Mathematical Experiments: Numerical Differentiation and Integration with MATLAB Implementation

This article explores numerical differentiation and integration experiments using MATLAB. The course provides detailed instructional materials and practical assignments containing executable code implementations along with complete analysis procedures to enhance understanding of these fundamental numerical methods. We will introduce core concepts of numerical differentiation and integration, demonstrating how to implement and analyze these calculations using MATLAB's built-in functions like diff() for differentiation and integral()/trapz() for integration. The discussion covers key algorithms including finite difference methods (forward, backward, central differences) for differentiation and Newton-Cotes formulas (trapezoidal rule, Simpson's rule) for integration. Additionally, we examine the practical significance of these numerical techniques in real-world applications, showing how to apply them to solve engineering and scientific problems. The materials include parameter optimization examples, error analysis techniques, and convergence studies. Finally, we provide supplementary resources and practice exercises to help master these essential computational skills for research and professional applications.