Differentials represent the change in a function's linear approximation as a variable changes. Specifically, for a function f(x), the differential dy is defined as dy = f '(x) dx, where dx is an infinitesimally small change in x. This concept is crucial for understanding calculus and thermodynamics, as it relates to the family of tangent lines to the curve y = f(x). Recommended readings include Tenenbaum and Pollard's "Ordinary Differential Equations" and Loomis and Sternberg's text, particularly chapter 3, section 5.
PREREQUISITESStudents preparing for calculus and thermodynamics, particularly those seeking a practical understanding of differentials and their applications in mathematical modeling.
Howers said:Can someone give me an intuitive definition for differentials? My prof said to brush up on them because we'll be seeing them lots in thermo. I don't need all the theory because I'll be seeing them in november in calc. Right now I just have to work with them. Are they just infinitely small differences?