課程大綱及進度表

(1)

課程大綱及進度表

開課系所化工系(甲乙)

開課學年

101

開課學期

1

課程名稱(中文) 微積分(一) 課程名稱（英文） Calculus (1) 課程碼 E315610

分班碼 1

先備能力高中數學

學分數 3

開課教師章源慶

e-mail

keng@mail.ncku.edu.tw

電話(校內分機)

65136

Office Hours 預約

課程概述

介紹微積分的基本理論、方法及應用，亦論及一些微分方程的課題。

教學目標

充分掌握微積分的基本概念，熟悉微積分的計算技巧，奠定紮實的數學基礎以應用在化工及相關領域。

授課課程大綱明細 1. Pre-Calculus

(1) Limits (Intuitive) (2) Continuity

(3) Transcendental functions 2. The Derivative

(1) Definition

(2) Differentiation Formulas (3) Chain Rule

(4) Implicit Differentiation

(5) Differentiating the Elementary Functions

(6) Higher Order Derivatives

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3. Applications of the first and second derivatives

(1) The Mean-Value Theorem (2) Extreme Values

(3) Curve Sketching (4) Differentials (5) Newton Method (6) Taylor Polynomials 4. Integration

(1) The Definite Integral

(2) The Fundamental Theorem of Integral Calculus

(3) Techniques of Integration 5. Applications of Integration

(1) Area and Volume

(2) Pappus’s Theorem on Volumes (3) Arc length and Surface Area

(4) Pappus’s Theorem on Surface Areas 6. Some Differential Equations

(1) 1^st Order Linear Equations (2) Separation of Variables

(3) Method of Integrating Factors (4) 2^nd Order Linear Equations 7. Some Reviews

(1) Sequences and Series

(2) Limits and Indeterminate Form

(3)

Taylor Series

參考書目

Salas, Hille, Etgen – Calculus: one and several variables (10

^th

edition)

評量方式

 期中考 (35%)，期末考 (35%)

 小考共 2 次，每次佔 15%

課程網址

http://moodle.ncku.edu.tw/

備註

課程大綱及進度表