http://www.lehigh.edu/~wes1/apci
For example, an introduction to the numerical integration of ordinary differential equations (ODEs) (75 pages) and an introduction to the numerical integration of partial differential equations (PDEs) (115 pages) are available in .pdf (Portable Document Format). The list of available files is in files.txt (a small file in text format).
These notes were prepared for a course offered to scientists and engineers in industry through sponsorship of the PITA program of the Commonwealth of Pennsylvania.