Calculus I, Fall 2025.

A undergraduate course in Mathematics at the Department of Mathematics, National Tsing Hua University.

Instructor: Professor Wei-Cheng Wang (王偉成).

Office Hours:
T,R: 12:00-13:00 綜三721, 分機62231 or by Email appointment.

Teaching Assistant:

• 台達B08: 柯秉辰, 綜三215, 分機33076. Office hour: F13:00-F15:00. Email: f8220219@gmail.com
• 台達B09: 鄭亦展, 綜三209, 分機33070. Office hour: T8T9. Email: a60929069@gmail.com

Lecture: Delta building (台達館), classroom B03, T3T4R3R4.

Recitation: Delta building (台達館), classrooms B08(學號末位數: 2, 4, 6, 8), B09 (學號末位數: 0, 1, 3, 5, 7, 9). Tuesdays 19:00-21:00.

Grading: 40% quiz(pick n-2 best from n quizzes)+attendance, 20% midterm I, 20% midterm II + 20% final exam. Extra credits for significant contributions to the class (correcting mistakes, etc.).

Textbook: G. B. Thomas, M. D. Weir and J. R. Hass: Thomas's Calculus Early Transcendentals, 13th edition in SI units (華通書局有販售,詳見校務資訊系統課程大綱).

Contents:

• Calculus I:
• Chapter 2: Limits and Continuity.
• Chapter 3: Derivatives.
• Chapter 4: Application of Derivatives.
• Chapter 5: Integrals
• Chapter 6: Applications of Definite Integrals.
• Chapter 7: Integrals and Transcendental Functions.
• Chapter 8: Techniques of Integration.

Syllabus, study guide and exam solutions:

• Calculus I:
• Syllabus (updated 20250901).
• quiz 01 (section 2.2-2.3) study guide. Quiz 01 solutions.
• quiz 02 (section 2.4-2.5) study guide. Quiz 02 solutions.

Lecture notes, homework assignments and solutions:

• Homework policy.
  
• Week 01: No recitation this week.
  Lecture 01 (20250902, 75 mins)
  Section 2.2: Review Limit laws; Limits involving quotients; Sandwich Theorem. Section 2.3: Precise definition of limit.
  Lecture 02 (20250904, 75 mins) (v02, revised)
  Section 2.3: Continued; How to prove lim_{{x → c}} = L using the ε-δ argument.
  Supplement to Lecture 02 (an essential remark on how to deal with larger ε).
  Homework 01 (lecture 01-02). Homework 01 solutions.
  
• Week 02: Recitation starts this week (Rb,Rc) (Sep 09, 19:00-21:00).
  Quiz 01 (Sep 11, 10:10AM).
  Lecture 03 (20250909, updated, 85 mins)
  Section 2.4: One sided limit; Limits involving sinθ/θ.
  Section 2.5: Definition of continuity; Left and right continuity; Basic properties of continuous functions;
  Lecture 04 (20250911, 50 mins)
  Section 2.5: Composite of continuous functions and generalization; Intermediate Value Theorem and application in root allocating.
  Homework 02 (lecture 03-04). Homework 02 solutions.
  
• Week 03: Quiz 02 (Sep 18, 10:10AM).
  Lecture 05 (20250916, updated, 80 mins)
  Section 2.6: Limits Involving Infinity (SKIP the asymptotes);
  Section 3.2: Definition of derivative; One-sided derivative; Differentiable functions; Examples of functions not differentiable at a point; proof of "Differentiability implies Continuity".
  Lecture 06 (20250918, updated, 50 mins)
  Section 3.3: Differentiation rules; Derivative of xⁿ for some integer n's and rational n's; proof of Product rule and Quotient rule; Derivative of exponential functions;
  Homework 03 (lecture 05-06).
• Week 04: Quiz 03 (Sep 25, 10:10AM).
  
• Week 05: Quiz 04 (Oct 02, 10:10AM).
  
• Week 06: Midterm 01 (Oct 09, 10:10AM).
  
• Week 07: No quiz this week.
  
• Week 08: Quiz 05 (Oct 23, 10:10AM).
  
• Week 09: Quiz 06 (Oct 30, 10:10AM).
  
• Week 10: Quiz 07 (Nov 06, 10:10AM).
  
• Week 11: Midterm 02 (Nov 13, 10:10AM).
  
• Week 12: No quiz this week.
  
• Week 13: Quiz 08 (Nov 27, 10:10AM).
  
• Week 14: Quiz 09 (Dec 04, 10:10AM).
  
• Week 15: Quiz 10 (Dec 11, 10:10AM).
  
• Week 16: Final Exam (Dec 18, 10:10AM).
  
• Homework assignments of this semester (temporary, subject to minor revisions): Chapter 02. Chapter 03. Chapter 04. Chapter 05. Chapter 06. Chapter 07. Chapter 08.