課程大綱及進度表
開課系所
工科系開課學年
95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
E915610分班碼
先修科目或先備能力
高中數學學分數
3開課教師
林 牛電話
略Office Hours
略課程概述
這是一個學年介紹應用微積分的課程。主要是針對工學院的學生，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
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﹕Chapter 1 Limit and Continuity Ideal and definition of limit.
The Pinching Theorem & Trigonometric limit.
Continuity and properties of continuous functions Chapter 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.
Chapter 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.
Chapter 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.
Chapter 5 Transcendental functions Inverse function.
Logarithm and exponential function.
The inverse trigonometric functions The hyperbolic sine and cosine functions Chapter 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
Chapter 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 form(0/0) and other indeterminate forms.
Improper integrals.
