CHEM 5 Lecture Notes - Intermedio, Wolfram Mathematica (Software), Nonlinear System
Document Summary
Differential equation: the determination of a function that satisfies an equation containing derivatives of an unknown function. Contain only ordinary derivatives dy/dx and d2 y dx2. The order of an ordinary differential equation is the order of the highest derivative that appears in the equation. examples: 1: newton"s second law of motion in one dimension can be written as an ordinary, second order differen- tial equation dp/dt = f[t,x(t),p(t)] where p(t) = mv(t) = mdx/dt is the momentum. 2: the diffusion equation in one-dimension is an example ofa partial differential equation that is second order in teh spatial variable, x, and first-order in time, t: !c !t = d!2 c !x2 where c is the concentration of the diffusing species, and d is its diffusion constant. Differential equations are also classified accoring to whetehr they are linear or nonlinear .
