M3 (Unit-4) Numerical solution of 1st order eq

The unit covers following points - Introduction to numerical methods for solving ordinary differential equations (ODEs) using vectors - Explanation of Picard's method, an iterative approach for approximating solutions to initial value problems - Overview of Taylor's series expansion method, which provides a systematic way to approximate solutions near a given point - Introduction to Runge-Kutta methods, including Runga's method and the popular fourth-order Runge-Kutta method, for solving ODEs numerically - Explanation of Euler's method, a simple and widely used numerical technique for solving first-order ODEs - Introduction to Euler's modified method, a variation of Euler's method that improves accuracy by considering the slope at intermediate points - Illustrative examples demonstrating the application of these numerical methods to solve ODEs involving vector functions