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	English	Semester	2026-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				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
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 2.5 The Chain Rule 2.6 Implicit Differentiation Week 4 2.8 Related Rates 2.9 Linear Approximations and Differentials 6.2 Exponential Functions and Their Derivatives 6.1 Inverse Functions and Their Derivatives Week 5 3.1 Maximum and Minimum Values 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 Week 6 3.4 Limits at Infinity; Horizontal Asymptotes 3.5 Summary of Curve Sketching 3.7 Optimization Problems Week 7 4.1 The Area and Distance Problems 3.9 Antiderivatives 4.2 The Definite Integral 4.3 The Fundamental Theorem of Calculus Week 8 4.4 Indefinite Integrals and the Net Change Theorem Review Midterm Week 9 4.5 The Substitution Rule 7.1 Integration by Parts 5.1 Areas Between Curves Week 10 5.2 Volumes 5.3 Volumes by Cylindrical Shells 5.5 Average Value of a Function 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 (optional) 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
Attendance: 10% Assignment and Quizzes: 20% Midterm: 35% Final: 35% Midterm, Final exams and discussions by TA are mandatory.
Textbook & other References
Calculus, Metric version 9E; James Stewart, Daniel Clegg, Saleem Watson
Teaching Aids & Teacher's Website
Office Hours
by appointments
Sustainable Development Goals, SDGs(Link URL)
include experience courses：N

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Update Date, year/month/day：2026/10/08 08:45:36	Printed Date, year/month/day：2026 / 10 / 17
The second-hand book website：http://www.myub.com.tw/