ABSTRACT
This chapter discusses numerical techniques for the basic operations of calculus. It describes the basic methods for numerically finding the value of the limit of an indeterminate form, the value of a derivative, the value of a convergent infinite sum, and the value of a definite integral. Using an improved form of the differentiator, the chapter presents first-order iterator techniques for solving ordinary first- and second-order linear differential equations. It shows that analytically the integral equation equivalent to ordinary differential equations with given boundary conditions. The chapter also discusses a simple algorithm to obtain numerically the limit using MATLAB. It also shows that the numerical differentiator is the inverse of the numerical integrator. The chapter explores the different methods lead to different levels of accuracy.
