Mathematical analysis serves as a common foundation for many research areas of pure and applied mathematics. It is also an important and powerful tool used in many other fields of science, including physics, chemistry, biology, engineering, finance, and economics. In this book, some basic theories of analysis are presented, including metric spaces and their properties, limit of sequences, continuous function, differentiation, Riemann integral, uniform convergence, and series.

After going through a sequence of courses on basic calculus and linear algebra, it is desirable for one to spend a reasonable length of time (ideally, say, one semester) to build an advanced base of analysis sufficient for getting into various research fields other than analysis itself, and/or stepping into more advanced levels of analysis courses (such as real analysis, complex analysis, differential equations, functional analysis, stochastic analysis, amongst others). This book is written to meet such a demand. Readers will find the treatment of the material is as concise as possible, but still maintaining all the necessary details.

�ber die Autorin bzw. den Autor:

Jiongmin Yong is a Professor of Mathematics at University of Central Florida. He obtained a BS degree at Fudan University (China) and a PhD degree at Purdue University (USA). His main research interests include optimal control theory, stochastic differential/integral equations, mathematical finance. He has published over 150 research articles, 5 research monographs and 4 graduate/undergraduate textbooks. He is currently an associate editor of several journals, including ESAIM: Control, Optimisation, Calculus of Variations, Mathematical Control and Related Fields, and was an associate editor of SIAM Journal on Control and Optimization. He was a winner of the 2011 SIAG/CST Best SICON paper prize, and a 45-minute invited speaker at the 2014 ICM.

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