Approximations in Engineering: Leading Digits and Dominant Balance

This lecture introduces the concept of approximations in engineering, focusing on the importance of leading digits and dominant balance. Through examples from algebra and mechanics, the instructor demonstrates how engineers historically used slide rules to make accurate approximations. The lecture covers non-dimensionalization, key parameter identification, and the application of dominant balance in solving challenging problems. The discussion extends to the continuum hypothesis and its relevance in continuum mechanics, emphasizing the value of approximate approaches in interpreting complex equations.