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 | Please select： | |