Introduction to Numerical Analysis and Scientific Computing

Chapter 5

Numerical Differentiation and Integration

5.1Introduction

5.2Mathematical Prerequisites

5.3Numerical Differentiation

5.3.1Approximation of First Derivatives: Error Analysis

5.3.2Approximation of Second Derivatives: Error Analysis

5.4Richardson Extrapolation

5.5Richardson Extrapolation in Numerical Differentiation

5.5.1Richardson Extrapolation for First Derivatives

5.5.2Richardson Extrapolation for Second Derivatives

5.6Numerical Integration

5.6.1The Rectangular Rules

5.6.2The Trapezoidal Rule

5.6.3The Midpoint Rectangular Rule

5.6.4Recurrence Relation for Trapezoid Rule

5.6.5Simpson’s Rule

5.7Romberg Integration

5.8Appendix: Error Term for Midpoint Rule,

5.9Exercises

5.10Computer Projects

5.1 Introduction

As in the previous ...