Mehrdimensionale Analysis (English shop)

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Table of Contents, Datei (49 KB)
Preface, Datei (48 KB)
Extract, Datei (110 KB)

Wassim El-Benny’s exercise book “Mehrdimensionale Analysis” provides a comprehensive introduction to multivariable mathematical analysis, primarily addressing students of mathematics, physics, and computer science. The book follows a practice-oriented approach that combines mathematical definitions and theorems with illustrative examples, exercises, and detailed solutions. Starting with metric spaces, topological properties, connectedness, and compactness, it introduces the foundations of normed spaces, Banach spaces, and Hilbert spaces. Further topics include continuity and differentiability of multivariable functions, partial derivatives, the Jacobian matrix, and Taylor’s theorem. The book also examines implicit functions, inverse functions, and the determination of local extrema with and without constraints. Subsequent chapters explore curves, line integrals, conservative vector fields, multiple integrals, and surface integrals. By systematically connecting mathematical theory with fully worked solutions, the publication supports independent learning, mathematical problem-solving skills, and preparation for university examinations.