Chapter 7
Numerical Integration
This chapter develops methods for evaluating definite integrals that cannot be obtained conveniently in closed form, as frequently happens in physics. It begins with Newton–Cotes formulas derived from the interpolating polynomials of Chapter 5 and then introduces Gaussian quadrature, which improves efficiency by choosing nodes and weights together. Adaptive (automatic) integration uses error estimates to control accuracy and concentrate computational effort where the integrand is difficult. The chapter then addresses improper and singular integrals, rapidly oscillating integrands, and multidimensional integration.
In this chapter
- 7.1 Foundations and motivation
- 7.2 Interpolation and Newton–Cotes formulas
- 7.3 Gaussian quadrature
- 7.4 Automatic integration
- 7.5 Improper and challenging integrals
- 7.6 Integration of rapidly oscillating functions
- 7.7 Multidimensional integration
- 7.8 Summary and best practices
- 7.9 Computational exercises and projects
Companion resources
Codes
MATLAB, Python, C++, and Fortran programs illustrating Newton–Cotes rules, adaptive Gauss–Kronrod quadrature, and challenging examples involving narrow peaks and oscillatory integrands.
View Chapter 7 codes →Exercises & Projects
Additional exercises for practice and homework, together with physics projects that use numerical integration in larger problems.
View Chapter 7 exercises & projects →Resources
Numerical-library links, benchmark integrals, method-selection guidance, and selected references.
View Chapter 7 resources →Updates & Errata
Corrections, clarifications, and post-publication updates associated with Chapter 7.
View Chapter 7 updates & errata →