微積分甲(二)109學年度 – Calculus I (B) Academic Year 109 | 應用數學系蘇承芳老師

Calculus I (B) - Academic Year 109

微積分甲(二) - 109學年度

課程首頁
課程影音
課程綱要

微積分在物理學、生物學、統計學、天文學、經濟學、資訊科學與財務工程等領域都是相當重要的基礎工具，它同時也是許多課程的先備知識，例如工程數學、微分方程、統計學與金融數學。

微積分甲（二）延續（一）的學習，課程內容包括數列與級數的收斂性與應用，多變數函數的極限、連續性、偏導數、方向導數、梯度與函數的可微分性，也將介紹重積分的計算與應用，最後講述基礎的向量微積分理論。這些內容對於電磁學、流體力學、經濟學等領域中的實際問題分析非常重要，本課程希望能幫助學生建立多變數函數微積分的基本理論與計算技巧，以應用於後續的相關課程和研究。

課程用書：

Stewart, James. Calculus: Early Transcendentals., 8th ed. Cengage Learning, 2015.

為求學習成效完美，請購買課本！

授課教師	應用數學系蘇承芳老師
課程學分	4學分
授課年度	109學年度
授課對象	大學部
預備知識	微積分甲(一)
課程提供	課程影音課程綱要

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音	課程下載
1	Chapter 8 Sequences, Series, and Power Series Introduction 8.1 Sequences	線上觀看	MP4下載
2	8.1 Sequences 8.2 Series 8.3 The Integral Test	線上觀看	MP4下載
3	8.1-8.3的補充例題 (Other Examples for 8.1-8.3) 8.4 Comparison Tests	線上觀看	MP4下載
4	正項級數斂散性的複習 (Review of the Test for Convergence of Series with Non-negative Terms) 8.5 The Ratio and Root Tests	線上觀看	MP4下載
5	8.6 Alternating Series and Absolute Convergence	線上觀看	MP4下載
6	8.7 Power Series 8.8 Representation of Functions as Power Series(1/2)	線上觀看	MP4下載
7	8.8 Representation of Functions as Power Series(2/2) 8.9 Taylor Series and Maclaurin Series(1/3)	線上觀看	MP4下載
8	8.9 Taylor Series and Maclaurin Series(2/3)	線上觀看	MP4下載
9	8.9 Taylor Series and Maclaurin Series(3/3)	線上觀看	MP4下載
10	Rearrangement of Series and Binomial Series	線上觀看	MP4下載
11	Chapter 9 Vector and the Geometry of Space 9.1 Vectors in the Plane 9.2 Vectors in Space 9.3 The Dot Product of Two Vectors in Space	線上觀看	MP4下載
12	Chapter 10 Vector Functions 10.1 Vector Functions and Space Curves(1/2)	線上觀看	MP4下載
13	10.1 Vector Functions and Space Curves(2/2) 10.2 Differentiation and Integration of Vector Function(1/2)	線上觀看	MP4下載
14	10.2 Differentiation and Integration of Vector Function(2/2) 10.3 Arc Length and Curvature(1/2)	線上觀看	MP4下載
15	10.3 Arc Length and Curvature(2/2) Chapter 11 Partial Derivatives 11.1 Functions of Several Variables 11.2 Limits and Continuity(1/3)	線上觀看	MP4下載
16	11.2 Limits and Continuity(2/3)	線上觀看	MP4下載
17	11.2 Limits and Continuity(3/3)	線上觀看	MP4下載
18	11.3 Partial Derivatives 11.4 Tangent Plane and Linear Approximation(1/2)	線上觀看	MP4下載
19	11.4 Tangent Plane and Linear Approximation(2/2) 11.5 The Chain Rule(1/2)	線上觀看	MP4下載
20	11.5 The Chain Rule(2/2) 11.6 Directional Derivatives and the Gradient Vector(1/3)	線上觀看	MP4下載
21	11.6 Directional Derivatives and the Gradient Vector(2/3)	線上觀看	MP4下載
22	11.6 Directional Derivatives and the Gradient Vector(3/3) 11.7 Maximum and Minimum Values(1/2)	線上觀看	MP4下載
23	11.7 Maximum and Minimum Values(2/2) 11.8 Lagrange Multiplier Method	線上觀看	MP4下載
24	Chapter 12 Multiple Integrals 12.1 Iterated Integrals(1/2)	線上觀看	MP4下載
25	12.1 Iterated Integrals(2/2) 12.2 Double Integrals(1/2)	線上觀看	MP4下載
26	12.2 Double Integrals(2/2)	線上觀看	MP4下載
27	12.3 Double Integrals in Polar Coordinates 12.4 Surface Area	線上觀看	MP4下載
28	12.5 Triple Integrals(1/2)	線上觀看	MP4下載
29	12.5 Triple Integrals(2/2) 12.6 Triple Integrals in Cylindrical Coordinates	線上觀看	MP4下載
30	12.7 Triple Integrals in Spherical Coordinates	線上觀看	MP4下載
31	12.8 Change of Variables in Multiple Integrals	線上觀看	MP4下載

目前顯示第 1 至第 31 個資料列，總計 31 個資料列

課程目標

課程章節

章節	章節內容
Chapter 8 Sequences, Series, and Power Series	8.1 Sequences 8.2 Series 8.3 The Integral Test 8.4 Comparison Tests 8.5 The Ratio and Root Tests 8.6 Alternating Series and Absolute Convergence 8.7 Power Series 8.8 Representation of Functions as Power Series 8.9 Taylor Series and Maclaurin Series Rearrangement of Series and Binomial Series
Chapter 9 Vector and the Geometry of Space	9.1 Vectors in the Plane 9.2 Vectors in Space 9.3 The Dot Product of Two Vectors in Space
Chapter 10 Vector Functions	10.1 Vector Functions and Space Curves 10.2 Differentiation and Integration of Vector Function 10.3 Arc Length and Curvature
Chapter 11 Partial Derivatives	11.1 Functions of Several Variables 11.2 Limits and Continuity 11.3 Partial Derivatives 11.4 Tangent Plane and Linear Approximation 11.5 The Chain Rule 11.6 Directional Derivatives and the Gradient Vector 11.7 Maximum and Minimum Values 11.8 Lagrange Multiplier Method
Chapter 12 Multiple Integrals	12.1 Iterated Integrals 12.2 Double Integrals 12.3 Double Integrals in Polar Coordinates 12.4 Surface Area 12.5 Triple Integrals 12.6 Triple Integrals in Cylindrical Coordinates 12.7 Triple Integrals in Spherical Coordinates 12.8 Change of Variables in Multiple Integrals

課程書目

Stewart, James. Calculus: Early Transcendentals., 8th ed. Cengage Learning, 2015.