Calculus II, Spring 2026.
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
Google meet 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: R5R6. Email: a60929069@gmail.com
Lecture:
MXIC building (旺宏館), classroom 243, T3T4R3R4.
Recitation:
Delta building (台達館), classrooms B08(學號末位數:0, 2, 4, 6, 8),
B09 (學號末位數: 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 II:
- Chap 08: Section 8.8: Improper Integrals.
- Chap 10: Infinite Sequences and Series.
- Chap 14: Partial Derivatives.
- Chap 15: Multiple Integrals.
- Chap 16: Integration in Vector Fields.
Syllabus and study guide:
Lecture notes, homework assignments and solutions:
- Homework policy.
- Week 01:
Lecture 01 (20260224):
A4, 800x700
Section 8.8: Definition of improper integrals, type I and type II and examples.
Direct computation to find out convergence and divergence.
Integrals ∫01 x-p dx
and ∫1∞ x-p dx
and related integrals.
Lecture 02 (20260226):
A4, 800x700
Section 8.8: Direct Comparison Test (Theorem 2).
Limit Comparison Test (Theorem 3). Examples.
Homework 01.
Homework 01 solutions.
- Week 02: Quiz 01 (Section 8.8), Mar 05, 10:10AM.
Lecture 03 (20260303):
A4, 800x700
Section 10.1:
Definition of limit of sequences, including the limit = +- ∞ cases.
Find limit of a sequence using the Sandwich Theorem and L’Hôpital’s Rule.
Section 10.2: Infinite series, definition and example of convergent and divergent series.
Geometric Series, telescoping sum. The n-th term test and its proof.
Examples of divergent series.
Lecture 04 (20260305):
A4, 800x700
Section 10.3: The integral test and Remainder estimate, Proof and examples.
Section 10.4: Direct comparison test; Limit comparison test.
Examples for both Direct and Limit comparison tests.
Homework 02.
Homework 02 solutions.
- Week 03: Quiz 02 (Section 10.1-10.3; Mar 12, 10:10AM).
Lecture 05 (20260310, page 1-2 reorganized, page 10 corrected):
A4, 800x700
Section 10.5: The Absolute Convergence Test and proof.
Ratio test and Root test. Examples of both tests.
Section 10.5: Proof of the Ratio Test.
Lecture 06 (20260312, added page 5-6):
A4, 800x700
Section 10.6: Definition of Conditional convergence and Absolute convergence;
The Alternating Series Test (Leibniz Test) and remainder estimate; Examples
and proof. Statement and proof of The Monotone Sequence Theorem (Section 10.1, Theorem 6);
Section 10.7: Definition and examples of power series,
including geometric series; Examples of power series whose radius of convergence
is finite, zero and ∞, respectively.
Homework 03.
Homework 03 solutions.
- Week 04: Quiz 03 (Section 10.4, 10.5, 10.6: Mar 19, 10:10AM).
Lecture 07-08
(pre-class version)
Section 10.7: Definition and examples of power series, including geometric series;
The convergence Theorem for power series (Theorem 10) and proof;
Definition of the "radius of convergence"
and the "interval of convergence";
Finding radius of convergence using ratio and root test;
Examples of convergence/divergence when |x-a| = R.
Section 10.7:
Algebraic manipulation of power series: addition, subtraction, multiplication,
Section 10.7: Algebraic manipulation of power series:
Division: find the power series of A(x)/B(x) by long division.
Remark on radius of convergence of A(x)/B(x).
Term by term differentiation and integration and application.
Homework 04.
Homework 04 solutions.
- Homework assignments of this semester (temporary):
Chapter 10.
Chapter 14.
Chapter 15.
Chapter 16.