TY  - BOOK
AU  - Murty, Maruti Ram
AU  - Murty, Maruti Ram
TI  - A Second Course in Analysis
T2  - Institute of Mathematical Science Lecture Note 4
SN  - 97893806279842
U1  - 515 MUR 
PY  - 2020///
CY  - New Delhi, India 
PB  - : Hindustan Book Agency
KW  - Mathematics
KW  - Analysis
KW  - Mathematical analysis
N1  - Background --
Measure theory --
Fourier transforms --
Complex analysis --
Introduction to algebraic topology
N2  - This book represents material suitable for a two semester graduate course in analysis. Based on courses given by the author since 2007, it is targeted towards graduate students preparing for a research career in mathematics. After reviewing what a typical student would have learned in single variable and multivariable calculus courses, the first chapter presents familiar material from a mature mathematical perspective. The second chapter surveys measure theory and highlights the essential theorems that have now become ubiquitous in mathematics. The third chapter on Fourier transforms derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. The fourth chapter reviews complex analysis giving a synthetic, rigorous development of the calculus of residues and its applications to a wide array of problems. The final chapter is an introduction to algebraic topology and is included to show the symbiosis between algebra and analysis
ER  -