Ole Christensen

SE VIDEOER TIL HVERT KAPITEL HER Dette er en grundbog til undervisningen på første studieår af pædagoguddannelsen. Den kan desuden bruges i studiegrupper og som opslagsbog på resten af uddannelsen. Uddannelsen til pædagog betyder, at man som studerende skal tilegne sig en masse ny viden – både om det at være pædagog i praksis og om nye begreber og måder at tænke på. Pædagoguddannelsen er en akademisk uddannelse, og det stiller store og nye, men også spændende krav til de studerende. Som noget nyt er bogens opbygning og sproglige niveau tilrettelagt på baggrund af dels samtaler med studerende om deres behov, dels en undersøgelse af akademisk litteraturs læsbarhed for unge studerende. Kapitlerne er derfor skrevet i et enkelt sprog, der kan forstås uden de store forkundskaber, men som samtidig holder det akademiske niveau, og som giver fagets begreber både teoretisk og praktisk substans. Bogen er fuld af konkrete eksempler fra praksis, så man som studerende derigennem kommer tæt på pædagogikken. Alle kapitler er bygget op på samme måde og indledes med en konkret case, som kapitlets analyser bygger videre på. I starten af hvert kapitel er der en oversigt over indholdet, og der er mange illustrationer og figurer, som forklarer tingene på en anden måde end selve teksten, og som gør bogen visuelt indbydende. Endelig kan man som studerende finde støtte til forståelsen af bogens indhold i en række videoer – en til hvert kapitel. Heri fortæller bogens forfattere levende, hvad deres kapitel handler om.

This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include:*Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs included in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems* Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further reading* Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition:"Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field … . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005

The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har­ monic analysis to basic applications. The title of the series reflects the im­ portance of applications and numerical implementation, but richness and relevance of applications and implementation depend fundamentally on the structure and depth of theoretical underpinnings. Thus, from our point of view, the interleaving of theory and applications and their creative symbi­ otic evolution is axiomatic. Harmonic analysis is a wellspring of ideas and applicability that has flour­ ished, developed, and deepened over time within many disciplines and by means of creative cross-fertilization with diverse areas. The intricate and fundamental relationship between harmonic analysis and fields such as sig­ nal processing, partial differential equations (PDEs), and image processing is reflected in our state of the art ANHA series. Our vision of modern harmonic analysis includes mathematical areas such as wavelet theory, Banach algebras, classical Fourier analysis, time­ frequency analysis, and fractal geometry, as well as the diverse topics that impinge on them.

Klinikpersonale i almen praksis – en basisbog er en bred introduktion til arbejdet i almen praksis for klinikpersonale, uanset uddannelsesmæssig baggrund. Bogens kapitler dækker sundhedsvæsenets opbygning, organiseringen af almen praksis i Danmark samt detaljerne i det kliniske arbejde og klinikpersonalets rolle i relation hertil. Det er af flere årsager mere og mere almindeligt, at arbejdsopgaver forskydes mellem de forskellige personalegrupper i almen praksis. Klinikpersonalet varetager derfor ofte opgaver, som den enkelte oprindeligt ikke var uddannet til. Bogen forsøger at dække det heraf opståede behov for grundlæggende viden og et fælles fundament for den enkelte praksis. Kapitlerne giver ikke endegyldige svar, men kan betragtes som en række forslag til, hvordan man med fordel kan organisere sig i en almen praksis. Klinikpersonale i almen praksis – en basisbog kan læses fra ende til anden eller benyttes som opslagsværk i dagligdagen. Bogen bør findes på bogreolen i enhver almen praksis som daglig inspiration for hele personalegruppen.

This graduate-level textbook is a detailed exposition of key mathematical tools in analysis aimed at students, researchers, and practitioners across science and engineering. Every topic covered has been specifically chosen because it plays a key role outside the field of pure mathematics. Although the treatment of each topic is mathematical in nature, and concrete applications are not delineated, the principles and tools presented are fundamental to exploring the computational aspects of physics and engineering. Readers are expected to have a solid understanding of linear algebra, in Rn and in general vector spaces. Familiarity with the basic concepts of calculus and real analysis, including Riemann integrals and infinite series of real or complex numbers, is also required.

Based on a streamlined presentation of the author's previous work, An Introduction to Frames and Riesz Bases, this new textbook fills a gap in the literature, developing frame theory as part of a dialogue between mathematicians and engineers. Newly added sections on applications will help mathematically oriented readers to see where frames are used in practice and engineers to discover the mathematical background for applications in their field. Key features include results presented in a way that is accessible to graduate students, mathematicians, and engineers; a presentation of basic results in finite-dimensional vector spaces, enabling readers with a basic knowledge of linear algebra to understand the idea behind frames without the technical complications in infinite-dimensional spaces; extensive exercises; and a detailed description of frames with full proofs, an examination of the relationship between frames and Riesz bases, and a discussion of various ways to construct frames. Frames and Bases: An Introductory Course will be an excellent textbook for graduate students as well as a good reference for researchers working in pure and applied mathematics, mathematical physics, and engineering. Practitioners working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find the book a useful self-study resource.

Bogen giver en indføring i de fleste centrale problemstillinger inden for regnskab og omkostningsteori. Der tages udgangspunkt i virksomhedens værdikredsløb, hvorefter der gives en introduktion til omkostningsteori. Forskellige omkostningsbegreber defineres og anvendes til at analysere forskellige beslutningssituationer. Dernæst gives en introduktion til bogholderisystemet. En økonomisk beskrivelse af en virksomhed omfatter også vurderinger af periodens ressourceforbrug samt beholdninger på statustidspunktet, og derfor gennemgås opgørelse af vareforbrug og nogle periodiseringsproblemer. Perspektiverne for virksomhedens interne og eksterne regnskaber behandles kort i to kapitler. Der er lagt vægt på at give læseren en forståelse for, at regnskab ikke bør betragtes som et ´håndværk´, der kan udøves ved brug af et antal relativt simple værktøjer. Erhvervsøkonomisk teori er væsentlig for udformning og forståelse af regnskaber.

This book gives an elementary introduction to a classical area of mathemat­ ics - approximation theory - in a way that naturally leads to the modern field of wavelets. The main thread throughout the book is the idea of ap­ proximating "complicated expressions" with "simpler expressions," and how this plays a decisive role in many areas of modern mathematics and its applications. One of the main goals of the presentation is to make it clear to the reader that mathematics is a subject in a state of continuous evolution. This fact is usually difficult to explain to students at or near their second year of uni­ versity. Often, teachers do not have adequate elementary material to give to students as motivation and encouragement for their further studies. The present book will be of use in this context because the exposition demon­ strates the dynamic nature of mathematics and how classical disciplines influence many areas of modern mathematics and applications. The book may lead readers toward more advanced literature, such as the other pub­ lications in the Applied and Numerical Harmonic Analysis series (ANHA), by introducing ideas presented in several of those books in an elementary context. The focus here is on ideas rather than on technical details, and the book is not primarily meant to be a textbook.