課程大綱及進度表
開課系所
數學系開課學年
101開課學期
1課程名稱(中文)
微積分(一)課程名稱（英文）
Calculus (I)課程碼
I615610分班碼
先修科目或先備能力
學分數
2開課教師
吳順益電話
略Office Hours
By Appointment課程概述
主要是討論微分跟積分之概念，注重計算 與應用，較不注重理論，大部分都是很基 本的。教學目標
主要是讓選這門課程的學生對積分與微 分之概念清楚及其應用。授課課程大綱明細
Chapter 1 Introduction to Calculus: The Derivative1.1 Functions and Intervals 1.2 Limits
1.3 The Derivative
1.4 The Derivative by the Four‐Step Process 1.5 Derivatives of Polynomials
1.6 Instantaneous Rates of Change 1.7 Differentiation Formulas 1.8 Implicit Differentiation 1.9 Higher Derivatives
Chapter 2 Applications of the Derivative
2.1 The first-Derivative Test 2.2 The second-Derivative Test
2.3 Exploring with Graphing Utilities (Optional)
2.4 Applications of Minima and Maxima 2.5 Related Rates
2.6 Differentials
Chapter 3 The Integral 3.1 Antiderivatives
3.2 The Area Problem
3.3 The fundamental Theorem of Calculus
3.4 The Integral: Notation and General Definition 3.5 Basic Integration Formulas
3.6 Area Between Curves 3.7 Improper Integrals
3.8 The Constant of Integration
Chapter 4 Applications of the Integral
4.1 Means and Root Mean Squares
4.2 Volumes of Revolution: Disk and Washer Methods
4.3 Volumes of Revolution: Shell Method 4.4 Centroids
4.5 Moments of Inertia 4.6 Work and Fluid Pressure
Chapter 5 Derivatives of Transcendental Functions
5.1 Review of Trigonometry
5.2 Derivatives of Sine and Cosine Functions 5.3 Other Trigonometric Functions
5.4 Inverse Trigonometric Functions
5.5 Derivatives of Inverse Trigonometric Functions 5.6 Exponential and Logarithmic Function
5.7 Derivative of the Logarithmic Function 5.8 Derivative of the Exponential Function 5.9 L’Hospital’s Rule
5.10 Application 5.11 Newton’s Method
Chapter6 Integration Techniques
6.1 The Power Formula Again
6.2 The Logarithmic and Exponential Forms 6.3 Trigonometric Forms
6.4 Further Trigonometric Forms 6.5 Inverse Trigonometric Forms
6.6 Integration by Trigonometric Substitution 6.7 Integration by Parts
6.8 Integration of Rational Functions
6.9 Integration by Use of Tables 6.10 Additional Remarks
Chapter 7 Parametric Equations, Vectors, and Polar Coordinates
7.1 Vectors and Parametric Equations 7.2 Arc Length
7.3 Polar Coordinates
7.4 Curves in Polar Coordinates 7.5 Areas in Polar Coordinates
Chapter 8 Three-Dimensional Space;
Partial Derivatives; Multiple Integrals 8.1 Surfaces in Three Dimensions
8.2 Partial Derivatives
8.3 Application of Partial Derivatives 8.4 Curve Fitting
8.5 Iterated Integrals
8.6 Volumes by Double Integration
8.7 Mass, Centroids, and Moments of Inertia 8.8 Volumes in Cylindrical Coordinates
Chapter 9 Infinite Series 9.1 Introduction to Infinite Series
9.2 Tests for Convergence 9.3 Maclaurin Series 9.4 Operations with Series
9.5 Computations with Series; Applications 9.6 Fourier Series
Chapter10 First-Order Differential Equations
10.1 What Is a Differential Equation?
10.2 Separation of Variables
10.3 First-Order Linear Differential Equations 10.4 Applications of First-Order Differential Equations
10.5 Numerical Solutions
參考書目 Real Analysis (Fourth Edition) by Halsey Royden and Patrick Fitzpatrick
課程要求
評量方式
助教成績：佔 20%期中考 2 次：各佔 25%
期末考 1 次：佔 25%
出席率：5%
