Interpolation Methods in Numerical Analysis: Trapezoidal Rule, Simpson's Rule, and Their Composite Forms

Numerical interpolation techniques including the Trapezoidal Rule, Simpson's Rule, Composite Trapezoidal Rule, and Composite Simpson's Rule with implementation insights for numerical integration algorithms

Implementing Euler's Forward, Backward, and Trapezoidal Formulas

1. Implement Euler's Forward Difference, Backward Difference, and Trapezoidal Formulas. 2. Develop universal programs for second-order and third-order Runge-Kutta methods. 3. Create a general-purpose program for Hamming's integration method. 4. Design a universal program for discretizing continuous system state equations using state transition methods.