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Charles Jordan, "Calculus of Finite Differences"

This book discusses difference calculus, sum calculus, and difference equations as well as discusses applications. With each chapter, there are plenty of explanations and examples. It is elementary, and might not cover all the latest advances, yet it has a wealth of examples, beautiful explanations, and a very nice assortment of subjects. I particularly liked his lozenge diagram approach to methods of integration, his concise and lucid explanation of the Euler-Maclaurin sum formula, applications of the sum calculus, and clear parallels to standard calculus (ininitesimal) throughout.

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