Computing for Numerical Methods Using Visual C++

Chapter 8. Differentiation and Integration

• 8.1 Introduction

• 8.2 Numerical Differentiation

• 8.3 Numerical Integration

• 8.4 Visual Solution: Code8

• 8.5 Summary

• Numerical Exercises

• Programming Challenges

INTRODUCTION

The derivative of a function gives a clear indication of the rate of increase or decrease of the function with respect to its domain. The rate of increase or decrease of a function contributes to the overall understanding of a system that is governed by such parameters. In general, the derivatives of a function contribute to the modeling of a given problem, which describes the properties and dynamics of the elements in the problem. For example, in studying the electrostatic field properties of an area, the solution requires a graphing of the first and second derivatives of the points in the area. We will discuss some useful properties of the derivatives of a function for modeling in the next few chapters.

The analytical derivative of a function f (x) with respect to the variable x is denoted by f' (x) or

By default, a digital computer does not have the processing capability to produce the analytical derivative of a function. However, this analytical solution can still be produced through a software that stores a list of primitive functions and its derivatives in a numerical database. On the computer, the analytical solution to a derivative is a complex problem that requires several ...