| 課程名稱 |
(中文) 微積分(二) (英文) Calculus |
開課單位 | 機械工程學系 | ||
| 課程代碼 | G1012L | ||||
| 授課教師 | 蔡援宗 | ||||
| 學分數 | 3.0 | 必/選修 | 必修 | 開課年級 | 大一 |
| 先修科目或先備能力：微積分(一) | |||||
| 課程概述與目標：(1)訓練學生能從本課程中學習並熟練基礎數學的觀念及其運用，建立良好的數學基礎，作為日後進一步學習的根基。 (2)指導學生學習將工程的基本概念建立數學模式並作分析。 | |||||
| 教科書 | 作者：Larson, Edwards 書名：Essential Calculus 3nd Edition 出版社：Houghton Mifflin |
||||
| 參考教材 | |||||
| 課程大綱 | 學生學習目標 | 單元學習活動 | 學習成效評量 | 備註 | ||
| 週 | 單元主題 | 內容綱要 | ||||
| 1 | Applications of Integration I | 1. Area of a Region Between Two Curves 2. Volume: The Disk Method |
1. 了解如何以積分來計算兩曲線間所圍面積 2. 了解如何以圓盤法來計算旋轉體之體積 |
|
||
| 2 | Applications of Integration II | 1. Volume: The Shell Method 2. Arc Length and Surfaces of Revolution |
1. 了解如何以剝殼法來計算旋轉體之體積 2. 了解如何以積分來計算曲線弧長及旋轉體之表面積 |
|
||
| 3 | Improper Integrals | Improper Integrals (小考: Applications of Integration) |
熟悉瑕積分性質 |
|
||
| 4 | Infinite Series I | Sequences | 熟悉數列及其極限計算 |
|
|
|
| 5 | Infinite Series II | 1. Series and Convergence 2. The Integral Test and Ratio Test |
熟悉級數及其斂散性判斷 |
|
||
| 6 | Infinite Series III | Taylor Series and Maclaurin Series | 認識Taylor Series，Maclaurin Series及其應用 |
|
|
|
| 7 | Parametric Equations and Polar Coordinates | 1. Parametric Equations 2. Polar Coordinates (小考: L'Hopital Rule，數列及級數) |
認識 參數及極座標 |
|
||
| 8 | Vectors and Vector-valued functions | 1. The Cross Product of Two Vectors in Space 2. Lines and Planes in Space 3. Surfaces in Space 4. Vector-valued functions |
1. 向量空間基本認識 2. 認識向量函數及其圖形性質 |
|
||
| 9 | 期中考 | L'Hopital Rule Infinite Series Parametric Equations Vector-valued Functions |
檢視上半學期學習成效 |
|
|
|
| 10 | Functions of Several Variables I | Limits and Continuity Partial Derivatives |
熟悉實多變數函數極限，連續性及偏導數 |
|
||
| 11 | Functions of Several Variables II | 1. Differentials and Chain Rules 2. Directional Derivatives and Gradients |
熟悉實多變數函數導數性質 |
|
||
| 12 | Functions of Several Variables III | 1. Extrema of Functions of Two Variables 2. Lagrange Multipliers |
熟實多變數函數極值計算 |
|
||
| 13 | Multiple Integration I | 1. Iterated Integrals and Area 2. Double Integrals and Volume (小考: 實多變數函數) |
熟悉實多變數函數積分及其應用 |
|
|
|
| 14 | Multiple Integration II | 1. Change of Variables 2. Polar Coordinates |
熟悉實多變數函數變數變換及其積分計算 |
|
||
| 15 | Multiple Integration III | 1. Surface Area 2. Triple Integrals |
熟悉實多變數函數積分及其應用 |
|
||
| 16 | Multiple Integration IV | 1. Triple Integrals 2. Triple Integrals in Cylindrical and Spherical Coordinates 4. Jacobians |
熟悉實多變數函數積分及其應用 |
|
|
|
| 17 | Multiple Integration V | 1. Related topics in multiple integrations (小考: Mulitple Integrations) |
熟悉積分及其應用 |
|
||
| 18 | 期末考 | 1. Functions of Several Variables 2. Multiple Integration |
檢視下半學期學習成效 |
|
|
|
|
教學要點概述： |