LAMBDA CALCULUS FOR ENGINEERS PIETER H. HARTEL AND WILLEM G. VREE Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente e-mail address: pieter.hartel@utwente.nl Faculty of Technology, Policy and Management, Technical University of Delft e-mail address: w.g.vree@tudelft.nl Abstract. Inpurefunctionalprogrammingitisawkwardtouseastatefulsub-computation in a predominantly stateless computation. The problem is that the state of the sub- computation has to be passed around using ugly plumbing. Classical examples of the plumbing problem are: providing a supply of fresh names, and providing a supply of random numbers. We propose to use (deterministic) inductive denitions rather than recursion equations as ...
Confirming Pages Mathematical Appendix Some Standard Models in Labor Economics This appendix presents the mathematics behind some of the basic models in labor econom- ics. None of the material in the appendix is required to follow the discussion in the text, but it does provide additional insight to students who have the mathematical ability (in particu- lar, calculus) and who wish to see the models derived in a more technical way. Because the text discusses the economic intuition behind the various models in depth, the presentation in this appendix focuses solely on the mathematical details. 1. The Neoclassical Labor-Leisure Model ...
28.10 #20, from Basic Technical Mathematics with Calculus (8th Edition) by Allyn J. Washington. Z 3 2 −x +x +x+3 2 2 dx (x+1)(x +1) This example involves a repeated irreducible quadratic factor. The partial fractions set-up is 3 2 −x +x +x+3 = A +Bx+C+ Dx+E . 2 2 2 2 2 (x+1)(x +1) x+1 x +1 (x +1) 2 2 Multiplying both sides by (x + 1)(x +1) we obtain 3 2 2 2 2 −x +x +x+3=A(x +1) +(Bx+C)(x+1)(x +1)+(Dx+E)(x+1). (1) For x = −1, we get: 4=4A+0+0 =⇒ A=1. To obtain B ...
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