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 2025-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 have 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 and double integrals 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 Section 6.6 Inverse Trigonometric Functions
Section 7.1 Integration by Parts
Week 2 Section 7.2 Trigonometric Integrals
Section 7.3 Trigonometric Substitution
Week 3 Section 7.4 Integration of Rational Functions by Partial Fractions
Section 7.8 Improper Integrals
Week 4 Section 11.1 Sequences
Section 11.2 Series
Week 5 Section 11.3 The Integral Test and Estimates of Sums
Section 11.4 The Comparison Tests
Week 6 Section 11.5 Alternating Series and Absolute Convergence
Section 11.6 The Ratio and Root Tests
Preliminary Exam Before the Course Dropping Deadline at 08:00, March 29th, 2025
Week 7 Make-up holiday for University Anniversary and Annual Sports Meet
Week 8 Section 11.7 Strategy for Testing Series
Section 11.8 Power Series
Week 9 Section 11.9 Representations of Functions as Power Series
Section 11.10 Taylor and Maclaurin Series
Week 10 Section 11.11 Application of Taylor Polynomials
Section 14.1 Functions of Several Variables
Week 11 Section 14.2 Limits and Continuity
Section 14.3 Partial Derivatives
Week 12 Section 14.4 Tangent Planes and Linear Approximations
Section 14.5 The Chain Rule
Week 13 Midterm Exam Before the Course Withdrawal Deadline at 08:00, May 17th, 2025
Week 14 Section 14.6 Directional Derivatives and the Gradient Vector
Section 14.7 Maximum and Minimum Values
Week 15 Section 14.8 Lagrange Multipliers
Section 15.1 Double Integrals over Rectangles
Week 16 Section 15.2 Double Integrals over General Regions
Section 15.3 Double Integrals in Polar Coordinates
Week 17 Final Exam in June 12th, 2025
Week 18 Self-Study
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 + 25% Preliminary Exam + 25% Midterm Exam + 20% 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, and the others are the general reference.

References
[1] R. D. Yates and D. J. Goodman, Probability and stochastic processes : a friendly introduction for electrical and computer engineers, 3 ed., John Wiley & Sons Singapore Pte. Ltd., 2015.
[2] K. Rosen, Discrete Mathematics and Its Applications, 8 ed., McGraw-Hill Education, 2019.
[3] D. Giancoli, Physics for Scientists and Engineers with Modern Physics, 5 ed., Pearson Education, 2023.
[4] J. Stewart, D. Clegg and S. Watson, Calculus, Metric Version, 9 ed., Cengage Learning, Inc., 2021.
Teaching Aids & Teacher's Website
● iLearning 3.0 ( https://lms2020.nchu.edu.tw/ )
● 中興大學微積分教學網 ( http://amath2.nchu.edu.tw/cal/ )
● 微積分線上測驗系統 ( http://calctest.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
09.Industry, Innovation and Infrastructureinclude experience courses：Y
Please respect the intellectual property rights and use the materials legally.Please repsect gender equality.
Update Date, year/month/day：2025/01/21 19:39:41 Printed Date, year/month/day：2025 / 1 / 22
The second-hand book website：http://www.myub.com.tw/