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A total differential equation is a differential equation expressed in terms of total derivatives. Since the exterior derivative is coordinate-free, in a sense that can be given a technical meaning, such equations are intrinsic and geometric .
A number of properties of the differential follow in a straightforward manner from the corresponding properties of the derivative, partial derivative, and total derivative. These include: [ 11 ] Linearity : For constants a and b and differentiable functions f and g , d ( a f + b g ) = a d f + b d g . {\displaystyle d(af+bg)=a\,df+b\,dg.}
An exact differential is sometimes also called a total differential, or a full differential, or, in the study of differential geometry, it is termed an exact form. The integral of an exact differential over any integral path is path-independent, and this fact is used to identify state functions in thermodynamics.
The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an ...
Given a simply connected and open subset D of and two functions I and J which are continuous on D, an implicit first-order ordinary differential equation of the form (,) + (,) =,is called an exact differential equation if there exists a continuously differentiable function F, called the potential function, [1] [2] so that
The best linear approximation to a differentiable function : at a point in is a linear map from to which is often denoted by or () and called the differential or total derivative of at . The function d f {\displaystyle df} , which maps x {\displaystyle x} to d f x {\displaystyle df_{x}} , is called the total differential or exterior derivative ...
A new sex trend among college students is getting attention on TikTok − and it has doctors worried.. That trend is using honey packets, a controversial supplement marketed for sexual enhancement ...
Numerical ordinary differential equations – Methods used to find numerical solutions of ordinary differential equations; Numerical smoothing and differentiation – Algorithm to smooth data points; List of numerical-analysis software