Lecture
This lecture introduces the importance of '=' versus approximations in simple numerical relations for engineers, showcasing examples like springs in series and parallel. It explores the historical significance of slide rules and the transition to electronic calculators. The instructor demonstrates approximation techniques with simple algebraic examples, emphasizing the focus on leading digits. The lecture covers non-dimensionalization, key parameter identification, and dominant balance in solving challenging problems. It highlights the relevance of these concepts in continuum mechanics, particularly in launching rockets. The discussion extends to asymptotic expansion and the continuum hypothesis, emphasizing the value of approximate approaches in interpreting and evaluating engineering problems.