This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Moebius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes's theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.

This book presents a step-by-step guide to the basic theory of multivectors and spinors, with a focus on conveying to the reader the geometric understanding of these abstract objects. Following in the footsteps of M. Riesz and L. Ahlfors, the book also explains how Clifford algebra offers the ideal tool for studying spacetime isometries and Moebius maps in arbitrary dimensions. The book carefully develops the basic calculus of multivector fields and differential forms, and highlights novelties in the treatment of, e.g., pullbacks and Stokes's theorem as compared to standard literature. It touches on recent research areas in analysis and explains how the function spaces of multivector fields are split into complementary subspaces by the natural first-order differential operators, e.g., Hodge splittings and Hardy splittings. Much of the analysis is done on bounded domains in Euclidean space, with a focus on analysis at the boundary. The book also includes a derivation of new Dirac integral equations for solving Maxwell scattering problems, which hold promise for future numerical applications. The last section presents down-to-earth proofs of index theorems for Dirac operators on compact manifolds, one of the most celebrated achievements of 20th-century mathematics. The book is primarily intended for graduate and PhD students of mathematics. It is also recommended for more advanced undergraduate students, as well as researchers in mathematics interested in an introduction to geometric analysis.

Philipp Andreas Rosen untersucht Ansatze zur Optimierung von Wasserstoffdruckgasspeichern fur die automotive Anwendung. In den Vordergrund stellt er die Optimierung der Speichergeometrie und die thermischen Eigenschaften des Zylindermaterials. Die Geometrieoptimierung gliedert sich in zwei Hauptaspekte: Zum einen bewertet der Autor die konventionelle, zylindrische Speicherform mit einem 1D-Modell. Zum anderen untersucht er verschiedene Speicher geometrien. Zwei favorisierte Formen bildet er anschliessend zur Analyse in CFK-gerechten FEM-Simulationen ab. Zur thermischen Optimierung betrachtet der Autor insbesondere den Tankinnenbehalter (Liner) mit dem Ziel, Warme aus dem Zylinder besser nach aussen zu transportieren. Dazu versetzt er Linermaterialien mit Fullstoffen in unterschiedlichen Fullgraden und untersucht deren thermische sowie mechanische Eigenschaften. Die ermittelten thermischen Materialeigenschaften werden abschliessend in CFD-Simulationen verwendet, um das Potenzial von thermisch verbesserten Typ IV-Zylindern (Typ IV advanced) zu bewerten. Der Autor Philipp Andreas Rosen ist Entwicklungsingenieur im Bereich Gasspeichersysteme fur CNG und Wasserstoff.