Do you understand how [itex]\Delta y/\Delta yx\approx dy/dx\ ?[/itex]rsaad said:Homework Statement
How is
Δy/Δx = [itex]\partial y[/itex] / [itex]\partial x[/itex] ?
I just don't know the logic behind this.
A partial differential is a type of differential equation that involves multiple independent variables and their corresponding partial derivatives. It is used to model relationships between variables that are continuously changing.
An ordinary differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. Additionally, the derivatives in a partial differential equation are partial derivatives, which only consider the change in one variable while holding the others constant.
Partial differential equations are commonly used in physics, engineering, and other fields to describe systems that involve continuous change, such as heat transfer, fluid flow, and wave motion. They can also be used in economics, biology, and other social sciences to model complex systems.
In some cases, partial differential equations can be solved analytically using mathematical techniques such as separation of variables, Fourier series, or Laplace transforms. However, for more complex problems, numerical methods are often used to approximate the solution.
Partial differential equations have numerous applications in real life, including predicting weather patterns, designing aircraft and cars, simulating fluid flow in pipes and channels, and modeling the spread of diseases. They are also used in financial modeling and risk management.