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Consider a linear non-homogeneous ordinary differential equation of the form = + (+) = where () denotes the i-th derivative of , and denotes a function of .. The method of undetermined coefficients provides a straightforward method of obtaining the solution to this ODE when two criteria are met: [2]
In respiratory physiology, the ventilation/perfusion ratio (V/Q ratio) is a ratio used to assess the efficiency and adequacy of the ventilation-perfusion coupling and thus the matching of two variables: V – ventilation – the air that reaches the alveoli; Q – perfusion – the blood that reaches the alveoli via the capillaries
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
If a system initially rests at its equilibrium position, from where it is acted upon by a unit-impulse at the instance t=0, i.e., p(t) in the equation above is a Dirac delta function δ(t), () = | = =, then by solving the differential equation one can get a fundamental solution (known as a unit-impulse response function)
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
These results were later generalized to spatially homogeneous random media modeled by differential equations with random coefficients which statistical properties are the same at every point in space. [5] [6] In practice, many applications require a more general way of modeling that is neither periodic nor statistically homogeneous. For this ...
The classic definition by MP Spencer and AB Denison of compliance (C) is the change in arterial blood volume (ΔV) due to a given change in arterial blood pressure (ΔP). They wrote this in the "Handbook of Physiology" in 1963 in work entitled "Pulsatile Flow in the Vascular System". So, C = ΔV/ΔP. [4]
Staverman's reflection coefficient, σ, is a unitless constant that is specific to the permeability of a membrane to a given solute. [6] The Starling equation, written without σ, describes the flow of a solvent across a membrane that is impermeable to the solutes contained within the solution. [7]