課程大綱及進度表
開課系所
都計、工設開課學年
100開課學期
1課程名稱(中文)
微積分課程名稱（英文）
CALCULUS課程碼
F212000分班碼
先修科目或先備能力
高中數學學分數
3開課教師
吳順益e-mail soonyi@mail.ncku.edu.tw
電話
65133Office Hours
By Appointment課程概述
單變數及多變數函數的特性、微分、積 分，以及其應用。教學目標
加強學生的數學邏輯與應用現代數學工 具的能力。授課課程大綱明細
1. INTRODUCTION TO CALCULUS: THE DERIVATIVE.The Derivative. The Derivative by the Four-Step Process. Derivatives of
Polynomials. Instantaneous Rates of Change.
Differentiation Formulas. Implicit Differentiation. Higher Derivatives.
2. APPLICATIONS OF THE DERIVATIVE.
The First-Derivative Test. The
Second-Derivative Test. Applications of Minima and Maxima. Differentials.
3. THE INTEGRAL.
Antiderivatives. The Area Problem. The Fundamental Theorem of Calculus. The Integral: Notation and General Definition.
Basic Integration Formulas. Area Between Curves. Improper Integrals.
4. APPLICATION OF THE INTEGRAL.
Volumes of Revolution: Disk and Washer Methods. Volumes of Revolution: Shell Method.
5. DERIVATIVES OF TRANSCENDENTAL FUNCTIONS.
Review of Trigonometry. Derivatives of Sine and Cosine Functions. Other Trigonometric Functions. Inverse Trigonometric Functions.
Derivatives of Inverse Trigonometric Functions. Exponential and Logarithmic Functions. Derivative of the Logarithmic Function. Derivative of the Exponential Function. L'Hospital's rule.
6. INTEGRATION TECHNIQUES.
The Power Formula Again. The Logarithmic and Exponentials Forms. Trigonometric Forms.
Inverse Trigonometric Forms. Integration by Trigonometric Substitution. Integration by Parts. Integration of Rational Functions.
7. THREE-DIMENSIONAL SPACE; PARTIAL DERIVATIVES; MULTIPLE INTEGRALS.
Surfaces in Three Dimensions. Partial Derivatives. Applications of Partial Derivatives. Integrated Integrals. Volumes by Double Integration.
參考書目
Technical Calculus with Analytic Geometry, Fourth Edition, by Peter Kuhfittig課程要求
課程包含課堂講授、研討課以及期中期末 考試三部份。每一部份皆需親力親為，方 可取得成績。評量方式
兩次期中考: 各佔 25%期末考: 25%
小考成績: 20%
平時分數: 5%
