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Scientific significance of Differential equation?
A differential equation is a measure of change. If differencing with respect to time, it is the rate of change. Location, when differentiated, gives velocity. Velocity, when differentiated, gives acceleration. There are significant applications across all aspects of science.
Steady state in partial differential equations?
In the context of partial differential equations (PDEs), a steady state refers to a condition where the system's variables do not change over time, meaning that the time derivative is zero. This implies that the solution to the PDE is time-independent, and any spatial variations in the solution remain constant. Steady state solutions are often sought in problems involving heat diffusion, fluid flow, and other dynamic processes to simplify analysis and understand long-term behavior. In mathematical terms, steady state can be represented by setting the time-dependent term in the governing equation to zero.
What does a variable do in a math problem?
Variables in a math problem vary or change. If in an equation, different variables change values depending on constants, evanuations, etc. For example: in y = x + 2, y can be any number as long as x is that number plus two. The varibles in this equation change value but are defined by the equation.
What is the equation used to find power?
Power is the change of work over the change of time, ΔW/Δt, or in differential form, dW/dt
What is the differecnce between independent variables and dependent variables?
Every time the independent variables change, the dependent variables change.Dependent variables cannot change if the independent variables didn't change.
