This text serves as an introduction to the modern theory of analysis and differential equations
with applications in mathematical physics and engineering sciences. Having outgrown from a
series of half-semester courses given at University of Oulu this book consists of four
self-contained parts. The first part Fourier Series and the Discrete Fourier Transform is
devoted to the classical one-dimensional trigonometric Fourier series with some applications to
PDEs and signal processing. The second part Fourier Transform and Distributions is concerned
with distribution theory of L. Schwartz and its applications to the Schrödinger and magnetic
Schrödinger operations. The third part Operator Theory and Integral Equations is devoted
mostly to the self-adjoint but unbounded operators in Hilbert spaces and their applications to
integral equations in such spaces. The fourth and final part Introduction to Partial
Differential Equations serves as an introduction to modernmethods for classical theory of
partial differential equations.Complete with nearly 250 exercises throughout this text is
intended for graduate level students and researchers in the mathematical sciences and
engineering.
