This is a class at NTU by the professor Siao-Hao Guo. The main textbook is Introduction to Calculus and Analysis I written by Courant, Richard and John, Fritz.
HW1, Construction of R form Q, Completion of Q. note
HW2. note
HW3, Quiz1. note
HW4. note
HW5. note
HW6. note
HW7, Quiz3, Mean Value Theorem. note
Midterm Discussion. note
x^a sin(1/x), Transcendental of e. note
HW8, Law of Reflection and Refraction, Introduction to Taylor Expansion. note
HW9. note
HW10, Quiz4, Extreme Values, Remarks on Integrations. note
HW11. note
HW12, Stirling Formula. note
HW13. note
HW14. note