教學大綱 Syllabus

科目名稱：微積分

Course Name: Calculus
  • 學年學期：114-1 Fall Semester, 2025
  • 科目代碼：000711021 Course No.000711021

修別：必

Type of Credit: Required

3.0

學分數

Credit(s)

150

預收人數

Number of Students

課程資料Course Details
  • 開課單位：應數系 Course Department:Mathematical Sciences
  • 授課老師：蔡承育 Instructor: TSAI CHENG-YU
  • 先修科目：無Prerequisite(N/A)
  • 上課時間：四D56 Session: thu13-16

課程簡介Course Description

Calculus is a foundational, university-entrance-level mathematics subject and serves as a prerequisite for most advanced university-level mathematics courses. The primary goal of this course is to equip students with essential concepts and techniques in calculus, while fostering rigorous analytical thinking and problem-solving skills. Emphasis will be placed on developing a solid understanding of limits, derivatives, and integrals.

核心能力分析圖 Core Competence Analysis Chart

能力項目說明

    課程目標與學習成效Course Objectives & Learning Outcomes

    Students will develop the ability to compute limits and derivatives, apply differentiation to solve practical problems, perform integration using standard and advanced techniques, and apply integration in various contexts. In addition, they will gain familiarity with foundational results in calculus, including the Extreme Value Theorem, the Mean Value Theorem, and the Fundamental Theorem of Calculus.

    每周課程進度與作業要求 Course Schedule & Requirements

    週次
    Week

     

     

    課程主題

     Topic

     

    課程內容與指定閱讀

    Content and Reading 
    Assignment

    教學活動與作業

    Teaching 
    Activities and Homework

    學習投入時間 Student workload expectation

    課堂講授 
    In-class Hours

    課程前後

    Outside-of-class Hours

    1

    Function and Logarithms

    1

    Selected Exercises

    3

    5

    2

    Limits and Continuity

    2

    Selected Exercises

    3

    5

    3

    Limits at Infinity and Derivatives

    2

    Selected Exercises

    3

    5

    4

    Differentiation Rules I

    3

    Selected Exercises

    3

    5

    5

    Differentiation Rules II

    3

    Selected Exercises

    3

    5

    6

    Extreme Values and Shape of graph

    4

    Selected Exercises

    3

    5

    7

    Indeterminate Forms, Optimization and Antiderivatives

    4

    Selected Exercises

    3

    5

    8

    Midterm Exam

    		        

    9

    Definite Integrals 

    5

    Selected Exercises

    3

    5

    10

    Fundamental Theorem of Calculus and Indefinite integral

    5

    Selected Exercises

    3

    5

    11

    Substitution Rule

    5

    Selected Exercises

    3

    5

    12

    Areas between Curves

    6

    Selected Exercises

    3

    5

    13

    Volumes

    7

    Selected Exercises

    3

    5

    14

    Integration by Parts and Trigonometric Integrals

    7

    Selected Exercises

    3

    5

    15

    Trigonometric Substitution and Integration by Partial Fractions

    7

    Selected Exercises

    3

    5

    16

    Final Exam

     

     

    		    

    授課方式Teaching Approach

    90%

    講述 Lecture

    10%

    討論 Discussion

    0%

    小組活動 Group activity

    0%

    數位學習 E-learning

    0%

    其他： Others:

    評量工具與策略、評分標準成效Evaluation Criteria

    作業 15% (兩週一次)

    隨堂小考 15% (每週一次)

    期中考 30% 

    期末考 40%

    指定/參考書目Textbook & References

     

    James Stewart, Daniel K. Clegg, Saleem Watson, Calculus:  Early Transcendentals, Metric Version 9th Edition.

    已申請之圖書館指定參考書目 圖書館指定參考書查詢 |相關處理要點

    維護智慧財產權，務必使用正版書籍。 Respect Copyright.

    本課程可否使用生成式AI工具Course Policies on the Use of Generative AI Tools

    本課程無涉及AI使用 This Course Does Not Involve the Use of AI.

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                        Approval
                
    
            
    
        
    
    
    
    
    
    
        
        
    
            
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