NCHU Course Outline
Course Name (中) 微積分(一)(1220)
(Eng.) Calculus(I)
Offering Dept Department of Applied Mathematics
Course Type Required Credits 3 Teacher CHIEN YU HUNG
Department Department of Electrical Engineering/Undergraduate Language English Semester 2024-FALL
Course Description Calculus is a science that studies the phenomena of change. Its primary content includes differentiation, integration, and computations and applications. Calculus is a branch of mathematics that explores the concept of limits, with two specific definitions: differentiation and integration. The course will cover the concepts of limits, differentiation, and integration, along with their applications. For students outside of science departments, learning calculus is not about becoming a mathematician but rather about utilizing it to support their studies in other professional fields, such as engineering or business management. For business majors, mastering calculus paves the way for further studies in probability theory, statistics, economics, managerial mathematics, compound interest mathematics, and investment and financial management. For engineering or agricultural majors, mastering calculus is essential for further studying in engineering mathematics, statistics, operational research, algorithms, and programming. This highlights the importance of learning calculus. In summary, calculus is a crucial computational science that can enhance your abilities in analytical reasoning and precise calculation—skills fundamental for building a solid foundation for pursuing more advanced knowledge.
Mathematics is the foundation of all sciences, and calculus is a cornerstone of analytical mathematics. Whether undergraduate or graduate students are majoring in science, engineering, business, agriculture, or medicine, mastering calculus is essential for advancing to higher-level courses. Moreover, in today's world, where every industry is globalized, in addition to having foreign language skills and information technology, individuals can train their logical reasoning skills by learning calculus.
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
This course is grounded in the concept of limits, establishing the operations of differentiation and integration to explore the local properties and overall behavior of fundamental functions. The instructional objectives are to guide students in progressively understanding the basic concepts of calculus. Various functions and their properties will be discussed, and the idea of limits will be introduced to derive concepts such as continuity and differentiation. Additionally, examining fundamental concepts and application methods of calculus is expected to help students become familiar with the mathematical tools commonly applied in related disciplines such as economics, management, and engineering. The course also aims to develop students' logical analysis skills through mathematical computations, enabling them to effectively apply the skills they have learned to related courses in the future.
Lecturing
Assignment
Quiz
Course Content and Homework/Schedule/Tests Schedule
Week Course Content
Week 1 1.1 Four ways to represent a function, 1.2 Mathematical models: a catalog of essential functions, 1.3 New functions from old functions, 1.4 The tangent and velocity problems
Week 2 1.5 The limit of a function, 1.6 Calculating limits using the limit laws, 1.7 The precise definition of a limit
Week 3 1.8 Continuity, 2.1 Derivatives and rates of change, 2.2 The derivative as a function, 2.3 Differentiation formulas
Week 4 2.4 Derivatives of Trigonometric functions, 2.5 The chain rule, 2.6 Implicit differentiation
Week 5 2.7 Rates of change in the Natural and social sciences, 2.8 Related rates, 2.9 Linear approximations, and differentials
Week 6 3.1 Maximum and Minimum values, 3.2 The mean value theorem, 3.3 How derivatives affect the shape of a graph
Week 7 3.4 Limits at infinity and horizontal asymptotes, 3.5 Summary of curve sketching, 3.6 Graphing with calculus and technology
Week 8 3.7 Optimization problems, 3.8 Newton’s method, 3.9 Antiderivatives
Week 9 Midterm
Week 10 4.1 The area and distance problems, 4.2 The definite integral, 4.3 The fundamental theorem of calculus
Week 11 4.4 Indefinite integrals and the net change theorem, 4.5 The substitution rule, 5.1 Areas between curves
Week 12 5.2 Volume, 5.3 Volumes by cylindrical shells, 5.4 Work, 5.5 Average value of a function
Week 13 6.1 Inverse functions and their derivatives, 6.2 Exponential functions and their derivatives, 6.3 Logarithmic functions, 6.4 Derivatives of logarithmic functions
Week 14 6.5 Exponential Growth and decay, 6.6 Inverse Trigonometric functions, 6.7 Hyperbolic functions, 6.8 Indeterminate forms and L’Hospital’s rule
Week 15 7.1 Integration by parts, 7.2 Trigonometric integrals, 7.3 Trigonometric substitution
Week 16 7.4 Integration of rational functions by partial fractions, 7.5 Strategy for Integration, 7.6 Integration using tables and technology
Week 17 7.7 Approximate integration, 7.8 Improper integrals
Week 18 Final
Evaluation
期中考(30%) 期末考(30%) 平時成績(40%)
Textbook & other References
CALCULUS metric version 9E, James Stewart, Daniel Clegg and Saleem Watson, CENGAGE (滄海圖書代理)
Teaching Aids & Teacher's Website

Office Hours
預約
Sustainable Development Goals, SDGs
include experience courses:N
Please respect the intellectual property rights and use the materials legally.Please repsect gender equality.
Update Date, year/month/day:2024/09/23 10:52:42 Printed Date, year/month/day:2024 / 10 / 13
The second-hand book website:http://www.myub.com.tw/