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This lecture covers the fundamentals of electromagnetism, including mathematical tools, vector calculus, and electromagnetic theory. Topics include derivatives, vector calculus, scalar and vector products, and the rules for calculating vector products. The lecture also explores the applications of electromagnetism in physics and engineering, emphasizing the importance of experimental validation. Dr. Sylvain Bréchet guides students through the theoretical concepts and practical exercises, aiming to develop a systematic approach to modeling physical phenomena and solving complex equations.