CCU Course Intro
Course Title (Chinese): 高等微積分(一) Teaching Unit: 數學系(Department of Mathematics)
Course Title (English) Advanced Calculus (I) Course Code 2102001_01
Lecturer: Number of Credits 4.5
Mandatory/Elective Mandatory Year 2
Prerequisites:
Calculus and linear algebra
Course Introduction:
Introduction to analysis in one variable
Learning Goals:
1.
Textbook:
Wade: An introduction to analysis

Course Syllabus Number of Hours Core Capabilities Remarks
Topic Content Lecture Demonstration Assignment Others
Real number system
1. Completeness axiom
2. Mathematical induction
3. Countable and uncountable sets
Sequence in R
1. Limits of sequences
2. Limit Theorem
3. Bolzano-Weierstrass Theorem
4. Cauchy sequences
Functions on R
1. Two sided limits
2. One sided limits
3. Continuity
4. Uniform continuity
Differentiability on R
1. The derivative
2. Differentiability theorems
3. The mean value theorem
4. Taylor's theorem
5. Inverse function theorem
Integrability on R
1. The Riemann integral
2. Riemann sums
3. Fountamental theorem of calculus
4. Improper integral
Infinite series of functions
1. Uniform convergence of sequences
2. uniform convergence of series
3. Power series
4. Analytic functions


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 Exam0%, Final Exam0%, 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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