I want to create a web application that uses a custom database with a web api where javascript calls the api from html pages to perform basic crud operations.
The end game though is to surface this through SharePoint 2013 as a provider hosted application.
Can anyone advise on how I might go about this? I am particularly wondering how making ajax api calls to the application via the html pages surfaced from within sharepoint 2013 will work and authenticate.
Is the application using SharePoint data or are you just using your custom database? If you are just using your custom database, you can use the page viewer web part to display the application: http://office.microsoft.com/en-us/sharepoint-foundation-help/display-a-web-page-on-a-sharepoint-page-by-adding-the-page-viewer-web-part-HA101857182.aspx
If you are consuming SharePoint data, that is a different beast and your best bet is reading the docs here: http://msdn.microsoft.com/en-us/library/office/fp142381(v=office.15).aspx
