MaplePrimes own Jim Herod has a wonderful set of lecture notes—accompanied by a collection of Maple worksheets—which introduce linear operators on infinite-dimensional Hilbert spaces to beginning graduate students in science and engineering. Entitled Linear Algebra, Infinite Dimensions, and Maple, these notes were developed from a one quarter course which Prof. Herod taught many times at the Georgia Institute of Technology. The notes are very concise and have been refined and improved many times over the years in response to student feedback.

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Frederick W. Chapman, Postdoctoral Fellow, University of Waterloo
http://www.scg.uwaterloo.ca/~fwchapman/