Anders Vretblad – författare

Algebra och geometri är avsedd att användas vid de inledande matematikstudierna på universitetsnivå. Den är en omarbetning och utökning av den välkända Algebra och kombinatorik som först kom 1985. Det som nu tillkommit i boken är främst ett par kapitel om geometri. Dessutom finns nu en inledning med repetition av viktiga hantverksmoment ur gymnasiekursen. Exempel och övningar, framför allt enklare övningar, har blivit fler. Nu finns totalt 555 övningsproblem, många av dem med fler delproblem.

Författaren Anders Vretblad är FD i matematik och sedan 1970 universitetslektor vid Uppsala universitet.

Kerstin Ekstig är FL i matematik och har under många år arbetat med lärarutbildning vid högskolan i Gävle och sedan 1988 vid Uppsala universitet.

This book is a carefully prepared account of the basic ideas in Fourier analysis and its applications to the study of partial differential equations. The author succeeds to make his exposition accessible to readers with a limited background, for example, those not acquainted with the Lebesgue integral. Readers should be familiar with calculus, linear algebra, and complex numbers. At the same time, the author has managed to include discussions of more advanced topics such as the Gibbs phenomenon, distributions, Sturm-Liouville theory, Cesaro summability and multi-dimensional Fourier analysis, topics which one usually does not find in books at this level. A variety of worked examples and exercises will help the readers to apply their newly acquired knowledge.

TheclassicaltheoryofFourierseriesandintegrals,aswellasLaplacetra- forms, is of great importance for physical and technical applications, and its mathematical beauty makes it an interesting study for pure mathema- cians as well. I have taught courses on these subjects for decades to civil engineeringstudents,andalsomathematicsmajors,andthepresentvolume can be regarded as my collected experiences from this work. There is, of course, an unsurpassable book on Fourier analysis, the tr- tise by Katznelson from 1970. That book is, however, aimed at mathem- ically very mature students and can hardly be used in engineering courses. Ontheotherendofthescale,thereareanumberofmore-or-lesscookbo- styled books, where the emphasis is almost entirely on applications. I have felt the need for an alternative in between these extremes: a text for the ambitious and interested student, who on the other hand does not aspire to become an expert in the ?eld. There do exist a few texts that ful?ll these requirements (see the literature list at the end of the book), but they do not include all the topics I like to cover in my courses, such as Laplace transforms and the simplest facts about distributions.