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This is the mathematical reference book for the first and the second year students who are interested in the calculation methods and skills for non-standard problems arising in the mathematical analysis.The problems concerned with the integration term by term in the analytical properties of the functional series will give a powerful stimulus to the development of the mathematical analysis.This book can be widely used by students in mathematics and physics, and everyone who is interested in mathematical analysis.It is certain that this will be contributed to the students , the graduates and researchers who are going to analyze the physical situations with the aid of mathematical tools.