C o u r s e D e s c r i p t i o n ( 暫 定 )
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)、莊武諺(09)、莊正良(10)、周謀鴻(11)、黃漢水(12) I. Contents:微甲
08-11班小考時間:有標示”Quiz”的該週三 9 實習課上學期:單變數微積分
章節 週次 課次 課程進度
1. Functions
and Models 第一週 9/13-9/17
1
[1.5] Exponential Functions[1.6] Inverse Functions and Logarithms
2. Limits and Derivatives
2
[2.1] The Tangent and Velocity Problems [2.2] The Limit of a Function第二週 9/20-9/24
1
9/22(三)中秋節放假一天2
[2.3] Calculating Limits Using the Limit Laws [2.4] The Precise Definition of a Limit第三週 9/27-10/1
(Quiz1)
1
[2.5] Continuity
[2.6] Limits at Infinity; Horizontal Asymptotes [2.7] Derivatives and Rates of Change
2
[2.8] The Derivative as a Function[3.1] Derivative of Polynomials and Ex onential Functions
3. Differentiation Rules
第四週 10/4-10/8
1
[3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions2
[3.4] The Chain Rule [3.5] Implicit Differentiation第五週 10/11-10/15
(Quiz2)
1
[3.6] Derivatives of Logarithmic Functions
[3.7] Rates of Change in the Natural and Social Sciences(※)
[3.8] Exponential Growth and Decay
2
[3.9] Related Rates
[3.10] Linear Approximations and Differentials [3.11] Hyperbolic Functions(※)
4. Applications of iff rentiation
第六週 10/18-10/22
1
[4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem2
緩衝時間第七週
10/25-10/29 1
[4.3] How Derivatives Affect the Shape of a Graph [4.4] Indeterminate Forms and L’Hospital’s Rule(Quiz3)
2
[4.5] Summary of Curve Sketching
[4.6] Graphing with Calculus and Calculators [4.7] Optimization Problems
第八週 11/1-11/5
1
[4.8] Newton’s Method(※)
[4.9] Antiderivatives [5.1] Areas and Distances
5. Integrals
2
[5.2] The Definite Integral[5.3] The Fundamental Theorem of Calculus
第九週
11/8-11/12
(Quiz4)1
[5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule2
緩衝時間11/13(六)09:00~11:30 期中考 考試範圍 1.5~5.5 (英文命題)
6. Applications of Integration
第十週 11/15-11/19
1
[6.1] Areas between Curves [6.2] Volumes[6.3] Volumes by Cylindrical Shells [6.4] Work(※)
第十一週 11/22-11/26
(Quiz5)
1
[6.5] Average Value of a Function [7.1] Integration by Parts7. Techniques of Integration
2
[7.2] Trigonometric Integrals第十二週
11/29-12/3
1
[7.3] Trigonometric Substitution2
[7.4] Integration of Rational Functions by Partial Fractions第十三週
12/6-12/10
(Quiz6)1
[7.5] Strategy for Integration
[7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration
2
[7.8] Improper Integrals8. Further
Applications of Integration
第十四週 12/13-12/17
1
緩衝時間2
[8.1] Arc Length[8.2] Area of a Surface of Revolution
9. Differential Equations
第十五週 12/20-12/24
(Quiz7)
1
[9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method2
[9.3] Separable Equations[9.4] Models for Population Growth
第十六週 12/27-12/31
1
[9.5] Linear Equations[9.6] Predator-Prey Systems (※)
10. Parametric Equations and Polar Coordinates
2
[10.1] Curves Defined by Parametric Equations [10.2] Calculus with Parametric Curves第十七週 1/3-1/7
(Quiz8)1
[10.3] Polar Coordinates[10.4] Areas and Lengths in Polar Coordinates
2 緩衝時間
1/9(日) 09:00~11:30 期末考 考試範圍 6.1~10.4 (英文命題)