M. Schreiber – författare

A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given "surfaces" in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end.

A working knowledge of differential forms so strongly illuminates the calculus and its developments that it ought not be too long delayed in the curriculum. On the other hand, the systematic treatment of differential forms requires an apparatus of topology and algebra which is heavy for beginning undergraduates. Several texts on advanced calculus using differential forms have appeared in recent years. We may cite as representative of the variety of approaches the books of Fleming [2], (1) Nickerson-Spencer-Steenrod [3], and Spivak [6]. . Despite their accommodation to the innocence of their readers, these texts cannot lighten the burden of apparatus exactly because they offer a more or less full measure of the truth at some level of generality in a formally precise exposition. There. is consequently a gap between texts of this type and the traditional advanced calculus. Recently, on the occasion of offering a beginning course of advanced calculus, we undertook the expe- ment of attempting to present the technique of differential forms with minimal apparatus and very few prerequisites. These notes are the result of that experiment. Our exposition is intended to be heuristic and concrete. Roughly speaking, we take a differential form to be a multi-dimensional integrand, such a thing being subject to rules making change-of-variable calculations automatic. The domains of integration (manifolds) are explicitly given "surfaces" in Euclidean space. The differentiation of forms (exterior (1) Numbers in brackets refer to the Bibliography at the end.

Quasicrystals have been the object of intense research efforts for a good 16 years now. In recent years, this area of solid state physics and crystallogra­ phy has grown into a mature field in its own right. Hence, several books on quasicrystals have appeared in the interim (see Appendix) and chapters on quasicrystals have been introduced into new books on solid state physics and l into new editions of existing monographs. However, most of the former have been written for scientists specialised in this field rather than for students, and the latter additions are often rat her brief. We therefore decided to fill the gap between these two extremes with a book which provides an introduction to the structure and physical properties oi quasicrystals and covers, in sufficient detail, all important fields in qua­ sicrystal research and even applications. The chapters have been written by specialists and each is based on the author's insight into this field. Howe­ ver, much effort has been put into achieving an introductory character and making the text accessible to newcomers to the field.

Quasicrystals have been the object of intense research efforts for a good 16 years now. In recent years, this area of solid state physics and crystallogra­ phy has grown into a mature field in its own right. Hence, several books on quasicrystals have appeared in the interim (see Appendix) and chapters on quasicrystals have been introduced into new books on solid state physics and l into new editions of existing monographs. However, most of the former have been written for scientists specialised in this field rather than for students, and the latter additions are often rat her brief. We therefore decided to fill the gap between these two extremes with a book which provides an introduction to the structure and physical properties oi quasicrystals and covers, in sufficient detail, all important fields in qua­ sicrystal research and even applications. The chapters have been written by specialists and each is based on the author's insight into this field. Howe­ ver, much effort has been put into achieving an introductory character and making the text accessible to newcomers to the field.