📄️ Ordinary Differential Equations
Ordinary Differential Equations (ODEs) are equations that contain one or more derivatives of an unknown function with respect to a single independent variable. They are fundamental in modeling various physical, biological, and economic phenomena.
📄️ Partial Differential Equations
Partial Differential Equations (PDEs) are equations that involve partial derivatives of an unknown function with respect to two or more independent variables. They are fundamental in modeling complex physical phenomena and have wide-ranging applications in physics, engineering, and applied mathematics.
📄️ Separation of Variables
Separation of Variables is a powerful method for solving certain types of partial differential equations (PDEs). It's particularly useful for linear PDEs in simple geometries and is often one of the first analytical methods taught for solving PDEs.
📄️ Series solutions
Series solutions are a powerful method for solving linear ordinary differential equations (ODEs), particularly when other methods like separation of variables or integrating factors are not applicable. This approach involves representing the solution as an infinite series of terms.