Calculus (I) - Academic Year 109

微積分甲(一) - 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。

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 

週次課程內容課程影音課程下載
Syllabus and Teaching Philosophy線上觀看MP4下載
Preliminaries and Notations線上觀看MP4下載
Chapter 1 Limits and Derivatives
1.1 Limits of Sequences
1.2 Limits of Functions
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1.2 Limits of Functions
1.3 Evaluating Limits Analytically
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1.3 Evaluating Limits Analytically線上觀看MP4下載
1.4 Continuous Functions線上觀看MP4下載
1.5 Limits at infinity; Asymptotes
1.6 Differentiation
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1.6 Differentiation線上觀看MP4下載
1.6 Differentiation

Chapter 2 Rules of Differentiation
2.1 Rules of Differentiation
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2.1 Rules of Differentiation
2.2 Chain Rule
2.3 Implicit Differentiation
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2.3 Implicit Differentiation
2.4 The Differentiation of the Inverse Functions
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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
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3.1 Extreme Values on an Interval線上觀看MP4下載
3.2 The First Derivative Test
3.3 Concavity and the Second Derivative Test
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3.3 Concavity and the Second Derivative Test
3.4 Summary of Curve Sketching
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3.4 Summary of Curve Sketching
3.5 Rolle’s Theorem and the Mean Value Theorem
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3.5 Rolle’s Theorem and the Mean Value Theorem
3.6 Indeterminate Forms and L'Hospital’s Rule
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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
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Chapter 5 Techniques of Integrals
(1)The Substitution Rule
(2) Integration by Parts
(3) Trigonometric Integrals I
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Chapter 5 Techniques of Integrals
Review of (1)-(3)
(4) Trigonometric Integrals II
(5) Trigonometric Substitution
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Chapter 5 Techniques of Integrals
(5) Trigonometric Substitution
(6) Half-Angle Substitution
(7) Integration of Rational Functions by Partial Fractions
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Chapter 5 Techniques of Integrals
(7) Integration of Rational Functions by Partial Fractions
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Chapter 4 Integration
4.1 Area
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4.1 Area
4.2 Properties of Integrals
4.3 Fundamental Theorem of Calculus
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Chapter 5 Techniques of Integrals
(8) Improper Integrals
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Chapter 6 Applications of Integration
6.1 Area of a Region Between Two Curves
6.2 Volume
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6.2 Volume
6.3 Arc Length
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7.1 Curves Defined by Parametric Equations
7.2 Calculus with Parametric Curves
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7.3 Polar Coordinates
7.4 Calculus with Parametric Curves
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Polar Curves線上觀看MP4下載
Review線上觀看MP4下載
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
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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 Derivatives1.1 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 Differentiation2.1 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 Differentiation3.1 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 Integration4.4 Indefinite Integrals
Chapter 5 Techniques of Integrals5.1 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 Integration4.1 Area
4.2 Properties of Integrals
4.3 Fundamental Theorem of Calculus
Chapter 5 Techniques of Integrals5.8 Improper Integrals
Chapter 6 Applications of Integration6.1 Area of a Region Between Two Curves
6.2 Volume
6.3 Arc Length
Chapter 77.1 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.