Geometric Theory of Generalized Functions with Applications to General Relativity

The textbook "Geometric Theory of Generalized Functions with Applications to General Relativity" offers a comprehensive analysis of the theory of generalized functions, particularly in the context of the algebras of J. F. Colombeau. It highlights the developments in the theory that have arisen from applications to geometric questions. The content is structured to cover both the fundamental and more complex aspects of the theory. The book begins with an introductory presentation based on a specific variant of the algebras to clearly and understandably present the central ideas. This approach facilitates the understanding of the more challenging concepts addressed later. The selection of applications is representative and demonstrates the versatility of the theory in mathematics and the natural sciences, especially concerning nonlinear partial differential equations and singularities.