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Calculus I (B) - Academic Year 109

微積分甲(二) - 109學年度

本課程是由 國立陽明交通大學應用數學系提供。

 

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 

週次課程內容課程影音課程下載
1Chapter 8 Sequences, Series, and Power Series
Introduction
8.1 Sequences		線上觀看MP4下載
28.1 Sequences
8.2 Series
8.3 The Integral Test		線上觀看MP4下載
38.1-8.3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
58.6 Alternating Series and Absolute Convergence線上觀看MP4下載
68.7 Power Series
8.8 Representation of Functions as Power Series(1/2)		線上觀看MP4下載
78.8 Representation of Functions as Power Series(2/2)
8.9 Taylor Series and Maclaurin Series(1/3)		線上觀看MP4下載
88.9 Taylor Series and Maclaurin Series(2/3)線上觀看MP4下載
98.9 Taylor Series and Maclaurin Series(3/3)線上觀看MP4下載
10Rearrangement of Series and Binomial Series線上觀看MP4下載
11Chapter 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
12Chapter 10 Vector Functions
10.1 Vector Functions and Space Curves(1/2)		線上觀看MP4下載
1310.1 Vector Functions and Space Curves(2/2)
10.2 Differentiation and Integration of Vector Function(1/2)
線上觀看MP4下載
1410.2 Differentiation and Integration of Vector Function(2/2)
10.3 Arc Length and Curvature(1/2)		線上觀看MP4下載
1510.3 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
1611.2 Limits and Continuity(2/3)線上觀看MP4下載
1711.2 Limits and Continuity(3/3)線上觀看MP4下載
1811.3 Partial Derivatives
11.4 Tangent Plane and Linear Approximation(1/2)		線上觀看MP4下載
1911.4 Tangent Plane and Linear Approximation(2/2)
11.5 The Chain Rule(1/2)		線上觀看MP4下載
2011.5 The Chain Rule(2/2)
11.6 Directional Derivatives and the Gradient Vector(1/3)		線上觀看MP4下載
2111.6 Directional Derivatives and the Gradient Vector(2/3)線上觀看MP4下載
2211.6 Directional Derivatives and the Gradient Vector(3/3)
11.7 Maximum and Minimum Values(1/2)		線上觀看MP4下載
2311.7 Maximum and Minimum Values(2/2)
11.8 Lagrange Multiplier Method		線上觀看MP4下載
24Chapter 12 Multiple Integrals
12.1 Iterated Integrals(1/2)		線上觀看MP4下載
2512.1 Iterated Integrals(2/2)
12.2 Double Integrals(1/2)		線上觀看MP4下載
2612.2 Double Integrals(2/2)線上觀看MP4下載
2712.3 Double Integrals in Polar Coordinates
12.4 Surface Area		線上觀看MP4下載
2812.5 Triple Integrals(1/2)線上觀看MP4下載
2912.5 Triple Integrals(2/2)
12.6 Triple Integrals in Cylindrical Coordinates		線上觀看MP4下載
3012.7 Triple Integrals in Spherical Coordinates線上觀看MP4下載
3112.8 Change of Variables in Multiple Integrals線上觀看MP4下載

課程目標

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。

 

課程章節

章節 章節內容
Chapter 8 Sequences, Series, and Power Series8.1 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 Space9.1 Vectors in the Plane
9.2 Vectors in Space
9.3 The Dot Product of Two Vectors in Space
Chapter 10 Vector Functions10.1 Vector Functions and Space Curves
10.2 Differentiation and Integration of Vector Function
10.3 Arc Length and Curvature
Chapter 11 Partial Derivatives11.1 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 Integrals12.1 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.

課程專區
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