Department of Mathematics Nature of the course

(1)

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 01-05 Number of credits 4 Course title Calculus

Instructor 朱樺(01)、劉瓊如(02)、張志中(03)、蔡雅如(04)、薛克民(05) I. Contents：

II. 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

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] Derivatives of Polynomials and Exponential Functions

3. Differentiation Rules

第四週 10/4-10/8

1

[3.2] The Product and Quotient Rules [3.3] Derivatives of Trigonometric Functions

2

[3.4] The Chain Rule [3.5] Implicit Differentiation

第五週 10/11-10/15

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 Differentiation

第六週 10/18-10/22

1

[4.1] Maximum and Minimum Values [4.2] The Mean Value Theorem

2

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

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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

1

[5.4] Indefinite Integrals and the Net Change Theorem [5.5] The Substitution Rule

2

^緩衝時間

11/13(六)13:30～16:00 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

2

[6.3] Volumes by Cylindrical Shells [6.4] Work（※）

第十一週 11/22-11/26

1

[6.5] Average Value of a Function [7.1] Integration by Parts

7. Techniques of Integration

2

[7.2] Trigonometric Integrals

第十二週

11/29-12/3

1

[7.3] Trigonometric Substitution

2

[7.4] Integration of Rational Functions by Partial Fractions

第十三週

12/6-12/10

1

[7.5] Strategy for Integration

[7.6] Integration Using Tables and Computer Algebra Systems [7.7] Approximate Integration

2

[7.8] Improper Integrals

8. 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 [8.5] Probability

（※）

9. Differential Equations

第十五週 12/20-12/24

1

[9.1] Modeling with Differential Equations [9.2] Direction Fields and Euler’s Method

2

[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

1

[10.3] Polar Coordinates

[10.4] Areas and Lengths in Polar Coordinates

2 緩衝時間

1/9(日) 13:30～16:00 期末考考試範圍 6.1～10.4 (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。

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III. Course prerequisite：

High School Mathematics

IV. Reference material ( textbook(s) )：

James Stewart, Calculus Early Transcendentals, 6

^th

Department of Mathematics Nature of the course

C o u r s e D e s c r i p t i o n ( 暫 定 )