Title: Real Analysis I (previously MAT 544)

Description: Ordinary differential equations; Banach and Hilbert spaces; inverse and implicit function theorems; Lebesque measure; general measures and integrals; measurable functions; convergence theorems for integrals.

Offered: Fall

Credits: 3

Textbook:

Note: Subject to change - do not buy before confirming with the course instructor

Major Topics Covered:

• Measures
• Sigma-algebras
• Measures, Outer Measures
• Borel Measures on the Real Line, Non-measurable Sets
• Integration
• Measurable Functions
• Littlewood's Three Principles
• Integration of Nonnegative Functions
• Integration of Complex Functions
• Modes of Convergence
• Product Measures
• The N-dimensional Lebesgue Integral
• Integration in Polar Coordinates
• Signed Measures and Differentiation
• The Hardy-Littlewood Maximal Function
• Signed Measures
• $L^p$ Spaces
• Distribution Functions and Weak $L^p$
• Interpolation of $L^p$ Spaces