課程大綱及進度表

(1)

課程大綱及進度表

開課系所

機械一丙、化工一丙

開課學年

100

開課學期

2

課程名稱(中文)

微積分（二）

課程名稱（英文）

Calculus II

課程碼

E115620

分班碼

2

先修科目或先備能力

高中數學 Calculus I

學分數

3

開課教師

舒宇宸

e-mail

[email protected]

電話

06-2757575-65147

Office Hours

Monday, 9:00-12:00

課程概述（中文、英文）

本課程將延續上學期微積分的教學，介紹極座標、數列及無窮級數並推廣到多變數的微分、積分、微分方程及曲線、曲面積分

教學目標

教育學生瞭解數學、科學及工程的原理，並以系統化的方法透過微積分來解決機械及化工的問題

授課課程大綱明細

1. Polar Coordinates and

Parametric Equations (1) Curves in Polar

Coordinates (2) Curves Given

Parametrically (3) Arc Length

(4) Area of a Surface of

(2)

Revolution; Pappus’s Theorem

2. Sequences; Indeterminate forms; Improper Integral

(1) The Least Upper Bound Axiom

(2) Sequences of Real Number

(3) Limit of a Sequence (4) Some Important Limits (5) The Indeterminate

Forms

(6) Improper Integrals 3. Infinite Series

(1) Infinite Series (2) Convergence Test (3) Absolute Convergence

and Conditional Convergence

(4) Taylor Polynomials (5) Power Series

(6) Differentiation and Integration of Power Series

4. Vectors in Three Dimensional Space

(1) Vectors in

Three-Dimensional Space

(2) The Dot and Cross Products

(3)

(3) Lines and Planes (4) Higher Dimensions 5. Vector Calculus

(1) Limit, Continuity, Vector Derivative (2) The Rules of

Differentiation (3) Curves

(4) Curvilinear Motion:

Curvature

(5) Vector Calculus in Mechanics

6. Functions of Several Variables

(1) Elementary Examples (2) Graphs;

(3) Partial Derivatives (4) Open and Closed Sets (5) Limits and Continuity;

Equality of Mixed Partials

7. Gradients; Extreme Values;

Differentials

(1) Differentiability and Gradient

(2) Gradient and Directional Derivatives (3) The Chain Rule (4) Tangent Line and

Tangent Planes

(4)

(5) Local Extreme Values (6) Maxima and Minima with

Side Conditions (7) Differentials (8) Reconstructing a

Function from Its Gradient

8. Double and Triple Integrals (1) Multiple-Sigma

Notation

(2) Double Integrals (3) Applications

(4) Reduction to Repeated Integrals

(5) Cylindrical and

Spherical Coordinates (6) Triple Integrals

(7) Jacobians; Changing Variables in Multiple Integration

9. Line Integrals and Surface Integrals

(1) Line Integrals (2) The Fundamental

Theorem for Line Integrals

(3) Green’s Theorem (4) Parameterized

Surfaces; Surface Area (5) Surface Integrals (6) The Vector

(5)

Differential Operator (7) The Divergence Theorem (8) Stokes’s Theorem

參考書目

Calculus one and several

variables 10^th edition /

Saturnino Salas, Einer Hille, Garrett Etgen

課程要求

■ 學生需按時上課及繳交作業，

並遵守課堂基本規定

評量方式

■ 期中 (40%)

■ 期末 (40%)

■ 平時成績 (20%)

■ 微積分競試 (額外加分)

■ 缺席扣分原則：每次點名未到

扣學期總成績 1 分

課程網址

助教資訊

備註

■ 課程內容及相關訊息將會放在

moodle 平台，請每位修課學生密切注意 moodle 平台上之公告。