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 07-11 Number of credits 4 Course title Calculus
Instructor 陳鵬文(07)、周謀鴻(08)、莊正良(09)、劉瓊如(10)、郭鴻文(11) I. Contents：
章次 周次 課程進度
2. Limits and Continuity
第 1 週 9/10~9/14
[2.1] The Limit Process (An Intuitive Introduction).
[2.2] Definition of Limit.
[2.3] Some Limit Theorems.
[2.4] Continuity.
第 2 週 9/17~9/21
[2.5] The Pinching Theorem; Trigonometric Limits.
[2.6] Two Basic Theorems.
[3.1] The Derivative.
[3.2] Some Differentiation Formulas.
3. The Derivative;
The Process of
Differentiation 第 3 週 9/24~9/28
[3.3] The d/dx Notation; Derivatives of Higher Order.
[3.4] The Derivative as a Rate of Change.
[3.5] The Chain Rule.
[3.6] Differentiating the Trigonometric Functions.
[3.7] Implicit Differentiation; Rational Powers.
4. The Mean- Value Theorem;
Applications of the First and Second
Derivatives
第 4 週 10/1~10/5
[4.1] The Mean-Value Theorem.
[4.2] Increasing and Decreasing Functions.
[4.3] Local Extreme Values.
[4.4] Endpoint Extreme Values; Absolute Extreme Values.
第 5 週 10/8~10/12
[4.5] Some Max-Min Problems.
[4.6] Concavity and Points of Inflection.
第 6 週 10/15~10/19
[4.7] Vertical and Horizontal Asymptotes; Vertical Tangents and Cusps.
[4.8] Some Curve Sketching.
*[4.9] Velocity and Acceleration; Speed.
[4.10] Related Rates of Change Per Unit Time.
[4.11] Differentials.
*[4.12] Newton-Raphson Approximations.
5. Integration
第 7 週 10/22~10/26
[5.1] An Area Problem; A Speed-Distance Problem.
[5.2] The Definite Integral of a Continuous Function.
[5.3] The Function
[5.4] The Fundamental Theorem of Integral Calculus.
第 8 週 10/29~11/2
[5.5] Some Area Problems.
[5.6] Indefinite Integrals.
[5.7] Working Back from the Chain Rule; the u-Subtitution.
[5.8] Additional Properties of the Definite Integral.
[5.9] Mean-Value Theorems for Integrals; Average Value of a Function.
6. Some Applications of the
Integral
第 9 週 11/5~11/9
[6.1] More on Area.
[6.2] Volume by Parallel Cross-Sections; Discs and Washers.
11/10(六) 9:00~11:30 期中考 考試範圍 2.1~5.9 (英文命題).
第 10 週 11/12~11/16
[6.3] Volume by the Shell Method.
[6.4] The Centroid of a Region; Pappus’s Theorem on Volumes.
[7.1] One-to-One Functions; Inverse Functions.
[7.2] The Logarithm Function, Part I.
7. The Transcendental
Functions
第 11 週 11/19~11/23
[7.3] The Logarithm Function, Part II.
[7.4] The Exponential Function.
[7.5] Arbitrary Powers; Other Bases.
[7.6] Exponential Growth and Decay.
第 12 週 11/26~11/30
[7.7] The Inverse Trigonometric Functions.
[7.8] The Hyperbolic Sine and Cosine.
[8.1] Integral Tables and Review.
[8.2] Integration by Parts.
8. Techniques of
Integration 第 13 週 12/3~12/7
[8.3] Powers and Products of Trigonometric Functions.
[8.4] Integrals Featuring , , . [8.5] Rational Functions; Partial Functions.
[8.6] Some Rationalizing Substitutions.
*[8.7] Numerical Integration.
9. Differential
Equations 第 14 週 12/10~12/14
[9.1] First-Order Linear Equations.
[9.2] Integral Curves; Separable Equations.
[9.3] The Equation y''+ ay'+ by = 0.
[10.2] Polar Coordinates.
[10.3] Graphing in Polar Coordinates.
10. The Conic Sections; Polar
Coordinates;
Parametric Equations
第 15 週 12/17~12/21
[10.4] Area in Polar Coordinates.
[10.5] Curves Given Parametrically.
[10.6] Tangents to Curves Given Parametrically.
[10.7] Arc Length and Speed.
[10.8] The Area of a Surface of Revolution; Pappus’s Theorem on Surface Area.
11. Sequences;
Indeterminate Forms; Improper
Integrals
第 16 週 12/24~12/29
[11.1] The Least Upper Bound Axiom.
[11.2] Sequences of Real Numbers.
[11.3] The Limit of a Sequence.
[11.4] Some Important Limits.
[11.5] The Indeterminate Forms (0/0).
第 17 週 12/31~1/4
[11.6] The Indeterminate Form (∞/∞); Other Indeterminate Forms.
[11.7] Improper Integrals.
1/5(六) 9:00~11:30 期末考 考試範圍 6.1~11.7 (英文命題).
