NCHU Course Outline
Course Name (中) 微積分(一)(1200)
(Eng.) Calculus(I)
Offering Dept Department of Applied Mathematics (Data Science and Computing Program)
Course Type Required Credits 4 Teacher TENG CHUN HAO
Department Department of Applied Mathematics (Data Science and Computing Program)/Undergraduate Language 中/英文 Semester 2024-FALL
Course Description 微積分是一門進入高等數學的基礎學科,其內容討論函數的性質如極大極小、變化率等以及運作方式,如函數的微分、積分的運作方法。
Prerequisites
self-directed learning in the course Y
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
使得學生能夠了解微分積分的運作方式和運用,並做為下學期多變數微積分和高等數學基礎知識。
1.Basic Knowledge in Mathematical Sciences
8.English Language Ability
90
10
Practicum
Networking/Distance Education
Exercises
Lecturing
topic Discussion/Production
Assignment
Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 課程說明
The Limit of a Function
Calculating Limits Using the Limit Laws
Week 2 The Precise Definition of a Limit.
Continuity.
Derivatives and Rates of Change.
Week 3 The Derivative as a Function.
Differentiation Formulas.
Derivatives of Trigonometric Functions.
Week 4 The Chain Rule
Implicit Differentiation.
Rates of Change in the Natural and Social Sciences, and Related Rates
Week 5 Linear Approximations and Differentials.
Maximum and Minimum Values.
The Mean Value Theorem.
Week 6 期中考一
What Derivatives Tell Us About the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes.
Week 7 Summary of Curve Sketching and Graphing with Calculus and Technology.
Optimization Problems.
Antiderivatives.
Week 8 The Area and Distance Problems.
The Definite Integral.
The Fundamental Theorem of Calculus.
Week 9 Indefinite Integrals and the Net Change Theorem.
The Substitution Rule.
Areas Between Curves.
Week 10 Volumes.
Volumes by Cylindrical Shells.
Average Value of a Function.
Week 11 期中考二
Inverse Functions.
The Natural Logarithmic Function.
The Natural Exponential Function.
Week 12 General Logarithm and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions.
Week 13 Hyperbolic Functions
Indeterminate Forms and l’Hospital’s Rule
Integration by Parts
Week 14 Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Week 15 Improper Integrals
Arc Length
Area of a Surface of Revolution
Week 16 期末考
Week 17 課程含自主學習:由教學影片預習
Curves Defined by Parametric Equations
Calculus with Parametric Curves
Week 18 課程含自主學習:由教學影片預習
Polar Coordinates
Calculus in Polar Coordinates
Evaluation
作業和小考20%
期中考一25%
期中考二25%
期末考30%
(期中考與期末考日期依上課進度,於考試前兩週公布)
Textbook & other References
書名: Calculus 9th edition
作者: James Stewart

代理商:滄海書局

Teaching Aids & Teacher's Website
由ilearning 公布
Office Hours
Wed. 16:00-17:00
Sustainable Development Goals, SDGs
include experience courses:N
Please respect the intellectual property rights and use the materials legally.Please repsect gender equality.
Update Date, year/month/day:2024/09/23 11:04:06 Printed Date, year/month/day:2024 / 10 / 07
The second-hand book website:http://www.myub.com.tw/