指定用書：The Elements of Real Analysis, Secondd Edition, by Robert G. Bartle
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<br>教學方式：板書和演習課
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<br>教學進度：
<br>Introduction: 3. Finite and Infinite Sets
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<br>I. The Real Numbers:  6. The completeness Property of R
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<br>II. The Topology of Cartesian Spaces:  9. Open and Closed Sets, 10. The Nested Cells and Bolzano-
<br>Weierstrass Theorems, 11. The Heine-Borel Theorem, 12. Connected sets, 13. The complex number system
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<br>III. Convergence: 16. Two Criteria for Convergence, 17. Sequences of Functions, 18. The Limit Superior, 
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<br>IV. Continuous Functions: 20. Local Properties of Continuous Functions, 22 Global Properties of Continuous 
<br>Functions, 23. Uniform Continuity and Fixed points 25. Limits of Functions, 26. Some Further Results
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<br>V. Functions of One Variable: 27. 28. The Mean Value Theorem and Further Applications, 29. 30. 31. The 
<br>Riemann-Stieltjes Integral and Further Properties, 32. Improper and Infinite Integrals, 33. Uniform 
<br>convergence and Infinite Integrals
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<br>成績考核：
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<br>作業：20%
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<br>第一次期中考：20%
<br>第二次期中考：20%
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<br>期末考：40%
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<br>期中考，期末考試以實體考試為原則。