C o u r s e D e s c r i p t i o n
Department of Mathematics Nature of the course
; required elective
Area 麻煩老師勾選類別，或直接填寫 。 Algebra Analysis Geometry Statistics Applied Mathematics Discrete Mathematics Others Calculus ; Calculus A Calculus B
Course number 201 101A1 Section number 08-12 Number of credits 4 Course title Calculus
Instructor 陳鵬文(08)、周謀鴻(09)、劉瓊如(10)、容志輝(11)、朱 樺(12) I. Contents：
章節 週次 課程進度
1. Limits and Continuity
第 1 週 09/13-09/16
1.1 Examples of Velocity Growth Rate, and Area 1.2 Limit of Functions
1.3 Limits at Infinity and Infinite Limits 1.4 Continuity
第 2 週 09/19-09/23
1.5 The Formal Definition of Limit
2.
Differentiation
2.1 Tangent Lines and Their Slopes 2.2 The Derivative
2.3 Diff rentiation Rules
第 3 週 09/26-09/30
2.4 The Chain Rule
2.5 Derivatives of Trigonometric Functions 2.6 Higher-Order Derivatives
2.7 Using Differentials and Derivatives 2.8 The Mean-Value Theorem
第 4 週 10/03-10/07
2.9 Implicit Differentiation
.10 Antiderivatives and Initial-Value Problems 2.11 Velocity and Acceleration
緩衝時間
3.
Transcendental Function
第 5 週 10/10-10/14
3.1 Inverse Functions
3.2 Exponential and Logarithmic Functions 3.3 The Natural Logarithm and Exponential 3.4 Gro th and Decay
第 6 週 10/17-10/21
3.5 The Inverse Trigonometric Functions 3.6 Hyperbolic Functions
3.7 Second-Order Linear Des with Constant Coefficients
4. More Applications of
Differentiation
4.1 Related Rates
第 7 週 10/24-10/28
4.2 Finding Root of Equations 4.3 Indeterminate Forms 4.4 Extreme Values
4.5 Concavity and Inflections
第 8 週 10/31-11/04
4.6 Sketching the Graph of a Function 4.7 Graphing with Computers（※）
4.8 Extreme-Value Problems 4.9 Linear Approximations
第 9 週
11/0 -11 11
4.10 Taylor Polynomials
4.11 Roundoff Error, Truncation Error, and Computers（※）
緩衝時間
11/12(六) 09:00～11:30 期中考 考試範圍 1.1～4.10 (英文命題)
5. Integration
第 10 週 11/14-11/18
5.1 Sums and Sigma Notation 5.2 Areas as Limits of Sums 5.3 Definite Inte ral
5.4 Properties of the Definite Integral
第 11 週 11/21-11/25
5.5 The Fundamental Theorem of Calculus 5.6 The Method of Substitution
5.7 Areas of Plane Regions
6. Techniques of Integration
6.1 Integration by Parts
第 12 週 11/28-12/02
6.2 Integr ls f Rational Functions 6.3 Inverse Substitutions
6.4 Other Methods for Evaluating Integrals 6.5 Improper Integrals
第 13 週 12/05-12/09
6.6 The Trapezoid and Midpoint Rules 6.7 Simpson's Rule
6.8 Other Aspects of Approximate Integration（※）
緩衝時間
7. Applications of Integration
第 14 週 12/12-12/16
7.1 Volumes by Slicing ─ Solids of Revolution 7.2 More Volumes by Slicing
7.3 Arc Length and Surface Area
第 15 週 12/19-12/23
7.4 Mass, Moments, and Centre of Mass 7.5 Centroids（※）
7.6 Other Physical Applications（※）
7.7 Applications in Business, Finance, and Ecology（※）
7.8 Probability（※）
7.9 First-Order Differential Equations
8. Conics, Parametric Curves, and Polar Curves
第 16 週 12/26-12/30
8.2 Parametric Curves
8.3 Smooth Parametric Curves and Their Slopes 8.4 Arc Lengths and Areas for Parametric Curves
第 17 週
01/02-01/06
8.5 Polar Coordinates and Polar Curves
8.6 Slopes, Areas, and Arc Lengths for Polar Curves 緩衝時間
1/8(日) 09:00～11:30 期末考 考試範圍 5.1～8.6 (英文命題)
（※）此符號標示之課程，可由任課教師自行決定是否為教學內容，不列入考試範圍中。
