CCU Course Intro
Course Title (Chinese): 微積分(一) Teaching Unit: 數學系(Department of Mathematics)
Course Title (English) Calculus (I) Course Code 2101001_06
Lecturer: Number of Credits 4.5
Mandatory/Elective Mandatory Year 1
Prerequisites:
Course Introduction:
Calculus in one variable
Learning Goals:
1.
Textbook:
To be announced

Course Syllabus Number of Hours Core Capabilities Remarks
Topic Content Lecture Demonstration Assignment Others
Limits
1. Rate of change
2. Functions and graphs
3. Inverse functions
4. Exponential and logarithmic functions
5. Evaluating limits
6. Continuity and one sided limits
7. Infinite limits
Differentiation
1. Derivatives and tangent line
2. Basic differentiation rules
3. Product and quotient rules
4. Chain rule
5. Implicit differentiation
6. Derivatives of inverse function
Application of differentiation
1. Extrema on an interval
2. Rolle' theorem and mean value theorem
3. Increasing and decreasing functions and the first derivative test
4. Concavity and second derivative test
5. Limits at infinity
6. Optimization problem
7. Differentials
Integration
1. Antiderivatives and indefinite integration
2. Riemann sums and definite integrals
3. Fundamental theorem of calculus
4. Substitution
5. Indefinite form and L'Hopital rule
6. The natural logarithmic function
Application of integration
1. Area of a region between two curves
2. volume by disk method
3. volume by shell method
4. surfaces of revolution
Integration Techniques and improper integrals
1. Integration by parts
2. Trigonometric integrals
3. Trigonometric substitution
4. Partial fractions
5. Numerical integration
6. Improper integrals


Please respect to the intellectual property rights, do not photocopy the textbooks which assigned by professors.

Course Details:
1. Teaching Materials:Self DevelopedProvided by Textbook Authors
2. Teaching Method:Lecture SlidesBlackboard Teaching
3. Grading Method:Attendance 0%, Quiz0%, Assignment0%, Programming0%, Technical Report0%,
                       Project0%, Mid-Term Exam50%, Final Exam30%, Final Report0%, Others0%,
4. Teaching Resources:Course Web Site Downloadable Electronic Materials Lab Web Site
5. Other requirements:

Relationship between course education goals and core capabilities        
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