Current course · Fall 2026
Calculus A (I)
564004 微積分甲(一) / Calculus A (I)
National Yang Ming Chiao Tung University
Course information
- Instructor
- Cătălin I. Cârstea
- carstea@nycu.edu.tw
- Class meetings
- Mondays 15:30–17:20 and Thursdays 10:10–12:00
- Classroom
- SC152[GF]
- Teaching assistants
- 張嘉元、蔡翔宇 Students may contact the TAs through E3.
- Office hours
- Thursdays 13:00–14:00, SA338[GF], and by appointment
- Textbook
- James Stewart, Calculus: Early Transcendentals, 9th ed.
Homework
Students are strongly encouraged to work through all assigned problems and to do additional exercises whenever a topic is not yet comfortable. Regular practice is essential in this course.
Homework is the main preparation for quizzes and midterms; exam and quiz problems may be drawn from, or closely related to, assigned homework.
Course description and goals
This course develops the basic ideas and techniques of single-variable calculus: limits, derivatives, applications of differentiation, definite and indefinite integrals, the Fundamental Theorem of Calculus, applications of integration, and standard techniques of integration.
The emphasis is on both conceptual understanding and computational fluency. Important theorems will be stated and explained, and students should understand the role of their hypotheses as well as be able to use the results in calculations and applications. We follow the common departmental syllabus.
Assessment
- Quizzes
- 35%
- Two midterm examinations
- 35%
- Final examination
- 30%
A short quiz will be given at the beginning of almost every class. At the end of the semester, the six lowest quiz scores for each student will be dropped, and the quiz component of the final grade will be computed from the remaining quizzes.
The final examination is the departmental common final.
Communication
Most announcements and routine logistical information will be given in class and posted on the course website. E3 will be used mainly when an email needs to be sent to the entire class and as a channel for students to contact the teaching assistants.
Questions about course material are welcome in class, during office hours, or by appointment. For routine exercise questions, students are also encouraged to consult the teaching assistants.
Planned course outline
This is a pacing plan rather than a calendar. The listed hours are approximate and may be adjusted as needed.
| Chapter | Topics | Hours |
|---|---|---|
| 1 | Functions and Models: exponential functions; inverse functions and logarithms | 3 |
| 2 | Limits and Derivatives: limits, limit laws, precise definition of a limit, continuity, limits at infinity, derivatives and rates of change, derivative as a function | 8 |
| 3 | Differentiation Rules: polynomial, exponential and trigonometric derivatives; product and quotient rules; chain rule; implicit differentiation; logarithmic and inverse-trigonometric derivatives; linear approximation and differentials | 8 |
| 4 | Applications of Differentiation: extrema, Mean Value Theorem, monotonicity and concavity, L'Hospital's rule, curve sketching, antiderivatives | 7 |
| 5 | Integrals: area and distance problems, definite integral, Fundamental Theorem of Calculus, indefinite integrals and net change, substitution | 6 |
| 6 | Applications of Integration: areas between curves, volumes, cylindrical shells | 3 |
| 7 | Techniques of Integration: integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, improper integrals | 7 |
| 8 | Further Applications of Integration: arc length and surface area of revolution | 3 |
| Planned core lecture time | 45 |
Optional topics, as time permits. Transformations of functions; related rates; applications of rates of change; exponential growth and decay; hyperbolic functions; optimization; Newton's method; average value; strategy and approximate integration; selected physical, economic, biological, or probability applications; parametric curves and calculus with parametric curves.