We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
from Part II - Mathematical Methods
Published online by Cambridge University Press: 06 February 2025
In this chapter, we derive Sturm–Liouville theory that introduces a broad class of eigenfunctions that are convenient to use for representing functions. Sturm–Liouville theory provides the basis of the Fourier-series method of representing functions that is the main focus of the chapter and that also is the foundation of Fourier analysis. We show how to calculate Fourier series and to use Fourier series to obtain the solution of boundary-value problems posed in Cartesian coordinates. It is seen that the main advantage of an eigenfunction approach for solving boundary-value problems is that either the inhomogeneous source term in the differential equation or the boundary values may be time dependent, which they cannot be in the method of separation of variables.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
