基本素養 Basic Literacy

Humanism quality

Civic virtue

Social care

International vision

核心能力 Competence

Professional and transdisciplinary abilities

Professionalism

Thinking and judgement abilities

Language and communication abilities

Professional innovation and lifelong learning abilities

課程概述 Course Description

Based on the concept of limit, we discuss both differential calculus and integral calculus. These will be used as tools to discuss the local and global behavior of real-valued functions.

課程學習目標 Course Objectives

• 微積分基礎知識: 變化率、極限、微分、積分、泰勒展開式、機率與統計
• 微積分的應用: 微分方程式的數學建模與應用
• 抽象思維與批判性思考能力訓練
• 課程進度 Progress Description

進度說明 Progress Description
1Functions: polynomials; power functions; Trigonometrical functions; Exp-Log
2Transformation of functions; composite functions; Exponential deay and log-log plot
3Sequences and difference equations for discrete modles of dynamic systems
4Limits
5Monod Growth function; limit at infinity; symptotical lines
6Limit laws and continuity
7Derivatives and rate of changes, differential laws
8Product rule; chain rule
9Implicit differentiation
10First derivative test and second derivative test for extrema
11monotonicity and concavity; optimization with calculus
12Equilibria and stability
13Antiderivative and indefinite integrals; definite integrals
14Fundamental Theorem of Calculus, Substitution rule, Integration by parts, improper integrals
15Applications of Ingtegration: areas, arc length, flow, average
16Further Application in Biology (第六章結束); Modeling with differnetial equations (7.1)
17Phase plots, equilibria and stability(7.2), direction field (7.3)
18期末考
以上每週進度教師可依上課情況做適度調整。The schedule may be subject to change.

有關課程其他調查 Other Surveys of Courses

1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
2.本課程是否規劃含校外實習(並非參訪)? 否
Are there any internships involved in the course? How many hours? No