Peter Petersen – författare

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research.

Important additions to this new edition include:

- A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise

- An increased number of coordinate calculations of connection and curvature

- General fomulas for curvature on Lie Groups and submersions

- Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger

- Several recent results about manifolds with positive curvature

This textbook on linear algebra includes the key topics of the subject that most advanced undergraduates need to learn before entering graduate school. All the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra. This book has several distinguishing features that set it apart from other linear algebra texts.  For example: Gaussian elimination is used as the key tool in getting at eigenvalues; it takes an essentially determinant-free approach to linear algebra; and systems of linear differential equations are used as frequent motivation for the reader.  Another motivating aspect of the book isthe excellent and engaging exercises that abound in this text.  This textbook is written for an upper-division undergraduate course on Linear Algebra.  The prerequisites for this book are a familiarity with basic matrix algebra and elementary calculus, although any student who is willing to think abstractly should not have too much difficulty in understanding this text.

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of  Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups.

Important revisions to the third edition include:

From reviews of the first edition:

"The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type."

―Bernd Wegner, ZbMATH

150. Geburtstag Arnold Schönberg!Arnold Schönbergs Streichquartett op. 7 gehört zu den anspruchsvollsten Kammermusikwerken der Spätromantik.Die Monographie des Hamburger Musikwissenschaftlers Peter Petersen geht das Werk aus drei Richtungen an: (1) Themen und Motive werden identifiziert, wobei ein vom Komponisten unerwähntes Thema ans Licht kommt; (2) der Verlauf des Quartettsatzes wird musikdramaturgisch analysiert und so der Aspekt der Viersätzigkeit in der Einsätzigkeit erweitert; (3) das von Schönberg verschwiegene, inzwischen bekannte Programm einer Liebesgeschichte wird in seiner ästhetischen Relevanz für das Werkganze untersucht – mit dem Ergebnis, dass es nur teilweise den Gang der Komposition gesteuert, der musikalischen Phantasie aber eine Richtung gegeben hat.