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This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

Mathematics. --- Functional Analysis. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Fourier Analysis. --- Fourier analysis. --- Functional analysis. --- Differential Equations. --- Differential equations, partial. --- Mathématiques --- Analyse de Fourier --- Analyse fonctionnelle --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Differential equations. --- Partial differential equations. --- Partial differential equations --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Mathematical analysis --- 517.91 Differential equations --- Differential equations --- Theory of distributions (Functional analysis) --- Distribution (Functional analysis) --- Distributions, Theory of (Functional analysis) --- Functions, Generalized --- Generalized functions --- Functional analysis