NCHU Course Outline

Course Name	(中) 微積分(二)(1260)
	(Eng.) Calculus(II)
Offering Dept	Department of Applied Mathematics
Course Type	Required	Credits	3	Teacher	Yu-Tsung Tai
Department	Department of Computer Science and Engineering/Undergraduate	Language	English	Semester	2026-SPRING
Course Description	There are tremendous online and offline computational resources now a day. Although their results may sometimes be correct as we expected, these results are wrong other times; in the other situation, they are not what we expected but still are some of other correct answers. No matter in which situation, we need to have some knowledge to understand how to justify the answer we get, and modify these answers into the form we want. To have this ability, we will introduce the meaning of each symbol in Calculus and their complex relationship and interactions, so that students will not be afraid of these symbols and could trace and fix Calculus computations.
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
1、 Understand properties of series, double integrals, and (self-)study polar coordinates needed for Probability [1]. 2、 Understand properties of sequences and series needed for Discrete Mathematics [2]. 3、 Understand properties of partial derivatives, series, and (self-)study line integrals for General Physics [3].	1.Having abilities on computer science literacy, information theory, and mathematical analysis.	100	Exercises Lecturing	Assignment Quiz Attendance
Course Content and Homework/Schedule/Tests Schedule
Week Course Content Week 1 Introduction and Course Objectives Section 7.1 Integration by Parts Section 15.1 Double Integrals over Rectangles Week 2 Section 15.2 Double Integrals over General Regions Section 7.2 Trigonometric Integrals Week 3 Section 15.3 Double Integrals in Polar Coordinates Section 7.3 Trigonometric Substitution Week 4 Section 7.4 Integration of Rational Functions by Partial Fractions Section 7.8 Improper Integrals Week 5 Section 11.1 Sequences Preliminary Exam on March 25th, 2026 Week 6 Section 11.2 Series Section 11.3 The Integral Test and Estimates of Sums Course Dropping Deadline at 08:00, April 4th, 2026 Week 7 Adjusted holiday for Tomb Sweeping Festival on April 6th, 2026 Make-up holiday for University Anniversary and Annual Sports Meet on April 8th, 2026 Week 8 Section 11.4 The Comparison Tests Section 11.5 Alternating Series and Absolute Convergence Week 9 Section 11.6 The Ratio and Root Tests Section 11.7 Strategy for Testing Series Week 10 Section 11.8 Power Series Section 11.9 Representations of Functions as Power Series Week 11 Section 11.10 Taylor and Maclaurin Series Midterm Exam on May 6th, 2026 Week 12 Section 11.11 Application of Taylor Polynomials Section 14.1 Functions of Several Variables Week 13 Section 14.2 Limits and Continuity Section 14.3 Partial Derivatives Course Withdrawal Deadline at 08:00, May 23th, 2025 Week 14 Section 14.4 Tangent Planes and Linear Approximations Section 14.5 The Chain Rule Week 15 Section 14.6 Directional Derivatives and the Gradient Vector Section 14.7 Maximum and Minimum Values Week 16 Section 14.8 Lagrange Multipliers Final Exam on June 10th, 2026 self-directed learning Section 10.3 Polar Coordinates Section 10.4 Calculus in Polar Coordinates Section 15.8 Triple Integrals in Spherical Coordinates Section 16.2 Line Integrals Section 16.3 The Fundamental Theorem for Line Integrals
Evaluation
The overall grades will be the highest grade among the follow three grades: ● 5% Attendance + 25% Assignments + 27.5% Preliminary Exam + 27.5% Midterm Exam + 15% Final Exam, ● 5% Attendance + 25% Assignments + 35% Preliminary Exam + 35% Final Exam, and ● 5% Attendance + 25% Assignments + 35% Midterm Exam + 35% Final Exam. For those who attends every class and whose highest grade among the previous three grades is still ＜ 60 , your overall grade might be adjusted to pass this course.
Textbook & other References
Within the references, [4] is the textbook. If the proof of a theorem is not covered in 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠 [4], we might refer 𝐴𝑛 𝐼𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝐴𝑏𝑠𝑡𝑟𝑎𝑐𝑡 𝐴𝑙𝑔𝑒𝑏𝑟𝑎 [5], but these materials will not be in exams. The others are the general references. 參照 [1] Roy D. Yates and David J. Goodman, 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑎𝑛𝑑 𝑠𝑡𝑜𝑐ℎ𝑎𝑠𝑡𝑖𝑐 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑒𝑠 : 𝑎 𝑓𝑟𝑖𝑒𝑛𝑑𝑙𝑦 𝑖𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑓𝑜𝑟 𝑒𝑙𝑒𝑐𝑡𝑟𝑖𝑐𝑎𝑙 𝑎𝑛𝑑 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑒𝑛𝑔𝑖𝑛𝑒𝑒𝑟𝑠, 3rd ed. International Student Version: John Wiley & Sons Singapore Pte. Ltd., 2015. [2] Kenneth Rosen, 𝐷𝑖𝑠𝑐𝑟𝑒𝑡𝑒 𝑀𝑎𝑡ℎ𝑒𝑚𝑎𝑡𝑖𝑐𝑠 𝑎𝑛𝑑 𝐼𝑡𝑠 𝐴𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛𝑠, 8th ed.: McGraw-Hill Education, 2019. [3] Douglas Giancoli, 𝑃ℎ𝑦𝑠𝑖𝑐𝑠 𝑓𝑜𝑟 𝑆𝑐𝑖𝑒𝑛𝑡𝑖𝑠𝑡𝑠 𝑎𝑛𝑑 𝐸𝑛𝑔𝑖𝑛𝑒𝑒𝑟𝑠 𝑤𝑖𝑡ℎ 𝑀𝑜𝑑𝑒𝑟𝑛 𝑃ℎ𝑦𝑠𝑖𝑐𝑠, 5th ed.: Pearson Education, 2023. [4] James Stewart, Daniel Clegg, and Saleem Watson, 𝐶𝑎𝑙𝑐𝑢𝑙𝑢𝑠, 𝑀𝑒𝑡𝑟𝑖𝑐 𝑉𝑒𝑟𝑠𝑖𝑜𝑛, 9th ed.: Cengage Learning, Inc., 2016. [5] W. Keith Nicholson, 𝐼𝑛𝑡𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑡𝑜 𝐴𝑏𝑠𝑡𝑟𝑎𝑐𝑡 𝐴𝑙𝑔𝑒𝑏𝑟𝑎, 4th ed.: John Wiley & Sons, Inc., 2012.
Teaching Aids & Teacher's Website
iLearning 3.0 ( https://lms2020.nchu.edu.tw/ )
Office Hours
● Monday (15:10-16:00) and Wednesday (14:10-15:00) at AT336 ● Academic tutoring services ( https://cdtl.nchu.edu.tw/learningConsulting/ )
Sustainable Development Goals, SDGs(Link URL)
09.Industry, Innovation and Infrastructure include experience courses：Y

Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2026/03/09 16:04:41	Printed Date, year/month/day：2026 / 3 / 10
The second-hand book website：http://www.myub.com.tw/