ABSTRACT
This chapter discusses numerical methods to find estimates for derivatives and definite integrals. Finite-difference formulas can be derived to approximate derivatives of different orders at a specified point by using the Taylor series expansion. The chapter presents the derivation for finite-difference formulas to approximate first and second derivatives at a point, but those for the third and fourth derivatives will be provided without derivation. Derivative estimates using finite differences can clearly be improved by either reducing the spacing size or using a higher-order difference formula which involves more points. A third method is to use Richardson's extrapolation, which combines two derivative approximations to obtain a more accurate estimate. The MATLAB built-in function diff can be used to estimate derivatives for both cases of equally spaced and not equally spaced data. Newton-Cotes formulas provide the most commonly used integration techniques and are divided into two categories: closed form and open form.
