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微積分甲(一)109學年度 - Calculus (I) Academic Year 109

課程綱要

  • 微積分甲(一)109學年度 - Calculus (I) Academic Year 109

課程目標/概述

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。

 

課程大綱

單元主題 內容綱要
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.

 


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