Numerical Integration Techniques: Composite Quadrature Formulas

This lecture discusses numerical integration techniques, focusing on composite quadrature formulas. The instructor begins by explaining how to approximate the integral of a function over a specified interval by partitioning it into smaller subintervals. Each subinterval is treated individually, applying quadrature formulas to achieve greater accuracy. The lecture covers the definition and application of composite quadrature formulas, including the midpoint and trapezoidal rules. The instructor illustrates how to derive these formulas and emphasizes the importance of using equal-length subintervals for efficiency. The lecture also highlights the differences in error behavior between the midpoint and trapezoidal methods, demonstrating that the midpoint method can yield better accuracy for certain functions. The instructor concludes by addressing how to evaluate the errors associated with these composite formulas, setting the stage for further exploration of numerical integration methods in subsequent lectures.