Vector Analysis

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Focusing on vector fields, this text bridges classical and modern vector analysis, covering essential concepts such as the gradient, divergence, curl operators, and integral theorems. It introduces Cartan calculus and reinterprets classical methods within three-dimensional Euclidean space. Additionally, the book presents advanced topics like de Rham cohomology and Hodge theory. Designed for undergraduates familiar with calculus, linear algebra, and topology, it includes numerous figures, exercises with hints, and tests with answers, making it ideal for independent study.