微積分甲(一)109學年度 - Calculus I (A) Academic Year 109 | 應用數學系蘇承芳老師

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Calculus I (A) - Academic Year 109

微積分甲(一) - 109學年度

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課程影音
課程綱要
學習筆記

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。

而微積分甲（一）的課程主要先從單變數函數的觀點出發，講述單變數函數的微分學與積分學，內容大致有微分學中的函數的極限、連續性、微分理論，與積分學中的定積分、不定積分與其相關的應用，先讓同學對單變數函數的微積分有一定程度的掌握與理解，以便良好地銜接微積分甲（二）中向量值函數與多變數函數相關理論的學習。

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	高中數學
課程提供	課程影音課程綱要學習筆記

每頁顯示個資料列

搜尋:

週次	課程內容	課程影音
	Syllabus and Teaching Philosophy	線上觀看
	Preliminaries and Notations	線上觀看
	Chapter 1 Limits and Derivatives 1.1 Limits of Sequences 1.2 Limits of Functions	線上觀看
	1.2 Limits of Functions 1.3 Evaluating Limits Analytically	線上觀看
	1.3 Evaluating Limits Analytically	線上觀看
	1.4 Continuous Functions	線上觀看
	1.5 Limits at infinity; Asymptotes 1.6 Differentiation	線上觀看
	1.6 Differentiation	線上觀看
	1.6 Differentiation Chapter 2 Rules of Differentiation 2.1 Rules of Differentiation	線上觀看
	2.1 Rules of Differentiation 2.2 Chain Rule 2.3 Implicit Differentiation	線上觀看
	2.3 Implicit Differentiation 2.4 The Differentiation of the Inverse Functions	線上觀看
	2.4 The Differentiation of the Inverse Functions 2.5 Differential and Linear Approximation Chapter 3 Applications of Differentiation 3.1 Extreme Values on an Interval	線上觀看
	3.1 Extreme Values on an Interval	線上觀看
	3.2 The First Derivative Test 3.3 Concavity and the Second Derivative Test	線上觀看
	3.3 Concavity and the Second Derivative Test 3.4 Summary of Curve Sketching	線上觀看
	3.4 Summary of Curve Sketching 3.5 Rolle’s Theorem and the Mean Value Theorem	線上觀看
	3.5 Rolle’s Theorem and the Mean Value Theorem 3.6 Indeterminate Forms and L'Hospital’s Rule	線上觀看
	3.6 Indeterminate Forms and L'Hospital’s Rule 3.7 Antiderivative 4.4 Indefinite Integrals Chapter 5 Techniques of Integrals (1)The Substitution Rule	線上觀看
	Chapter 5 Techniques of Integrals (1)The Substitution Rule (2) Integration by Parts (3) Trigonometric Integrals I	線上觀看
	Chapter 5 Techniques of Integrals Review of (1)-(3) (4) Trigonometric Integrals II (5) Trigonometric Substitution	線上觀看
	Chapter 5 Techniques of Integrals (5) Trigonometric Substitution (6) Half-Angle Substitution (7) Integration of Rational Functions by Partial Fractions	線上觀看
	Chapter 5 Techniques of Integrals (7) Integration of Rational Functions by Partial Fractions	線上觀看
	Chapter 4 Integration 4.1 Area	線上觀看
	4.1 Area 4.2 Properties of Integrals 4.3 Fundamental Theorem of Calculus	線上觀看
	Chapter 5 Techniques of Integrals (8) Improper Integrals	線上觀看
	Chapter 6 Applications of Integration 6.1 Area of a Region Between Two Curves 6.2 Volume	線上觀看
	6.2 Volume 6.3 Arc Length	線上觀看
	7.1 Curves Defined by Parametric Equations 7.2 Calculus with Parametric Curves	線上觀看
	7.3 Polar Coordinates 7.4 Calculus with Parametric Curves	線上觀看
	Polar Curves	線上觀看
	Review	線上觀看
	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

目前顯示第 1 至第 32 個資料列，總計 32 個資料列

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。
而微積分甲（一）的課程主要先從單變數函數的觀點出發，講述單變數函數的微分學與積分學，內容大致有微分學中的函數的極限、連續性、微分理論，與積分學中的定積分、不定積分與其相關的應用，先讓同學對單變數函數的微積分有一定程度的掌握與理解，以便良好地銜接微積分甲（二）中向量值函數與多變數函數相關理論的學習。。

課程章節

章節	章節內容
Chapter 1 Limits and Derivatives	1.1 Limits of Sequences 1.2 Limits of Functions 1.3 Evaluating Limits Analytically 1.4 Continuous Functions 1.5 Limits at infinity; Asymptotes 1.6 Differentiation
Chapter 2 Rules of Differentiation	2.1 Rules of Differentiation 2.2 Chain Rule 2.3 Implicit Differentiation 2.4 The Differentiation of the Inverse Functions 2.5 Differential and Linear Approximation
Chapter 3 Applications of Differentiation	3.1 Extreme Values on an Interval 3.2 The First Derivative Test 3.3 Concavity and the Second Derivative Test 3.4 Summary of Curve Sketching 3.5 Rolle’s Theorem and the Mean Value Theorem 3.6 Indeterminate Forms and L'Hospital’s Rule 3.7 Antiderivative
Chapter 4 Integration	4.4 Indefinite Integrals
Chapter 5 Techniques of Integrals	5.1 The Substitution Rule 5.2 Integration by Parts 5.3 Trigonometric Integrals I 5.4 Trigonometric Integrals II 5.5 Trigonometric Substitution 5.6 Half-Angle Substitution 5.7 Integration of Rational Functions by Partial Fractions
Chapter 4 Integration	4.1 Area 4.2 Properties of Integrals 4.3 Fundamental Theorem of Calculus
Chapter 5 Techniques of Integrals	5.8 Improper Integrals
Chapter 6 Applications of Integration	6.1 Area of a Region Between Two Curves 6.2 Volume 6.3 Arc Length
Chapter 7	7.1 Curves Defined by Parametric Equations 7.2 Calculus with Parametric Curves 7.3 Polar Coordinates 7.4 Calculus with Parametric Curves
	Polar Curves
	上學期總複習影片

課程書目

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

學習筆記 Learning Notes

學習筆記-由光電工程學系陳啟馼同學提供
章節	下載連結
1. 單變數純量函數—極限與連續	PDF
2. 單變數純量函數—導數（概念篇）	PDF
3. 單變數純量函數—導數（應用篇）	PDF
4. 單變數純量函數—積分（概念篇）	PDF
5. 單變數純量函數—積分（技巧篇）	PDF
6. 單變數純量函數—瑕積分	PDF
7. 單變數純量函數—積分（應用篇）	PDF
8. 參數方程式	PDF
9. 數列與級數	PDF
10. 單變數向量函數（概念篇）	PDF
11. 單變數向量函數（應用篇）	PDF
12. 多變數純量函數—極限與連續	PDF
13. 多變數純量函數—偏導數（概念篇）	PDF
14. 多變數純量函數—偏導數（應用篇）	PDF
15. 多變數純量函數—重積分	PDF
16. 筆記（全）	PDF