Solved Exercises and Problems in Distributions

This collection of corrected exercises and problems on distributions, with course reminders, is intended for second cycle students, whether they are at university or engineering schools. It will interest, by its different reading levels, all students whether they specialize in mathematics, physics or any other scientific discipline. The book is organized as follows : Chapter 1 introduces test functions and provides definitions and examples of distributions. Chapter 2 covers differentiation and operations on distributions. Chapter 3 addresses the convergence problem in the space of distributions. Chapter 4 discusses tensor products and convolution. Chapter 5 explores Fourier series, Fourier and Laplace transforms. Chapter 6 offers an overview of the variational formulation of partial differential equations. Chapter 7 (appendix) contains a brief introduction and some summary notions on measure theory and the Lebesgue integral. The book concludes with a bibliography of fundamental texts and a detailed index, further enhancing its utility as a study aid. The course has been taught for several years to students of different specialities : mathematicians, physicists and engineers.