-2 極限與連續 8-3 偏導函數 8-4 鏈鎖律 8-4 極值 第九章重積分及其應用 9-1 二重積分 Chapter Six Indefinite Integral 6-1 Indefinite Integrals and Basic Integration Formulas 6-2 Integration by Variable Substitution 6-3 Integration by Parts 6-4 Integration of Trigonometric Functions 6-5 Integration by Trigonometric Substitution 6-6 Integration of Partial Fractions Chapter Seven Definite Integral and Its Applications 7-1 Definition of Definite Integral and Basic Properties 7-2 Improper Integral 7-3 Areas in the Planes 7-4 Volumes of Revolution Solid 7-5 Arc Length and Areas of Surface of Revolution Chapter Eight Derivatives of Milti-variable Functions 8-1 Multivariable Functions 8-2 Limits and Continuity 8-3 Partial Derivatives 8-4 Chain Rules 8-5 Extreme Values Chapter Nine Multiple Integrals and It's Applications 9-1 Double Integrals