NCHU Course Outline
Course Name (中) 微積分(一)(1199)
(Eng.) Calculus(I)
Offering Dept Department of Applied Mathematics
Course Type Required Credits 4 Teacher LIU, HSIAO-FAN
Department Department of Applied Mathematics / Undergraduate Language Chinese Semester 2025-FALL
Course Description We will cover elementary concepts of Calculus and students are expected to understand limits, derivatives of functions, integrals and their applications after taking this courses.
Prerequisites
Relevance of Course Objectives and Core Learning Outcomes(%) Teaching and Assessment Methods for Course Objectives
Course Objectives Competency Indicators Ratio(%) Teaching Methods Assessment Methods
Ch.1 Functions and Limits
Ch. 2 Derivatives
Ch. 3 Applications of Differentiation
Ch. 4 Integrals
Ch. 5 Applications of Integration
Ch. 6 Inverse Functions
Ch. 7 Techniques of Integration
1.Basic Knowledge in Mathematical Sciences
8.English Language Ability
90
10
Discussion
Lecturing
Attendance
Assignment
Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 1.1 Four Ways to Represent a Function
1.3 New Functions from Old Functions
1.5 The Limit of a Function
1.6 Calculating Limits Using the Limit Laws
Week 2 1.7 The Precise Definition of a Limit
1.8 Continuity
2.1 Derivatives and Rates of Change
2.2 The Derivative as a Function
Week 3 2.3 Differentiation Formulas
2.4 Derivatives of Trigonometric Functions
6.2 Exponential Functions and Their Derivatives
2.5 The Chain Rule
Week 4 2.6 Implicit Differentiation
2.8 Related Rates
2.9 Linear Approximations and Differentials
3.1 Maximum and Minimum Values
Week 5 3.2 The Mean Value Theorem
6.8 Indeterminate Forms and l’Hospital’s Rule
3.3 What Derivatives Tell Us about the Shape of a Graph
3.4 Limits at Infinity; Horizontal Asymptotes
Week 6 3.5 Summary of Curve Sketching
3.7 Optimization Problems
3.9 Antiderivatives
Week 7 4.1 The Area and Distance Problems
4.2 The Definite Integral
4.3 The Fundamental Theorem of Calculus
4.4 Indefinite Integrals and the Net Change Theorem
Week 8 4.5 The Substitution Rule
Review
Midterm
Week 9 7.1 Integration by Parts
5.1 Areas Between Curves
5.2 Volumes
5.3 Volumes by Cylindrical Shells
Week 10 5.5 Average Value of a Function
6.1 Inverse Functions and Their Derivatives
Week 11 6.3 Logarithmic Functions
6.4 Derivatives of Logarithmic Functions
General Logarithmic Functions
Week 12 6.6 Inverse Trigonometric Functions
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
Week 13 7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
Week 14 7.5 Strategy for Integration
7.8 Improper Integrals
Week 15 8.1 Arc Length
8.2 Area of a Surface of Revolution
Review for final
Week 16 Final
self-directed
learning		    02.Viewing multimedia materials related to industry and academia.
Self-learning: 1.4, 2.7, 3.6, 3.8, 5.4, 6.7
Evaluation
出席：10%
平時表現(作業)：20%
期中考：35%
期末考：35%
Textbook & other References
Calculus, Metric version 9E; James Stewart, Daniel Clegg, Saleem Watson
Teaching Aids & Teacher's Website

Office Hours
25
by appointments
Sustainable Development Goals, SDGs(Link URL)
04.Quality Educationinclude experience courses：N
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2025/09/01 12:11:02 Printed Date, year/month/day：2026 / 3 / 03
The second-hand book website：http://www.myub.com.tw/