CCU Course Syllabus
Course Title (Chinese): 數學分析(一) Teaching Unit: 應用數學研究所(Graduate Institute of Applied Mathematics)
Course Title (English) Matahematical Analysis (I) Course Code 2105005_01
Lecturer: Number of Credits 0
Mandatory/Elective Elective Year
Prerequisites:
Calculus and linear algebra
Course Introduction:
Introduction to analysis
Learning Goals:
1.
Textbook:

Course Syllabus Number of Hours Core Capabilities Remarks
Topic Content Lecture Demonstration Assignment Others
1. Real number system
1. Completeness axiom.
2. Mathematical induction
3. Countable and uncountable sets
2. Sequence in R
1. Limits of sequences
2. Limit theorems
3. Bolzano-Weierstrass theorem
4. Cauchy sequences
3. Functions on R
1. Two-sided limits
2. one sided limits
3. Continuity
4. Uniform cotinuity
4. Differentiability on R
1. The derivatives
2. Differentiability theorems
3. Mean-value theorem
4. Taylor's theorem
5. Integrability on R
1. The Riemann integral
2. Riemann sums
3. Fundamental theorem of calculus
4. Improper Riemann integrals


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Course Details:
1. Teaching Materials:Self DevelopedProvided by Textbook Authors
2. Teaching Method:Lecture SlidesBlackboard Teaching
3. Grading Method:Attendance 0%, Quiz0%, Assignment20.00%, Programming0%, Technical Report0%,
                       Project0%, Mid-Term Exam50.00%, Final Exam30.00%, 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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