Sample Sections from a Comprehensive Course in Analysis by Barry Simon

New This is a supplementary page to a basic page on a set of five books by Barry Simon.  This has links to ten sample sections, two from each part.

Part 1 - Real Analysis
Part 1 Real Analysis
Section 3.5 Classical Fourier Series
Section 7.2 Borel–Cantelli Lemmas and the Laws of Large Numbers and of the Iterated Logarithm                                                                                                                                                            
Part 2a - Basic Complex Analysis Part 2a Basic Complex Analysis. 
Section 3.1 Analyticity and Cauchy Estimates (part of a Chapter on Consequences of the Cauchy Integral Formula)
Section 9.6 The Gamma Function: Basics
Part 2b - Advanced Complex Analysis Part 2b Advanced Complex Analysis.
Section 13.4 Dirichlet’s Prime Progression Theorem
Section 15.4 The Method of Steepest Descent
Part 3 - Harmonic Analysis Part 3 Harmonic Analysis.
Section 2.8 Bonus Section: More Applications of the Ergodic Theorems (Skew shifts, Continued fractions, Geodesic flow)
Section 4.6 Wavelets
Part 4 - Operator Theory Part 4 Operator Theory. 
Section 2.4 The Square Root Lemma and the Polar Decomposition
Section 6.9 Bonus Section: Fourier Analysis on LCA Groups