教學大綱 Syllabus

科目名稱：微積分甲

Course Name: Calculus A
  • 學年學期：114-1 Fall Semester, 2025
  • 科目代碼：000713021 Course No.000713021

修別：必

Type of Credit: Required

3.0

學分數

Credit(s)

90

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：林俊良 Instructor: LIN CHUN-LIANG
  • 先修科目：無Prerequisite(N/A)
  • 上課時間：二234 Session: tue09-12

課程簡介Course Description

Calculus is a basic, university-entrance-level mathematics course that is needed as a prerequisite for the majority of the other university-level mathematics courses. The main goal of the course is to expose students to the fundamentals of calculus as well as provide rigorous training in analytic thinking and (mathematical) problem-solving.

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 learn how to compute limits and derivates, applications of differentiation, integration and techniques of integration as well as applications of integration. Moreover, students will learn key results such as the extreme value theorem, mean value theorem, fundamental theorem of calculus, etc.

    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

    Functions

    Ch 1

    Selected Exercises

    3

    5

    2

    		 Limits and Continuity Ch 2 Selected Exercises 3 5

    3

    Limits at Infinity and Derivatives

    Ch 2

    Selected Exercises

    		 3 5

    4

    Quiz, Differentiation Rules I

    Ch 3

    Selected Exercises

    3

    5

    5

    Differentiation Rules II

    Ch 3

    Selected Exercises

    3

    5

    6

    		 Quiz, Extreme Values and Shape of graph

    Ch 3

    Selected Exercises

    3

    5

    7

    Indeterminate Forms, Optimization

    Ch 4

    Selected Exercises

    3

    5

    8

    		 Midterm Exam

     

    Selected Exercises

    2

    6

    9

    		 Definite Integral and Fundamental Theorem of Calculus Ch 5

    Selected Exercises

    2

    6

    10

    		 Indefinite Integral and Substitution Rule I

    Ch 5

    Selected Exercises

    3

    5

    11

    Substitution Rule II and Integration by Parts

    Ch 5, 7

    Selected Exercises

    3

    5

    12

    Quiz, Trigonometric Integrals

    Ch 7

    Selected Exercises

    3

    5

    13

    Trigonometric  Substitution and Integration by Partial Fractions

    Ch 7

    Selected Exercises

    3

    5

    14

    		 Quiz, Improper Integrals

    Ch 7

    Selected Exercises

    3

    5

    15

    Areas between Curves and Volumes

    Ch 6

    Selected Exercises

    3

    5

    16

    Final Exam

     

    Selected Exercises

    2

    6

    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

    本課程無涉及 AI 使用。

    Quizzes: 20%

    Homework: 20%

    Midterm Exam: 30%

    Final Exam: 30%

    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

    書名 Book Title 作者 Author 出版年 Publish Year 出版者 Publisher ISBN 館藏來源* 備註 Note

    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.

    課程相關連結Course Related Links

    Moodle教學平台: http://moodle.nccu.edu.tw

    課程附件Course Attachments

    課程進行中，使用智慧型手機、平板等隨身設備 To Use Smart Devices During the Class

    是 Yes

    列印