Harmonic Analysis
Richard Melrose
Learn harmonic analysis with Prof. Melrose! This course covers distributions and key concepts.
More resources on Distributions
stattrek.com
StatTrek is an online statistics resource that provides clear tutorials and explanations of probability and statistics. It also features free calculators for distributions, hypothesis tests, confidence intervals, and other statistical methods.
Wolfram MathWorld
MathWorld is an online mathematics encyclopedia from Wolfram Research offering detailed, browsable articles on topics across the math spectrum, including algebra, geometry, calculus, and number theory. Each entry includes definitions, theorems, formulas, diagrams, worked examples, and links to further reading.
Fourier Analysis Notes
Archive of Terence Tao's blog posts and graduate lecture notes on Fourier analysis, covering the Fourier transform, Fourier series, Littlewood-Paley theory, and restriction problems. Readers gain rigorous, research-level working knowledge of harmonic analysis techniques and their applications to analysis and PDE.
Paul Garrett Notes on Distributions
Graduate-level lecture notes on distribution theory from Paul Garrett's functional analysis course at the University of Minnesota, covering generalized functions, test functions, Fourier transforms, and tempered distributions with worked examples and proofs.
nLab: Distribution
A collaborative wiki reference article on distributions (generalized functions) in functional analysis, covering their definition via test functions, derivatives, Fourier transforms, and connections to partial differential equations and category-theoretic perspectives.
Differential Analysis (MIT 18.155)
First semester of graduate differential analysis: fundamental solutions for elliptic, hyperbolic and parabolic operators, the method of characteristics, Lebesgue integration, distributions, homogeneous distributions, the Fourier transform and asymptotic methods. Provides 18 lecture note files and problem sets with solutions, preparing readers for modern PDE theory.