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Noone1982
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It is blaringly obvious I have forgotten most if not all I learned from DEs. Could anyone direct me to any good sites for review or suggest areas I should specifically review for physics?
Differential equations are mathematical equations that involve the derivatives of an unknown function. They are used to describe relationships between variables and their rates of change.
Differential equations are important because they are used to model and solve many real-world problems in fields such as physics, engineering, economics, and biology. They provide a fundamental tool for understanding and predicting how systems change over time.
Ordinary differential equations involve only one independent variable, while partial differential equations involve multiple independent variables. Ordinary differential equations are used to model phenomena that change over time, while partial differential equations are used to model phenomena that vary over multiple dimensions.
Some common techniques for solving differential equations include separation of variables, substitution, and using power series or Fourier series solutions. Numerical methods, such as Euler's method and Runge-Kutta methods, are also commonly used to approximate solutions for more complex equations.
Differential equations are used in various real-world applications, such as predicting population growth, modeling the spread of diseases, and analyzing the behavior of physical systems like circuits and pendulums. They are also used in financial modeling, weather forecasting, and many other fields where understanding and predicting change is important.