NCHU Course Outline
Course Name (中) 微積分(二)(1254)
(Eng.) Calculus(II)
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher Pei-Ju Lee
Department Department of Mechanical Engineering/Undergraduate Language 中/英文 Semester 2026-SPRING
Course Description This course provides a comprehensive study of advanced topics in calculus, emphasizing both theoretical understanding and practical problem-solving skills. Beginning with inverse functions, exponential and logarithmic functions, the course develops techniques for differentiation and integration, including methods such as integration by parts, trigonometric substitution, partial fractions, and improper integrals. Students are then introduced to sequences and series, with a focus on convergence tests, power series, and Taylor and Maclaurin expansions and their applications. The latter part of the course extends calculus concepts to functions of several variables, covering partial derivatives, optimization, multiple integrals, and coordinate transformations. Through systematic progression and rigorous applications, the course equips students with essential analytical tools for further study in mathematics, science, engineering, and related fields.
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. Learn integration techniques
2. Apply calculus methods to solve problems in physics or engineering
3. Learn basic concepts of mathematical analysis
4. Practice calculation techniques for multivariable calculus
1.The ability to apply the knowledge of math, science, and mechanical engineering.
5.The ability of continuing study and self-learning.
50
50
Discussion
Lecturing
Quiz
Assignment
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 6.1 Inverse Functions
6.2* The Natural Logarithmic Function
6.3* The Natural Exponential Function
Week 2 6.4* General Logarithmic and Exponential Functions
6.2 Exponential Functions and Their Derivatives
6.3 Logarithmic Function
Week 3 6.4 Derivatives of Logarithmic Function
6.6 Inverse Trigonometric Functions
Week 4 6.7 Hyperbolic Functions
6.8 Indeterminate Forms and l’Hospital’s Rule
7.1 Integration by Parts
Week 5 7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integration of Rational Functions by Partial Fractions
Week 6 7.7 Approximate Integration
7.8 Improper Integrals
11.1 Sequences
11.2 Series
Week 7 11.3 The Integral Test and Estimates of Sums
11.4 The Comparison Tests
11.5 Alternating Series
Week 8 Midterm Exam
Week 9 11.6 Absolute Convergence and the Ratio and Root Tests
11.7 Strategy for Testing Series
11.8 Power Series
Week 10 11.9 Representations of Functions as Power Series
11.10 Taylor and Maclaurin Series
11.11 Applications of Taylor Polynomials
Week 11 14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives
Week 12 14.4 Tangent Planes and Linear Approximations
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector
Week 13 14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers
15.1 Double Integrals over Rectangles
Week 14 15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals in Polar Coordinates
Week 15 15.5 Applications of Double Integrals
15.6 Triple Integrals
15.7 Triple Integrals in Cylindrical Coordinates
Week 16 Final Exam
self-directed
learning		    02.Viewing multimedia materials related to industry and academia.
Evaluation
Quiz:20%
Assignment:10%
Midterm:30%
Final:40%
Textbook & other References
Calculus, Metric Version, 9th edition/Stewart, Clegg, Watson
Teaching Aids & Teacher's Website

Office Hours
Wednesday 10:00am-12:00pm or by appointment
Sustainable Development Goals, SDGs(Link URL)
04.Quality Educationinclude experience courses：N
Please respect the intellectual property rights and use the materials legally.Please respect gender equality.
Update Date, year/month/day：2026/01/27 14:52:49 Printed Date, year/month/day：2026 / 1 / 29
The second-hand book website：http://www.myub.com.tw/