Multiplicative Infinitesimals: A New Calculus Approach

This paper introduces a new concept called "multiplicative infinitesimals," analogous to traditional additive infinitesimals, to construct a new calculus system. Unlike traditional calculus based on differences, multiplicative calculus is based on quotients, using a Leibniz-like notation but with 'q' instead of 'd', representing a multiplicative perturbation of an expression. The author establishes the relationship between 'q' and 'd' through logarithmic and exponential operations and applies it to elasticity theory and multiplicative derivative calculations. This approach may offer new solutions to problems intractable with traditional methods.