18.155
Differential Analysis I
First part of a two-subject sequence. Review of Lebesgue integration. Lp spaces. Distributions. Fourier transform. Sobolev spaces. Spectral theorem, discrete and continuous spectrum. Homogeneous distributions. Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Recommended prerequisite: 18.112 .
Fall 2004 · Differential Analysis
Topics
- Space of Continuous Functions, Dual Space, Positivity
- Outer Measures and Measures
- Caratheodory’s Theorem
- Measurable Functions and the Integral - Including Lebesgue’s Theorem of Dominated Convergence
- Riesz Representation, L p Spaces and Completeness, L 2 ( X ,μ) and Hilbert Space
- Singular Support, Hypoellipticity, Ellipticity - Parametrices for Elliptic Operators
- Operators and Schwartz’ Kernel Theorem
Readings
- Rudin, W. Real and Complex Analysis. 3rd ed. New York, NY: McGraw-Hill, 1987. ISBN: 0070542341.
Prerequisites & course information
Prereq: 18.102 or 18.103 G (Fall) 3-0-9 units
Sources
- Course catalogue ↗2026–2027
- MIT OpenCourseWare ↗Fall 2004
- MIT OCW calendar ↗
- MIT OCW syllabus ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.