課程大綱及進度表
開課系所 物理、光電 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 (1)
課程碼 C215610
分班碼
先修科目或先備能力
學分數 3
開課教師 黃柏嶧
e-mail [email protected]
電話 65153
Office Hours 上課時決定時間
課程概述 這是一個學年課程，講授微積分 及其應用。主要是針對理工學院 的學生，我們將注重實際例子的 計算和應用，並有一些定理的證 明。
教學目標 了解微分、 積分的意義。 熟練 微分、 積分的計算並能應用。
授課課程大綱明細 上學期我們教授單變數微積 分。講授內容如下﹕
1. Limit and Continuity Ideal and definition of limit.
The Pinching Theorem &
Trigonometric limit.
Continuity and properties of continuous functions
2. Differentiation
Derivative and formulas of Derivative.
Derivatives of higher order.
Rate of change.
Chain Rule.
Differentiating the
trigonometric functions.
Implicit differentiation &
Rational powers.
The applications of differentiation.
Newton-Raphson approximations.
3. Mean-Value Theorem and applications
Mean-Value Theorem.
Increasing and decreasing
functions.
Local extreme values.
Endpoint and absolute extreme values.
Max-Min problems.
Concavity and points of inflection.
Vertical and Horizontal asymptotes.
Curve sketching.
4. Integration
The definite integral.
The fundamental theorem of integral calculus.
Indefinite integral.
Change of variables.
Mean-Value Theorem for integrals.
Application on area.
Application on volume.
( parallel cross-section , discs and washers )
Volume by the shell method.
5. Transcendental functions Inverse function.
Logarithm and exponential function.
The inverse trigonometric functions
The hyperbolic sine and cosine functions
6. Technique of Integration Integral tables. Integration by parts.
Powers and products of trigonometric functions Trigonometric substitution Rational functions & Partial fractions
Rationalizing substitutions Numerical integral
7. Sequences, The
indeterminate form and Improper integrals
The least upper bound axiom Sequences of real numbers and the Limit of a sequence.
Some important limits of sequences.
The indeterminate forms and other indeterminate forms.
Improper integrals.
參考書目 “Calculus- One and several variables” by Salas, Hille and Etgen。
課程要求
評量方式 期中考(I)佔 30%，期中考(II) 佔 35%，期末考佔 35%。
課程網址 助教資訊 備註
