Mathematical Theory of the Differential Analyzer [offprint]
[Cambridge, Massachusetts]: [Massachusetts Institute of Technology] December 1941. 337-354 pages. 9 15/16 x 6 7/8 inches. Publisher's pale green printed wrappers. Stapled near the spine (slightly rusty). Soft crease to upper right corners. Near Fine. Wraps. 
The Journal of Mathematics and Physics, Vol XX, No. 4, December 1941, first published this paper. Here offered in offprint form.
As he was completing his undergraduate work in Michigan, Shannon noticed [a note tacked to a bulletin board] in the spring of 1936 "just as he was considering what was to come after his undergraduate days were over. The job - master's student and assistant on the differential analyzer at the Massachusetts Institute of Technology - was tailor-made for a young man who could find equal joy in equations and construction, thinking, and building. 'I pushed hard for that job and got it. That was one of the luckiest things of my life,' Shannon would later say...Shannon's study of the electrical switches directing the guts of that mechanical behemoth led him to an insight at the foundation of our digital age: that switches could do far more than control the flow of electricity through circuits - that they could be used to evaluate any logical statement we could think of, could even appear to 'decide'...That leap, as Walter Isaacson put it, 'became the basic concept underlying all digital computers..' It was Shannon's first great feat of abstraction. He was only twenty-one." (Mind at Play, xii, xiii, 20)
In 1938 in his monumental master's thesis "A Symbolic Analysis of Relay and Switching Circuits," Shannon published that leap. A few years later, he published the mathematical theory behind the Differential Analyzer [as here] in some detail.
"The Differential Analyzer is a machine developed at the Massachusetts Institute of Technology under the direction of Dr. V. [Vannevar] Bush for the purpose of obtaining numerical solutions to ordinary differential equations. The fundamental principles underlying the Differential Analyzer were first conceived by Lord Kelvin, but at the time, it was impossible, due to mechanical difficulties, to construct a machine of the type he contemplated. The same principles were discovered independently by Dr. Bush and his associates, and the first Differential Analyzer was completed in 1931. The inherent mechanical difficulties were overcome by means of several ingenious devices such as torque amplifiers, backlash correcting units, and improved machine working technologies … In this paper, the mathematical aspects of the Differential Analyzer will be considered. The most important results deal with conditions under which functions of one or more variables can be generated and conditions under which ordinary differential equations can be solved. Some attention will also be given to approximation of functions (which cannot be generated exactly), approximation of gear ratios, and automatic speed control" (Introduction, pp 337-338)
PROVENANCE: The personal files of Claude E. Shannon (unmarked). There were multiple examples of this item in Shannon's files.
Sloane and Wyner, "Claude Elwood Shannon Collected Papers," #6
Soni and Goodman, "A Mind at Play - How Claude Shanon Invented the Information Age," Simon and Schuster: 2017.