Partial Differentiation

• Partial Differentiation of a Multivariable Function
  • Differentiating with respect to only one variable
  • The variables that are held constant are treated as constants (obvious) #Mathematics

from University of Tokyo 1S Thermodynamics

• Partial Differentiation
  • Definition $\frac{\partial f(x,y,z)}{\partial x}:={\lim }_{\delta \to 0}\frac{f(x+\delta ,y,z)-f(x,y,z)}{\delta }$
    • Well, it’s kind of like the definition we imagined (blu3mo)
    • Yeah, it makes sense (blu3mo)
  • If we treat all variables except one as constants, we can use the same calculations as regular differentiation, right? (blu3mo)
    • Maybe we’ll learn about this in University of Tokyo 1S1 Mathematical Science Foundation: Differential and Integral Calculus
  • In thermodynamics, we often deal with functions that take multiple values and differentiate them at various values
    • So, we frequently use partial differentiation
    • As an analogy, it’s like fixing the value of P or V in the PV=nRT problem, where the variable being fixed changes
      • I see, it does seem useful in thermodynamics (blu3mo)