分析導論(二)

The purpose of this course is to study important topics such as uniform convergence of sequence of functions as defined on a closed interval. The clarification of this important concept will immediately lead to important results which allow the interchanging of the process of taking definite integral and that of taking infinite sum. Under the same framework of uniform convergence, one can also find sufficient condition for the successful interchanging of differentiation and taking infinite sum. Under these preparations, we will discuss how to approximate continuous functions on closed interval by smooth functions on the same interval. Moreover, special functions such as the Gamma function will be discussed. We also plan to study elementary topics in Fourier series in the framework of Hilbert space.

Undergraduate level analysis I, Linear Algebra.

Homework 20% Mid-Term One 25% Mid-Term Two 25% Final Exam 30%